DTU ProjectLab - User contributions [en-gb]

Metra Potential Method

2015-09-27T18:17:02Z

AugustinB: /* Assigning the tasks duration in the MPM grid */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France. <ref name="MPM5">[http://excerpts.numilog.com/books/9782124651382.pdf] ''Evolutions of the PERTT Method'' </ref>

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between [[Gantt Chart]] and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of [[The Gantt Chart]], taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1990. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost. <ref name="MPM3" />, <ref name="MPM7" />

'''Previous task:''' A task which, with respect to another, has to be performed before. <ref name="MPM3" />

'''Antecedent task:''' A task which is immediately prior to another task. <ref name="MPM3" />

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages. <ref name="MPM3" />

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending. It determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount. <ref name="MPM7"> F. Laroche. 2012. ''Introduction to Project Management'' </ref>, <ref name="MPM3" />

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process. <ref name="MPM6">[http://cpa.enset-media.ac.ma/methode_mpm.htm] P. Célier. 2004. ''Metra Potential and Antecedent Method'' </ref> [[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start. <ref name="MPM7" />

'''Latest start:''' It corresponds to the latest date when the task may start. <ref name="MPM7" />

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project. <ref name="MPM3" />

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and an earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''. <ref name="MPM6" />

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''. <ref name="MPM3" />, <ref name="MPM6" />

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. <ref name="MPM3" /> In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined. <ref name="MPM6" />

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development. <ref name="MPM3" />

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project. <ref name="MPM6" />

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. <ref name="MPM4" /> Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation. <ref name="MPM4" />

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-27T17:58:17Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France. <ref name="MPM5">[http://excerpts.numilog.com/books/9782124651382.pdf] ''Evolutions of the PERTT Method'' </ref>

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between [[Gantt Chart]] and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of [[The Gantt Chart]], taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1990. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost. <ref name="MPM3" />, <ref name="MPM7" />

'''Previous task:''' A task which, with respect to another, has to be performed before. <ref name="MPM3" />

'''Antecedent task:''' A task which is immediately prior to another task. <ref name="MPM3" />

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages. <ref name="MPM3" />

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending. It determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount. <ref name="MPM7"> F. Laroche. 2012. ''Introduction to Project Management'' </ref>, <ref name="MPM3" />

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process. <ref name="MPM6">[http://cpa.enset-media.ac.ma/methode_mpm.htm] P. Célier. 2004. ''Metra Potential and Antecedent Method'' </ref> [[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start. <ref name="MPM7" />

'''Latest start:''' It corresponds to the latest date when the task may start. <ref name="MPM7" />

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project. <ref name="MPM3" />

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''. <ref name="MPM6" />

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''. <ref name="MPM3" />, <ref name="MPM6" />

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. <ref name="MPM3" /> In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined. <ref name="MPM6" />

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development. <ref name="MPM3" />

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project. <ref name="MPM6" />

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. <ref name="MPM4" /> Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation. <ref name="MPM4" />

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-27T17:54:59Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France. <ref name="MPM5">[http://excerpts.numilog.com/books/9782124651382.pdf] ''Evolutions of the PERTT Method'' </ref>

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1990. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost. <ref name="MPM3" />, <ref name="MPM7" />

'''Previous task:''' A task which, with respect to another, has to be performed before. <ref name="MPM3" />

'''Antecedent task:''' A task which is immediately prior to another task. <ref name="MPM3" />

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages. <ref name="MPM3" />

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending. It determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount. <ref name="MPM7"> F. Laroche. 2012. ''Introduction to Project Management'' </ref>, <ref name="MPM3" />

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process. <ref name="MPM6">[http://cpa.enset-media.ac.ma/methode_mpm.htm] P. Célier. 2004. ''Metra Potential and Antecedent Method'' </ref> [[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start. <ref name="MPM7" />

'''Latest start:''' It corresponds to the latest date when the task may start. <ref name="MPM7" />

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project. <ref name="MPM3" />

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''. <ref name="MPM6" />

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''. <ref name="MPM3" />, <ref name="MPM6" />

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. <ref name="MPM3" /> In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined. <ref name="MPM6" />

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development. <ref name="MPM3" />

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project. <ref name="MPM6" />

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. <ref name="MPM4" /> Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation. <ref name="MPM4" />

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Talk:Metra Potential Method

2015-09-25T11:00:10Z

AugustinB:

Anna: Nice choice of method, you seem to have understood the requirements to both topic and structure, so I don't have any further comments.

Reviewer 1: Alise

* The layout of this article is very nice, and I like that it has pictures to help explain.
**''Thank you very much''
* When MPM is mentioned, why write Potential Metra Methods, and not Metra Potential Methods, as stated in the heading?
**''Well seen, it was a mistake from my part. It can be said both ways, but it is good to use the same one all the article long.''
* Writing the two last sentences about Bernard Roy seems kind of messy when it’s at the bottom of the subject, when you mention him in the beginning without giving him much attention.
**''Thanks, I moved these 2 last sentences in order to get something more coherent''
* I don’t think you should use “… “after any sentence. (See Overview)
**''You are right, it has been changed''
* I found the description in “List of task” not very easy to follow. Maybe structure this in another way?
**''Explain such process with words is not always easy, that's why I tried to illustrate as much as possible with an example and some tables and pictures. I made some minor changes in the text in order to ease the comprehension, I hope it will be fine''
* Why isn’t the method for calculating the duration of tasks not specified? Doesn’t it include in the implementation of the MPM?
** ''I thought that it should be a bit "out of the context" to explain in detail the calculation method in this article. From my point of view, explain how to calculate the duration of a task regarding the costs and resources should be the subject of an individual article. Ideally, I wanted to insert a link to another Wiki article about this specific point.''
* I had some problems understanding how to calculate “earliest start”
** ''I tried to explain it another way to ease the comprehension''
* You have some sentences that could be written better. For example: “It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.” You should write: “The result of this will be that the bigger the numbers of critical tasks with respect to the total number of tasks, the lower the elasticity of the project.” (this is just one)
** ''That's definitely true, I changed this sentence''
* Try not to use very long sentences as it makes it more difficult to follow.

* Remember references!
** ''Done !''
* I like how you have compared the MPM method to both the Gantt and the PERT method.
** ''Thank you very much''

Reviewer 3: s142581
* The article was very interesting and easy to read. It is very much related to the course and relevant for practitioners.
**''Thank you very much''
* In general, it follows a logical flow and it is very well explained. In my opinion, this is especially difficult to achieve when explaining these kind of processes, and you did a good job in this matter.
**''Thank you again !''
* In addition, it has a good paragraph structure, and the advantages and limitations sections were a wise choice. Maybe I would present the ''Overview'' section as the first one, or maybe you could change the title to ''Concept''.
**''I agree with you, I made a change''
* Another positive aspect is that you lean on one example when explaining the process.
**''Thank you''
* It was also a good idea to state a terminology list.
**''And thanks again''
* I would suggest introducing Bernard Roy (the year he was born and why he is recognized) at the beginning of the first paragraph, and not as a second paragraph, when you have already introduced the MPM. I think it would help the flow of the text.
**''Thanks, I moved these 2 last sentences in order to get something more coherent''
* You mention that the method can be considered to be half-way between Gantt Graph and PERT representation. In my opinion, this can be confusing if the lector has not previous knowledge of these methods. I would recommend that you mention the source, as it seems a subjective comment.
**''Reference added, I also need to add a link to Wiki Articles about GANTT of PERT''
* In terms of grammar, the text is well written. I just found some words that I think you could supplant. For example, it the sentence “taking into account the anteriority constraints linking these several tasks”, I would replace ''anteriority'' for ''previous''. Other word that you could modify is ''dependency'' in the sentence “taking into account the dependency relationships between multiple tasks”, where you could write ''dependent'' instead.
**''I don't think that it is the same meaning, anteriority is a name whereas previous is an adjective, same for dependency and dependent... Maybe an English mistake from, I will check again...''
* In the expression “realizing a table”, I suggest you write “making/doing a table”.,,
**''True''
* You make use of the apostrophe when you write ''don’t''. I would suggest to write ''do not''.
* In addition, you could rephrase the sentence “this method only takes into account the schedule aspects, deadlines, delays, etc.” for “this method only takes into account aspects such as scheduling, deadlines or delays”, to avoid writing etc.
**''Done, thanks for the tip''
* I think you made a mistake when mentioning the three convention rules, since there are four bullet points.
**''Totally true, firstly I putted the fourth rules in another paragraph, then I though that it could be easier to understand if it was on the same part as the three others rules, but I forgot to turn the 3 into a 4''
* Regarding the figures, I would recommend that you type "''':'''" after Figure X instead of "''','''"
**''Are you sure ?''
* In the first figures, you could increase the size, not because it is hard to read, but because it would achieve more importance when reading the text. In addition, I suggest you improve the alignment of the tables, for a better visualization of the process, and numerate them so you can mention them in the text.
**''Done, thank's !''
* I would also suggest to rephrase the last sentence of the ''Implementation'' section to “It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project”.
**''Done, thank's !''
* Finally, even if you mention that you will add a bibliography, I would recommend to integrate the sources in the text with numbers.
**''Done, thank's !''

'''Reviewer 2, s141530''':

*Very Nice structure, easy to follow the topic’s red-thread.
**''Thanks a lot !''
*From my perspective you should clarify a bit this sentence “….whose summits represent tasks and the connections represent anteriority constraints.” (3rd line) it was not entirely clear for me.
*In the History chapter you could mention a bit about the Graph Theory background so you can connect it with your Metra Potential Method.
*Good idea include “Terminology sections” and “Graphic representation” . However from my perspective could be useful to have few lines of introduction especially during the “Graphic representation” otherwise the reader is a bit lost.
**''Well seen, it has been updated''
*Enumerate the tables regarding the list of tasks and link them to the text.
**''Well seen, it has been updated''
*MPM explanation very well explains.
**''Thank you''
*Well written “Advantages” and “Limitations” section especially because you compare it with another method. However, you should remember to mention MPM absolute constraints and advantages.
*Sometimes the sentences are too long, try to short them.
*Remember to mentions sources especially regarding the comparison between Pert and Gantt, so the reader can get information also regarding those methods.
**''Done, thank's !''

Talk:Metra Potential Method

2015-09-25T10:48:43Z

AugustinB:

Anna: Nice choice of method, you seem to have understood the requirements to both topic and structure, so I don't have any further comments.

Reviewer 1: Alise

* The layout of this article is very nice, and I like that it has pictures to help explain.
**''Thank you very much''
* When MPM is mentioned, why write Potential Metra Methods, and not Metra Potential Methods, as stated in the heading?
**''Well seen, it was a mistake from my part. It can be said both ways, but it is good to use the same one all the article long.''
* Writing the two last sentences about Bernard Roy seems kind of messy when it’s at the bottom of the subject, when you mention him in the beginning without giving him much attention.
**''Thanks, I moved these 2 last sentences in order to get something more coherent''
* I don’t think you should use “… “after any sentence. (See Overview)
**''You are right, it has been changed''
* I found the description in “List of task” not very easy to follow. Maybe structure this in another way?
**''Explain such process with words is not always easy, that's why I tried to illustrate as much as possible with an example and some tables and pictures. I made some minor changes in the text in order to ease the comprehension, I hope it will be fine''
* Why isn’t the method for calculating the duration of tasks not specified? Doesn’t it include in the implementation of the MPM?
** ''I thought that it should be a bit "out of the context" to explain in detail the calculation method in this article. From my point of view, explain how to calculate the duration of a task regarding the costs and resources should be the subject of an individual article. Ideally, I wanted to insert a link to another Wiki article about this specific point.''
* I had some problems understanding how to calculate “earliest start”
** ''I tried to explain it another way to ease the comprehension''
* You have some sentences that could be written better. For example: “It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.” You should write: “The result of this will be that the bigger the numbers of critical tasks with respect to the total number of tasks, the lower the elasticity of the project.” (this is just one)
** ''That's definitely true, I changed this sentence''
* Try not to use very long sentences as it makes it more difficult to follow.

* Remember references!
** ''Done !''
* I like how you have compared the MPM method to both the Gantt and the PERT method.
** ''Thank you very much''

Reviewer 3: s142581
* The article was very interesting and easy to read. It is very much related to the course and relevant for practitioners.
**''Thank you very much''
* In general, it follows a logical flow and it is very well explained. In my opinion, this is especially difficult to achieve when explaining these kind of processes, and you did a good job in this matter.
**''Thank you again !''
* In addition, it has a good paragraph structure, and the advantages and limitations sections were a wise choice. Maybe I would present the ''Overview'' section as the first one, or maybe you could change the title to ''Concept''.
**''I agree with you, I made a change''
* Another positive aspect is that you lean on one example when explaining the process.
**''Thank you''
* It was also a good idea to state a terminology list.
**''And thanks again''
* I would suggest introducing Bernard Roy (the year he was born and why he is recognized) at the beginning of the first paragraph, and not as a second paragraph, when you have already introduced the MPM. I think it would help the flow of the text.
**''Thanks, I moved these 2 last sentences in order to get something more coherent''
* You mention that the method can be considered to be half-way between Gantt Graph and PERT representation. In my opinion, this can be confusing if the lector has not previous knowledge of these methods. I would recommend that you mention the source, as it seems a subjective comment.
**''Reference added, I also need to add a link to Wiki Articles about GANTT of PERT''
* In terms of grammar, the text is well written. I just found some words that I think you could supplant. For example, it the sentence “taking into account the anteriority constraints linking these several tasks”, I would replace ''anteriority'' for ''previous''. Other word that you could modify is ''dependency'' in the sentence “taking into account the dependency relationships between multiple tasks”, where you could write ''dependent'' instead.
**''I don't think that it is the same meaning, anteriority is a name whereas previous is an adjective, same for dependency and dependent... Maybe an English mistake from, I will check again...''
* In the expression “realizing a table”, I suggest you write “making/doing a table”.,,
**''True''
* You make use of the apostrophe when you write ''don’t''. I would suggest to write ''do not''.
* In addition, you could rephrase the sentence “this method only takes into account the schedule aspects, deadlines, delays, etc.” for “this method only takes into account aspects such as scheduling, deadlines or delays”, to avoid writing etc.
**''Done, thanks for the tip''
* I think you made a mistake when mentioning the three convention rules, since there are four bullet points.
**''Totally true, firstly I putted the fourth rules in another paragraph, then I though that it could be easier to understand if it was on the same part as the three others rules, but I forgot to turn the 3 into a 4''
* Regarding the figures, I would recommend that you type "''':'''" after Figure X instead of "''','''"
**''Are you sure ?''
* In the first figures, you could increase the size, not because it is hard to read, but because it would achieve more importance when reading the text. In addition, I suggest you improve the alignment of the tables, for a better visualization of the process, and numerate them so you can mention them in the text.
**''Done, thank's !''
* I would also suggest to rephrase the last sentence of the ''Implementation'' section to “It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project”.
**''Done, thank's !''
* Finally, even if you mention that you will add a bibliography, I would recommend to integrate the sources in the text with numbers.
**''Done, thank's !''

'''Reviewer 2, s141530''':

*Very Nice structure, easy to follow the topic’s red-thread.
*From my perspective you should clarify a bit this sentence “….whose summits represent tasks and the connections represent anteriority constraints.” (3rd line) it was not entirely clear for me.
*In the History chapter you could mention a bit about the Graph Theory background so you can connect it with your Metra Potential Method.
*Good idea include “Terminology sections” and “Graphic representation” . However from my perspective could be useful to have few lines of introduction especially during the “Graphic representation” otherwise the reader is a bit lost.
*Enumerate the tables regarding the list of tasks and link them to the text.
*MPM explanation very well explains.
*Well written “Advantages” and “Limitations” section especially because you compare it with another method. However, you should remember to mention MPM absolute constraints and advantages.
*Sometimes the sentences are too long, try to short them.
*Remember to mentions sources especially regarding the comparison between Pert and Gantt, so the reader can get information also regarding those methods.

Talk:Metra Potential Method

2015-09-25T10:36:33Z

AugustinB:

Anna: Nice choice of method, you seem to have understood the requirements to both topic and structure, so I don't have any further comments.

Reviewer 1: Alise

* The layout of this article is very nice, and I like that it has pictures to help explain.
**''Thank you very much''
* When MPM is mentioned, why write Potential Metra Methods, and not Metra Potential Methods, as stated in the heading?
**''Well seen, it was a mistake from my part. It can be said both ways, but it is good to use the same one all the article long.''
* Writing the two last sentences about Bernard Roy seems kind of messy when it’s at the bottom of the subject, when you mention him in the beginning without giving him much attention.
**''Thanks, I moved these 2 last sentences in order to get something more coherent''
* I don’t think you should use “… “after any sentence. (See Overview)
**''You are right, it has been changed''
* I found the description in “List of task” not very easy to follow. Maybe structure this in another way?
**''Explain such process with words is not always easy, that's why I tried to illustrate as much as possible with an example and some tables and pictures. I made some minor changes in the text in order to ease the comprehension, I hope it will be fine''
* Why isn’t the method for calculating the duration of tasks not specified? Doesn’t it include in the implementation of the MPM?
** ''I thought that it should be a bit "out of the context" to explain in detail the calculation method in this article. From my point of view, explain how to calculate the duration of a task regarding the costs and resources should be the subject of an individual article. Ideally, I wanted to insert a link to another Wiki article about this specific point.''
* I had some problems understanding how to calculate “earliest start”
** ''I tried to explain it another way to ease the comprehension''
* You have some sentences that could be written better. For example: “It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.” You should write: “The result of this will be that the bigger the numbers of critical tasks with respect to the total number of tasks, the lower the elasticity of the project.” (this is just one)
** ''That's definitely true, I changed this sentence''
* Try not to use very long sentences as it makes it more difficult to follow.

* Remember references!
** ''Done !''
* I like how you have compared the MPM method to both the Gantt and the PERT method.
** ''Thank you very much''

Reviewer 3: s142581
* The article was very interesting and easy to read. It is very much related to the course and relevant for practitioners.
* In general, it follows a logical flow and it is very well explained. In my opinion, this is especially difficult to achieve when explaining these kind of processes, and you did a good job in this matter.
* In addition, it has a good paragraph structure, and the advantages and limitations sections were a wise choice. Maybe I would present the ''Overview'' section as the first one, or maybe you could change the title to ''Concept''.
* Another positive aspect is that you lean on one example when explaining the process.
* It was also a good idea to state a terminology list.
* I would suggest introducing Bernard Roy (the year he was born and why he is recognized) at the beginning of the first paragraph, and not as a second paragraph, when you have already introduced the MPM. I think it would help the flow of the text.
* You mention that the method can be considered to be half-way between Gantt Graph and PERT representation. In my opinion, this can be confusing if the lector has not previous knowledge of these methods. I would recommend that you mention the source, as it seems a subjective comment.
* In terms of grammar, the text is well written. I just found some words that I think you could supplant. For example, it the sentence “taking into account the anteriority constraints linking these several tasks”, I would replace ''anteriority'' for ''previous''. Other word that you could modify is ''dependency'' in the sentence “taking into account the dependency relationships between multiple tasks”, where you could write ''dependent'' instead.
* In the expression “realizing a table”, I suggest you write “making/doing a table”.
* You make use of the apostrophe when you write ''don’t''. I would suggest to write ''do not''.
* In addition, you could rephrase the sentence “this method only takes into account the schedule aspects, deadlines, delays, etc.” for “this method only takes into account aspects such as scheduling, deadlines or delays”, to avoid writing etc.
* I think you made a mistake when mentioning the three convention rules, since there are four bullet points.
* Regarding the figures, I would recommend that you type "''':'''" after Figure X instead of "''','''"
* In the first figures, you could increase the size, not because it is hard to read, but because it would achieve more importance when reading the text. In addition, I suggest you improve the alignment of the tables, for a better visualization of the process, and numerate them so you can mention them in the text.
* I would also suggest to rephrase the last sentence of the ''Implementation'' section to “It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project”.
* Finally, even if you mention that you will add a bibliography, I would recommend to integrate the sources in the text with numbers.

'''Reviewer 2, s141530''':

*Very Nice structure, easy to follow the topic’s red-thread.
*From my perspective you should clarify a bit this sentence “….whose summits represent tasks and the connections represent anteriority constraints.” (3rd line) it was not entirely clear for me.
*In the History chapter you could mention a bit about the Graph Theory background so you can connect it with your Metra Potential Method.
*Good idea include “Terminology sections” and “Graphic representation” . However from my perspective could be useful to have few lines of introduction especially during the “Graphic representation” otherwise the reader is a bit lost.
*Enumerate the tables regarding the list of tasks and link them to the text.
*MPM explanation very well explains.
*Well written “Advantages” and “Limitations” section especially because you compare it with another method. However, you should remember to mention MPM absolute constraints and advantages.
*Sometimes the sentences are too long, try to short them.
*Remember to mentions sources especially regarding the comparison between Pert and Gantt, so the reader can get information also regarding those methods.

Metra Potential Method

2015-09-24T15:13:49Z

AugustinB: /* Determination of tasks levels */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France. <ref name="MPM5">[http://excerpts.numilog.com/books/9782124651382.pdf] ''Evolutions of the PERTT Method'' </ref>

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1990. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost. <ref name="MPM3" />, <ref name="MPM7" />

'''Previous task:''' A task which, with respect to another, has to be performed before. <ref name="MPM3" />

'''Antecedent task:''' A task which is immediately prior to another task. <ref name="MPM3" />

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages. <ref name="MPM3" />

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount. <ref name="MPM7"> F. Laroche. 2012. ''Introduction to Project Management'' </ref>, <ref name="MPM3" />

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process. <ref name="MPM6">[http://cpa.enset-media.ac.ma/methode_mpm.htm] P. Célier. 2004. ''Metra Potential and Antecedent Method'' </ref> [[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start. <ref name="MPM7" />

'''Latest start:''' It corresponds to the latest date when the task may start. <ref name="MPM7" />

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project. <ref name="MPM3" />

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''. <ref name="MPM6" />

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''. <ref name="MPM3" />, <ref name="MPM6" />

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. <ref name="MPM3" /> In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined. <ref name="MPM6" />

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development. <ref name="MPM3" />

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project. <ref name="MPM6" />

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation. <ref name="MPM4" />

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-24T15:12:28Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France. <ref name="MPM5">[http://excerpts.numilog.com/books/9782124651382.pdf] ''Evolutions of the PERTT Method'' </ref>

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1990. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost. <ref name="MPM3" />, <ref name="MPM7" />

'''Previous task:''' A task which, with respect to another, has to be performed before. <ref name="MPM3" />

'''Antecedent task:''' A task which is immediately prior to another task. <ref name="MPM3" />

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages. <ref name="MPM3" />

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount. <ref name="MPM7"> F. Laroche. 2012. ''Introduction to Project Management'' </ref>, <ref name="MPM3" />

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process. <ref name="MPM6">[http://cpa.enset-media.ac.ma/methode_mpm.htm] P. Célier. 2004. ''Metra Potential and Antecedent Method'' </ref> [[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start. <ref name="MPM7" />

'''Latest start:''' It corresponds to the latest date when the task may start. <ref name="MPM7" />

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''. <ref name="MPM6" />

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''. <ref name="MPM3" />, <ref name="MPM6" />

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. <ref name="MPM3" /> In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined. <ref name="MPM6" />

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development. <ref name="MPM3" />

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project. <ref name="MPM6" />

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation. <ref name="MPM4" />

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-24T15:04:32Z

AugustinB: /* Critical path */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France. <ref name="MPM5">[http://excerpts.numilog.com/books/9782124651382.pdf] ''Evolutions of the PERTT Method'' </ref>

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1990. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process. <ref name="MPM6">[http://cpa.enset-media.ac.ma/methode_mpm.htm] P. Célier. 2004. ''Metra Potential and Antecedent Method'' </ref> [[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''. <ref name="MPM6" />

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''. <ref name="MPM3" />, <ref name="MPM6" />

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. <ref name="MPM3" /> In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined. <ref name="MPM6" />

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development. <ref name="MPM3" />

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project. <ref name="MPM6" />

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation. <ref name="MPM4" />

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-24T15:02:56Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France. <ref name="MPM5">[http://excerpts.numilog.com/books/9782124651382.pdf] ''Evolutions of the PERTT Method'' </ref>

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1990. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process. <ref name="MPM6">[http://cpa.enset-media.ac.ma/methode_mpm.htm] P. Célier. 2004. ''Metra Potential and Antecedent Method'' </ref> [[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''. <ref name="MPM3" />, <ref name="MPM6" />

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. <ref name="MPM3" /> In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined. <ref name="MPM6" />

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development. <ref name="MPM3" />

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project. <ref name="MPM6" />

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation. <ref name="MPM4" />

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-24T14:58:09Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France. <ref name="MPM5">[http://excerpts.numilog.com/books/9782124651382.pdf] ''Evolutions of the PERTT Method'' </ref>

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1990. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''. <ref name="MPM3" />, <ref name="MPM6" />

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. <ref name="MPM3" /> In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined. <ref name="MPM6" />

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development. <ref name="MPM3" />

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project. <ref name="MPM6" />

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation. <ref name="MPM4" />

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-24T14:51:37Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France. <ref name="MPM5">[http://excerpts.numilog.com/books/9782124651382.pdf] ''Evolutions of the PERTT Method'' </ref>

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1990. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-24T14:47:39Z

AugustinB: /* Concept overview */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1990. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-24T14:47:07Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected. <ref name="MPM4">[http://marcpolizzi.free.fr/outilsgpi/doc_mpm/mpm.htm] M. Polizzi. 1999. ''Tool : The Potential Methods'' </ref>

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-24T14:43:06Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation <ref name="MPM1" />. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method. <ref name="MPM3" />

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them. <ref name="MPM1" />

==References==
<references />

Metra Potential Method

2015-09-24T14:39:17Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. <ref name="MPM3" /> The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow. <ref name="MPM3" />

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method <ref name="MPM3" /> :

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution. <ref name="MPM3" />

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task. <ref name="MPM3" />

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. <ref name="MPM3" /> The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration. <ref name="MPM3" />

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />

Metra Potential Method

2015-09-24T14:33:34Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>, <ref name="MPM3">[http://www.prismconseil.fr/site/index.php/planification/La-methode-MPM.html] ''Planning tools and methods'' </ref> MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />

Metra Potential Method

2015-09-24T14:24:39Z

AugustinB: /* References */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />

Metra Potential Method

2015-09-24T14:24:02Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''Metra Potential Method'' </ref>, <ref name="MPM2">[http://www.logistiqueconseil.org/Articles/Logistique/Methode-potentiel-metra.htm] ''Logistique & Conseil, The Metra Potential Method'' </ref>. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T14:19:11Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. <ref name="MPM1">[http://www.my-project-cafe.com/methode-potentiels-metra-mpm] JL. Brissard, M. Polizzi. 1999. ''The Metra Potential Method'' </ref>. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly .

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory. <ref name="MPM1" />

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T14:01:48Z

AugustinB: /* History */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support. In 1958, he invented the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French), a method based on the Graph Theory.

This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T13:58:59Z

AugustinB: /* Determination of tasks levels */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don't have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T13:56:04Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in making a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be created to identify which tasks don’t have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. The calculation of each earliest start may be performed using a table, as illustrated below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T13:52:01Z

AugustinB: /* Concept overview */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account aspects such as scheduling, deadlines or delays. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in realizing a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. The calculation of each earliest start may be performed using a table, as illustrated in the table below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T13:48:40Z

AugustinB: /* Overview */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Concept overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in realizing a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. The calculation of each earliest start may be performed using a table, as illustrated in the table below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T13:46:46Z

AugustinB: /* Adding the Earliest Start to the MPM grid */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in realizing a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point, task duration of the task upstream is added to its earliest start in order to obtain the earliest start of task downstream. The calculation of each earliest start may be performed using a table, as illustrated in the table below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T13:41:07Z

AugustinB: /* Implementation of the method */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.[[File:Case1.PNG|thumb|128px|'''Figure 1''', Task graphic representation]]

'''Earliest start:''' It corresponds to the earliest date when the task may start.

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in realizing a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T13:31:01Z

AugustinB: /* Implementation of the method */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.
The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;"|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;"|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in realizing a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;"|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;"|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;"|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T13:29:50Z

AugustinB: /* Adding the Earliest Start to the MPM grid */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.
The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in realizing a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;"|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T13:25:35Z

AugustinB: /* Implementation of the method */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the '''Figure 1''', on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.
The graphic representation of a succession constraint is illustrated in the '''Figure 2''', on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in realizing a table as illustrated on the '''Table 1''', on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the '''Table 2''', on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below ('''Table 3''') illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below ('''Figure 3''') in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration)
|+ style="caption-side:bottom;|'''Table 4''', Task duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left ('''Table 4''').

These information allows to fill partially the MPM grid, as illustrated below ('''Figure 4''').

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below ('''Table 5''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|+ style="caption-side:bottom;|'''Table 5''', Calculation of Earliest Starts
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below ('''Figure 5''').

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below ('''Table 6''') for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|+ style="caption-side:bottom;|'''Table 6''', Calculation of Latest Start
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below ('''Figure 6''').

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below ('''Figure 7'''), the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-24T12:05:05Z

AugustinB: /* Implementation of the method */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. The graphic representation of a task is illustrated in the Figure 1, on the right. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.
The graphic representation of a succession constraint is illustrated in the Figure 2, on the right.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|+ style="caption-side:bottom;|'''Table 1''', Identification of Previous tasks
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|+ style="caption-side:bottom;|'''Table 2''', Identification of Antecedent tasks
|}

A first approach is made by integrating as much as previous tasks as possible. An efficient way to list these previous tasks consists in realizing a table as illustrated on the Table 1, on the right. Indeed, as first step to determine the order of succession of tasks consists in writing for each task the list of previous tasks which need to be achieved before its execution.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the Table 2, on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consists in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below (Table 3) illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|+ style="caption-side:bottom;|'''Table 3''', Determination of tasks level
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below (Figure 3) in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below, the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-22T17:40:14Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below, the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that the bigger the number of critical tasks is with respect to the total number of tasks, the lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-22T17:35:21Z

AugustinB: /* Convention rules */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Four main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below, the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Talk:Lean Tools in Project Management

2015-09-22T16:44:13Z

AugustinB:

Mette: I like the idea and the topic you have chosen. Lean contains many tools, so you could maybe consider if you should focus on only one tool in case of not getting your hands too full. Your article may end up a bit generic, and not as interesting as it could be because it is too broad. So think about tool for risk management and then pick one you can really go into details with.

Reviewer 2: Alise

* Nicely structured. It is clean and has a good overview.
* There are some sentences that can be written better. F. Ex. “but during the past years have lean been established….” Which would be better when written like this “but during the past years lean has been established… “
* You should not write that something is impossible. If it is a process for something to be done, it does not encourage anyone when they read the word “impossible”. (Seek perfection)
* When writing about “From Lean to Lean Project Management”, the first sentence does not make much sense. What are you writing a brief summary about? Also, a summary would be more than four bullet points. It would explain something, either what you will write about or what you have written about.
* The definition of project management should be all the way at the top. People need to know what they are reading about. Also, make it clear what the definition actually is, and where it ends. Maybe start the next sentence as a new paragraph.
* “The 8 different relates to production” – 8 what?
* I don’t think you should use questions in the article.
* What is an A3 tool? A description of this would be good if it is a lean tool.
* Some pictures of the different tools would be nice.
* What is a leader imagination? (The Gemba Walk)
* Some of the examples you have used are a little too specific.
* See difference; effect vs. affect.
* You are not close to the 3000 word count yet, but keep working!
* Remember references!
* The article needs some more work, and be aware of grammar and structure of sentences. Try not to use very long sentences as it makes it difficult to read.

Wiki feedbacks from s142823

* Words missing to complete a sentence in the abstract : “The crucial for a p…”
* Good structure
* Very good brief introduction to Lean, clear and easy to understand
* Add a link when you quote the “8 wastes”
* About the A3 tool, it may be good to add a link to one of the article from Fall 2014
* Some grammatical mistakes, for example “methodology” instead of “mythology”
* Don’t forget to fill the missing parts
* Apparently there is still somework to do on it, good luck, you started it well
* Very interesting topic, it seems well documented

Talk:Multi project management

2015-09-22T16:25:33Z

AugustinB:

Josef: Hello, thank you for the abstract. "Multi project management" is a fairly broad category. I suggest that you re-think after todays program management lecture if you would like to take a program management or portfolio management angle. All the topics you raise are relevant, but there are also potentially a lot more that you could cover. So it is not entirely clear to me why you chose that particular subset. I would suggest to either focus on one particular aspect, or provide a more high-level overview that can then be "complete". Also please make sure to follow the suggested structure.

Reviewer 3: Alise

* A well-written article and nice structure.
* I don’t think you should use “I” and “we” in the article. It is supposed to be objective, and makes it look less professional.
* Try not to use questions. Try to structure it in a different way.
* I like the sentence you use to explain the difference. But since you have made it such a big deal, maybe use the italic or bold to highlight it.
* Try to stay away from words like “actually”, “just” and “only”. Depending on how they are used in a sentence it may not sound very professional.
* What are the 2 steps before reaching a Program Management point of view? Tell the reader where he or she will read about it.
* I like the pictures and how they relate to the text. They are not, however, directly mentioned in the text.
* Earlier, it was not right to start a sentence with “and” or “but”. This has changed, but you might just be aware of it and not use it all the time.
* Some sentences are very long. Try to shorten them.
* Remember references!

Wiki feedback From s117318

* Nice figures
* Great structure, easy o follow the topics
* Figure 1 could fit into the text
* For this sentence: In multiple project management, I will study the management of the schedules (Try to avoid using "I")
* Try to avoid using words as "actually".
* Easy to understand
* Create References to Figures you have added and tell why you have added these.
* Be specific, fx. Now, we will stop to see (Remove this, and write something more specific)
* Perhaps a brief discussion/conclusion?
* Make this setence with bold or as SubTopic: How Program Management can solve some uncertainty problem in a MPM?
* An idea: 4. Limitations of Program Management approach
4.1 Inability to “stick” with the project scope:
4.2 ecc..
* Be aware of adding more words.
* Be aware of gramma,
* Could Link to other Wiki Articles, like Project Management
* Remember References
* Remember biography

Wiki feedback from s142823
* Very interesting topic, it seems a bit challenging to cover within 3000 words but apparently you succeeded : reading your article hold the attention and it gives the feeling to learn a new concept
* Some grammatical mistakes
* Layout and article structure globally pleasant
* Try to be more objective in the article, avoid the words such as “I”, “me”, or even “you”.
* Try to avoid words such as “actually”, or “but” too often.
* Nice and clear pictures, but they should be more introduced and linked in the text

Talk:Gantt Chart

2015-09-22T16:03:09Z

AugustinB:

Kristine:
Great to see you have found a relevant tool to describe. Good to see you have the structure of the article all figured out.

Wiki feedback from s117318

* Nice figures, great references
* Be more specific for your topics. Fx. USE? Use of what? Edit the topic/headlines.
* Could you make even more topic? 1. Use 1.1 Dependencies... 1.2 Critical Path.. 1.3 Ects...
* Need discussion, maybe you could add more to the last topic "limitations"
* Be more specific: For instance, Here is an example of how to use. Could you be more concrete? Avoid words like "here"
* Great example, simple and easy to understand
* I think you can add some more text!
* Nice you are using the figures in your article.
* Your language is easy to understand, great work.

Wiki feedback from s142823

* Globally a nice article,well structured.
* Layout pleasant
* Some minor Grammatical mistakes
* Good idea to illustrate what is written with some GANTT pictures. However, maybe you should choose pictures easier to understand quickly.
* About the “Example of Managing a project with Gantt Charts”, it would be interesting to describe the all process more in detail with more illustrations such as one for the WBS
* Good presentation of references

Metra Potential Method

2015-09-22T15:02:17Z

AugustinB: /* Overview */

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc. It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below, the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-22T15:01:54Z

AugustinB:

The Metra Potential Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Metra Potential Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below, the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-21T21:38:37Z

AugustinB: /* Critical path */

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below, the critical path is highlighted with the red cells and red arrows.

[[File:CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

File:CriticalPath.PNG

2015-09-21T21:34:41Z

AugustinB:

Metra Potential Method

2015-09-21T21:34:24Z

AugustinB:

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length. In the figure below, the critical path is highlighted with the red cells and red arrows.

[[CriticalPath.PNG|center|thumb|550px|'''Figure 7''', Highlighting of the Critical Path]]

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-21T21:24:27Z

AugustinB:

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length.

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.

==References==
<references />
THE REFERENCES ARE NOT WRITTEN YET (Author)

Metra Potential Method

2015-09-21T21:01:35Z

AugustinB: /* Determination of tasks levels */

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length.

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.
==MPM in the today's industry==
==References==

Metra Potential Method

2015-09-21T21:00:35Z

AugustinB: /* Determination of tasks levels */

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|-
! scope="col"|colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length.

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.
==MPM in the today's industry==
==References==

Metra Potential Method

2015-09-21T20:58:50Z

AugustinB: /* Determination of tasks levels */

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
|colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length.

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.
==MPM in the today's industry==
==References==

Metra Potential Method

2015-09-21T20:56:39Z

AugustinB:

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
! scope="col"| Level 0
! scope="col"| Level 1
! scope="col"| Level 2
! scope="col"| Level 3
|-
| A
| -
| -
| -
| -
| -
|-
| B
| A
| <strike> A </strike>
| -
| -
| -
|-
| C
| A
| <strike> A </strike>
| -
| -
| -
|-
| D
| -
| -
| -
| -
| -
|-
| E
| B
| B
| <strike> B </strike>
| -
| -
|-
| F
| CD
| C<strike> D </strike>
| <strike> C </strike>
| -
| -
|-
| Z
| EF
| EF
| EF
| <strike> EF </strike>
| -
! scope="row" colspan="2"| Tasks constituting the level
| AD
| BC
| EF
| Z
|}

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length.

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.
==MPM in the today's industry==
==References==

Metra Potential Method

2015-09-21T20:33:50Z

AugustinB:

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

//TABLE TO ADD THERE

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| <strike> 3+6=9 </strike> or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or <strike> 11+5=16 </strike>
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| <strike> 7-3=4 </strike>or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length.

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.
==MPM in the today's industry==
==References==

Metra Potential Method

2015-09-21T20:27:34Z

AugustinB: /* Determination of tasks levels */

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

//TABLE TO ADD THERE

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph. This gives an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| 3+6=9 or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or 11+5=16
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| 7-3=4 or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length.

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.
==MPM in the today's industry==
==References==

Metra Potential Method

2015-09-21T20:26:58Z

AugustinB: /* Determination of tasks levels */

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

//TABLE TO ADD THERE

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

At this step of the methodology process, there are no numbers in the MPM grid, only the global layout of the graph, giving an overview about the succession order of the tasks.

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| 3+6=9 or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or 11+5=16
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| 7-3=4 or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length.

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.
==MPM in the today's industry==
==References==

Metra Potential Method

2015-09-21T20:24:42Z

AugustinB: /* Assigning the tasks duration in the MPM grid */

The Potential Metra Method, or MPM, is a project management tool, invented in 1958 by French researcher Bernard Roy. MPM is used to describe, organize and plan the several tasks constituting a project development. This management method is similar to the PERT method. It consists of an oriented graph, whose summits represent tasks and the connections represent anteriority constraints. Thanks to the use of the MPM method, a critical path is identified easily by simply reading the chart, and the length of the critical path is represented directly.

==History==
Invented in 1958 by French researcher Bernard Roy, the Potential Metra Method (MPM, for Méthode des Potentiels Metra in French) is based on the Graph Theory. This method was first created as a tool provided for a crank shafts factory called Mavilor. Very soon after its creation, MPM was used for the construction of the superstructures of cruise liner France. In the beginning of the 1960’s, this method was involved in the development of the airplane program Concorde, as well as in the construction of the first generation of nuclear plants in France.

Bernard Roy is a French researcher born in 1934, widely recognized as a pioneer in the field of operational research in France. His works form one of the foundations of scientific approaches to decision support.

==Overview==
Created the same year as the PERT method, the MPM method is a system of representation and optimization of project tasks. This method can be considered to be half-way between Gantt Graph and PERT representation. It allows the user to prioritize a large number of tasks, taking into account the anteriority constraints linking these several tasks.

The main goal leading to the creation of this new management method was to reduce the complexity of the Gantt chart, taking into account the dependency relationships between multiple tasks (precedence, inheritance, etc.) and also the evolution of these constraints along the time.

Similarly to the PERT method, the main benefit of MPM is to reduce the time required to achieve a project, but this method only takes into account the schedule aspects, deadlines, delays, etc… It cannot be used in the field of budget or resources management. By precisely describing the dependency between each task, MPM optimizes speediness of the process providing a graphical representation under the form of a network. Thus, all information related to a same operation are grouped under a single node, which facilitates the identification of the critical path.

Allowing an easy identification of the critical path, the MPM is used to determine the minimum time required to conduct a project. Moreover, this method affords to define the dates on which the various tasks involved in the project may or must begin to ensure that this minimum time is respected.

==Implementation of the method==
===Terminology===
'''Task:''' In the frame of project management, a task is the basic division of the work required to produce the result. The task evolves from an initial state to a final state. Each task has a duration and cost.

'''Previous task:''' A task which, with respect to another, has to be performed before.

'''Antecedent task:''' A task which is immediately prior to another task.

'''Stage:''' A step is the beginning or the end of a task. It has no time nor cost.

'''MPM grid:''' This is all of the tasks and stages that define the project. It highlights the relationships between tasks and stages.

'''Critical path:''' The longest possible continuous path from the initial task starting to the terminal task ending; it determines the total amount of time required for the project delivery. Any time delays along this path will delay the execution of the project by at least the same amount.

'''Float (or slack):''' A float is a measure of the available extra time and resources needed to complete a task. It indicates the possible delay that an individual task may have without delaying the all process.

'''Earliest start:''' It corresponds to the earliest date when the task may start. [[File:Case1.PNG|thumb|125px|'''Figure 1''', Task graphic representation]]

'''Latest start:''' It corresponds to the latest date when the task may start.

===Graphic representation===

'''Task:''' A task is represented by a frame and is identified by its name. The earliest start and latest start corresponding to the task are listed in the top of the frame. [[File:Case2.PNG|thumb|280px|'''Figure 2''', Succession constraint representation]]

'''Succession constraint:''' Succession constraints are represented by an arrow which goes from the antecedent task to the next one. The constraint duration corresponds to the starting task duration. This values is written above the arrow.

===Convention rules===
Three main rules apply when organizing the tasks network in the frame of MPM method:

* Any stage has an origin stage as beginning, and an end stage as end.

* A stage can be achieved only when all the tasks that precede it are finished.

* No task can be performed if the original stage has not been reached.

* By convention, a MPM network must be terminated with a single task (called Z generally) that determines the end of the project. This task will have no duration.

{| class="wikitable" style="float:right; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Previous tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| AB
|-
| F
| ACD
|-
| Z
| ABCDEF
|}

===Implementation of the methodology===

====List of tasks====

Achieving a graph showing the analysis of a scheduling problem requires a preliminary study of the various tasks to be considered, their duration, and the relationships between tasks (mainly constraints of anteriority and antecedence). A special attention should be paid when it comes to achieve this preliminary study.
{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Antecedent tasks
|-
| A
| -
|-
| B
| A
|-
| C
| A
|-
| D
| -
|-
| E
| B
|-
| F
| CD
|-
| Z
| EF
|}

An efficient way to list these tasks consists in realizing a table as illustrated on the right table. A first approach is made by integrating as much as previous tasks as possible.

Then, in order to ease the work, only the antecedent tasks will be kept. In the example case, task A is not directly prior to tasks E or F. As task A cannot be represented more than once in the MPM grid, it is useless to keep it on the table. This way, it is possible to obtain the table on the left.

====Determination of tasks levels====
In order to clearly establish the MPM grid, it is appropriate to define an achievement level for each task. Such a level is a moment in time. The higher the level is, the faster the task is from the first stage of the project.

The aim consist in identify the level of each tasks to obtain the global aspect of the MPM grid. To do so, a table may be realized to identify which tasks don’t have antecedent task for each level. The table below illustrates the method in the example case.

//TABLE TO ADD THERE

Create this table allows to plot the global layout of the MPM grid, as illustrated below in the case of the example.

[[File:MPM, step 1.PNG|center|thumb|550px|'''Figure 3''', MPM grid with tasks levels]]

{| class="wikitable" style="float:left; margin-left: 4px;"
|-
! scope="col"| Task
! scope="col"| Task duration
|-
| A
| 3
|-
| B
| 7
|-
| C
| 6
|-
| D
| 11
|-
| E
| 8
|-
| F
| 5
|-
| Z
| 0 (End task, no duration
|}

====Assigning the tasks duration in the MPM grid====
Each stage is characterized by an earliest start and a earliest finish. These specific dates are defined according to of the duration of tasks. The method to calculate the duration of tasks is not specified in this article. Briefly, this duration depends on the workload needed and the number of resources available to achieve the task.

In the example developed as an illustration for the MPM implementation, it is considered that the task duration were already set, as illustrated in the table on the left.

These information allows to fill partially the MPM grid, as illustrated below.

[[File:MPM, step 2.PNG|center|thumb|550px|'''Figure 4''', MPM grid with tasks duration]]

====Adding the Earliest Start to the MPM grid====
The initial stage of the project starts on day 0. From this point that we begin to accumulate the duration of each task to set the earliest starts of the following tasks. The calculation of each earliest start may be performed using a table, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Antecedent tasks
! scope="col"| Calculation of earliest start
! scope="col"| Earliest Start
|-
| A
| 3
| -
| 0 (level 0)
| 0
|-
| B
| 7
| A
| 0+3=3
| 3
|-
| C
| 6
| A
| 0+3=3
| 3
|-
| D
| 11
| -
| 0 (level 0)
| 0
|-
| E
| 8
| B
| 3+7=10
| 10
|-
| F
| 5
| CD
| 3+6=9 or 0+11=11
| 11
|-
| Z
| 0
| EF
| 10+8=18 or 11+5=16
| 18
|}

When a task is conditioned by more than one single antecedent task, the higher sum is kept as earliest start. Thus, in the example, F is conditioned by the execution of both tasks C and D, the earliest start for task F is set to be 11 days, corresponding to the minimum time needed to achieve D, higher than the minimum time to achieve C.

These information allows to fill the cells dedicated to the Earliest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 3.PNG|center|thumb|550px|'''Figure 5''', MPM grid with Earliest Starts]]

====Adding the Latest Start to the MPM grid====
For the last task (Z in the example), the earliest start is the same as the latest start. Then, from this last task of the project, the duration of the antecedent tasks are subtracted step by step to set the latest start of the downstream task. The latest start of a task corresponds to the difference between the latest start of the task directly upstream and its duration.

As for the earlier start, it could be useful to create a table in order to calculate the latest starts of each task, as illustrated in the table below for the example.

{| class="wikitable" style="margin: auto;"
|-
! scope="col"| Task
! scope="col"| Task duration
! scope="col"| Posterior tasks
! scope="col"| Calculation of latest start
! scope="col"| Latest Start
|-
| A
| 3
| BC
| 7-3=4 or 3-3=0
| 0
|-
| B
| 7
| E
| 10-7=3
| 3
|-
| C
| 6
| F
| 13-6=7
| 7
|-
| D
| 11
| F
| 13-11=2
| 2
|-
| E
| 8
| Z
| 18-8=10
| 10
|-
| F
| 5
| Z
| 18-5=13
| 13
|-
| Z
| 0
| -
| 18 (End Task)
| 18
|}

When a task is directly followed by more than one single posterior task, the lower subtraction is kept as latest start. Thus, in the example, A has B and C as posterior tasks, so the latest start for task A is set to be 0 and not 4. In this case, if the latest start for task A was 4, it would engender a potential 4 days delay for tasks B and E, leading to a 4 days delay for the all project.

These information allows to fill the cells dedicated to the Latest Starts in the MPM grid, as illustrated below.

[[File:MPM, step 4.PNG|center|thumb|550px|'''Figure 6''', MPM grid with Latest Starts]]

Now, the MPM grid is completed.

===MPM grid analysis===
Once the MPM grid is completed, it is possible to deduce the following characteristics: '''critical paths, free float and total float.'''

====Critical path====
When observing a MPM grid from the starting task to the end task (Z), it appears that it is generally possible to take various paths to connect the beginning to the end. Each paths is represented by a succession of tasks (rectangles) and succession constraints (arrows). The successive realization of the various tasks constituting a path has a total duration, depending on the duration of each of these tasks. This total duration is called: '''path length'''.

The minimum time to achieve a project corresponds to the length of the longest path. Indeed, the minimum duration of the project execution cannot be less than the sum of duration required to achieve the worst succession of asks in terms of time. This longest path is called '''critical path'''.

Graphically, the '''critical path''' is the suite of tasks of the MPM which have a zero float (earliest start=latest start). The tasks of this path are called '''critical tasks'''. The sum of all the critical tasks duration indicates the minimum length of the project. Any delay in one of these tasks causes an equal delay to the end date of the project. Sometimes, there may be several critical paths, which have obviously the same length.

====Floats====
For the task which don’t have a zero float (earliest start<latest start), two floats may be defined.

The '''free float''' is the maximum delay allowed to start a task without having an impact on the '''earliest starts''' of the following tasks.

The '''total float''' is the maximum delay allowed to start a task without having an impact on the latest starts of the following tasks.

The task with a free and total float (tasks non critical) are interesting from the project management perspective because they can be used to smooth the resources and the costs of the project throughout its development.

On the other hand, as said previously, on the critical path all floats worth zero. It results that bigger is the number of critical tasks with respect to the total number of tasks, lower is the elasticity of the project.

==Advantages==
By comparison to the PERT method, the MPM method has the advantage that its graphic representation doesn’t need to have recourse to fictive tasks, as it is sometimes needed for the implementation of the PERT method.

Although the PERT method was the first one imposed in project management, it appears that, from the 1980’s, the MPM method tends to supplant it. Indeed, this method is much more flexible and more easily adaptable to the automation of data processing, particularly when it deals with calculation algorithms and graphic representation.

==Limitations==
In contrast to the GANTT chart, the MPM method doesn’t provide directly a way to identify and manage the costs of tasks and the resources needed to achieve them.
==MPM in the today's industry==
==References==