DTU ProjectLab - User contributions [en-gb]

Project Network Diagram

2017-10-02T10:37:34Z

S124052: /* References */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Pros and Cons of Project Network Diagrams==

'''Pros'''

 Planning- Identify all tasks necessary to complete

 Identify ‘critical’ activities, also activities where ‘float’ exists

 Set deadlines to work towards. Interim + final

 Helps plan ordering of stocks/ materials or equipment

 It helps cashflow

 Network can help solve problems that arise during the project

'''Cons'''

 It takes time to produce

 It costs a lot to produce

 Is the network necessary? Is the task obvious or simple?

 It can become very complex- could be misinterpreted

 Reliability of data, e.g timescales, who has produced it and errors, e.g missing tasks

 Threat of external factors that cause problems, e.g weather

''These Pros and Cons are stated in an article [7] where the main conclusion as that the Network analysis and critical path is often necessary but not self-sufficient to generate success.''

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSEx2.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE2.PNG|400x800px|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|400x800px|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|400x800px|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|400x800px|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|400x800px|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

<math>TS = LF-EF</math>

where TS = Total Slack

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|400x800px|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|400x800px|Figure 8]]

==References==

[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
Article on Time management, by: Linh Tran, written April 2015.

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
Blog Article on Monte Carlo Simulation and its usage, by: Shim Marom, a project manager, written October 2009.

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s
Youtube video visualizing and teaching the PND for project management, by user: "Ob Wex" from November 2012.

[7] https://www.askwillonline.com/2012/01/pros-and-cons-of-network-diagrams.html
Online free-to-read article on Pros and Cons of Network Diagrams, written by: Joe Black (a writer from Review Cosmos), supposedly from November 2014.

Project Network Diagram

2017-10-02T10:35:25Z

S124052: /* Pros and Cons of Project Network Diagrams */

Project Network Diagram

2017-10-02T10:35:04Z

S124052: /* Pros and Cons of Project Network Diagrams */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Pros and Cons of Project Network Diagrams==

'''Pros'''

 Planning- Identify all tasks necessary to complete

 Identify ‘critical’ activities, also activities where ‘float’ exists

 Set deadlines to work towards. Interim + final

 Helps plan ordering of stocks/ materials or equipment

 It helps cashflow

 Network can help solve problems that arise during the project

'''Cons'''

 It takes time to produce

 It costs a lot to produce

 Is the network necessary? Is the task obvious or simple?

 It can become very complex- could be misinterpreted

 Reliability of data, e.g timescales, who has produced it and errors, e.g missing tasks

 Threat of external factors that cause problems, e.g weather

These Pros and Cons are stated in an article [7] where the main conclusion as that the Network analysis and critical path is often necessary but not self-sufficient to generate success.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSEx2.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE2.PNG|400x800px|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|400x800px|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|400x800px|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|400x800px|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|400x800px|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

<math>TS = LF-EF</math>

where TS = Total Slack

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|400x800px|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|400x800px|Figure 8]]

==References==

[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
Article on Time management, by: Linh Tran, written April 2015.

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
Blog Article on Monte Carlo Simulation and its usage, by: Shim Marom, a project manager, written October 2009.

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s
Youtube video visualizing and teaching the PND for project management, by user: "Ob Wex" from November 2012.

Project Network Diagram

2017-10-02T10:31:13Z

S124052:

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Pros and Cons of Project Network Diagrams==

'''Pros'''
 Planning- Identify all tasks necessary to complete

 Identify ‘critical’ activities, also activities where ‘float’ exists

 Set deadlines to work towards. Interim + final

 Helps plan ordering of stocks/ materials or equipment

 It helps cashflow

 Network can help solve problems that arise during the project

'''Cons'''
 t takes time to produce

 It costs a lot to produce

 Is the network necessary? Is the task obvious or simple?

 It can become very complex- could be misinterpreted

 Reliability of data, e.g timescales, who has produced it and errors, e.g missing tasks

 Threat of external factors that cause problems, e.g weather

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSEx2.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE2.PNG|400x800px|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|400x800px|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|400x800px|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|400x800px|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|400x800px|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

<math>TS = LF-EF</math>

where TS = Total Slack

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|400x800px|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|400x800px|Figure 8]]

==References==

[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
Article on Time management, by: Linh Tran, written April 2015.

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
Blog Article on Monte Carlo Simulation and its usage, by: Shim Marom, a project manager, written October 2009.

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s
Youtube video visualizing and teaching the PND for project management, by user: "Ob Wex" from November 2012.

Project Network Diagram

2017-10-02T10:27:36Z

S124052: /* References */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSEx2.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE2.PNG|400x800px|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|400x800px|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|400x800px|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|400x800px|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|400x800px|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

<math>TS = LF-EF</math>

where TS = Total Slack

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|400x800px|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|400x800px|Figure 8]]

==References==

[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
Article on Time management, by: Linh Tran, written April 2015.

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
Blog Article on Monte Carlo Simulation and its usage, by: Shim Marom, a project manager, written October 2009.

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s
Youtube video visualizing and teaching the PND for project management, by user: "Ob Wex" from November 2012.

Project Network Diagram

2017-10-02T09:56:36Z

S124052: /* Pre-processes for the Project Network Diagram (PND) */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSEx2.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE2.PNG|400x800px|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|400x800px|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|400x800px|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|400x800px|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|400x800px|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

<math>TS = LF-EF</math>

where TS = Total Slack

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|400x800px|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|400x800px|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-10-02T09:53:34Z

S124052: /* Defining the Project Network Diagram */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSEx2.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE2.PNG|400x800px|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|400x800px|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|400x800px|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|400x800px|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|400x800px|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

<math>TS = LF-EF</math>

where TS = Total Slack

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|400x800px|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|400x800px|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

File:WBSTABLE2.PNG

2017-10-02T09:53:27Z

S124052: S124052 uploaded a new version of "File:WBSTABLE2.PNG"

Project Network Diagram

2017-10-02T09:53:14Z

S124052: /* Work Breakdown Structure (WBS) */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSEx2.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|400x800px|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|400x800px|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|400x800px|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|400x800px|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|400x800px|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

<math>TS = LF-EF</math>

where TS = Total Slack

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|400x800px|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|400x800px|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

File:WBSEx2.PNG

2017-10-02T09:53:03Z

S124052:

File:WBSExample.PNG

2017-10-02T09:51:20Z

S124052: S124052 uploaded a new version of "File:WBSExample.PNG"

File:WBSTABLE2.PNG

2017-10-02T09:51:07Z

S124052:

File:WBSExample.PNG

2017-10-02T09:49:40Z

S124052: S124052 uploaded a new version of "File:WBSExample.PNG"

Project Network Diagram

2017-10-02T09:45:28Z

S124052: /* Critical path and overall duration of project */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|400x800px|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|400x800px|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|400x800px|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|400x800px|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|400x800px|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

<math>TS = LF-EF</math>

where TS = Total Slack

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|400x800px|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|400x800px|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-10-02T09:45:16Z

S124052: /* Slack */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|400x800px|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|400x800px|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|400x800px|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|400x800px|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|400x800px|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

<math>TS = LF-EF</math>

where TS = Total Slack

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|400x800px|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|0|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-10-02T09:42:53Z

S124052: /* Defining the Project Network Diagram */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|400x800px|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|400x800px|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|400x800px|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|400x800px|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|400x800px|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|0|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|0|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-10-02T09:41:30Z

S124052: /* Time estimation of the WBS */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2]

It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4]

In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|0|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|0|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|0|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|0|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|0|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|0|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|0|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-10-02T09:40:42Z

S124052: /* Work Breakdown Structure (WBS) */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|400x800px|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|0|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|0|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|0|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|0|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|0|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|0|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|0|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-10-02T09:33:05Z

S124052: /* Abstract */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). The PND tool is very useful for a project manager when the manager needs an overview of how different assignments in a project should be prioritized. Also, the PND can give the manager a clear view of the overall duration of the project, together with the critical path of the project, which is very helpful when one needs to keep important deadlines.

Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack/slippage, so the project manager will get a clearer vision of possibilities in regard to prioritizing resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|0|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|0|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|0|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|0|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|0|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|0|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|0|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-22T19:26:38Z

S124052: /* References */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|0|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|0|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|0|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|0|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|0|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|0|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|0|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017

[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/

[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146

[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research

[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/

[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-22T19:24:06Z

S124052: /* Critical path and overall duration of project */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|0|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|0|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|0|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|0|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|0|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|0|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more. The critical path is shown with orange arrows, as it is seen in Figure 8

[[File:PND MAP7.PNG|0|Figure 8]]

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017
[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146
[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research
[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-22T19:22:52Z

S124052: /* Defining the Project Network Diagram */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|0|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|0|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|0|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|0|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP4.PNG|0|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|0|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more.

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017
[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146
[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research
[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-22T19:21:53Z

S124052: /* Slack */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|0|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|0|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|0|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|0|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP3.PNG|0|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF

This formula is applied to every task, and the results are shown above the crosses for every task, on Figure 7

[[File:PND MAP6.PNG|0|Figure 7]]

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more.

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017
[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146
[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research
[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-22T19:20:24Z

S124052: /* Defining the Project Network Diagram */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|0|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.

After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|0|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in Figure 4.

[[File:PND MAP2.PNG|0|Figure 4]]

For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure 5

[[File:PND MAP3.PNG|0|Figure 5]]

As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.

After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see Figure 6

[[File:PND MAP3.PNG|0|Figure 6]]

Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF indsæt mathligning evt

This formula is applied to every task, and the results are shown above the crosses for every task, on figure …
Figur med TS’er (5’eren)

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more.

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017
[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146
[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research
[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-22T19:12:25Z

S124052: /* Defining the Project Network Diagram */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in Figure 2.

[[File:WBSTABLE.PNG|0|Figure 2]]

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In Figure 2 it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.
After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in Figure 3. and the explanation follows.

[[File:PND MAP1.PNG|0|Figure 3]]

The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in figure …
Insert figure of time numbers for PND
For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure …
Figure med ES og EF indsat
As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.
After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see figure …
Figur med alle LS og LF udfyldt.
Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF indsæt mathligning evt

This formula is applied to every task, and the results are shown above the crosses for every task, on figure …
Figur med TS’er (5’eren)

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more.

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017
[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146
[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research
[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-22T19:09:06Z

S124052: /* Work Breakdown Structure (WBS) */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in Figure 1.

[[File:WBSExample.PNG|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in figure ….
INDSÆT tabellen her

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In figure … (reference) it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.
After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in figure…. and the explanation follows.
Figure før tal indsættes
The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in figure …
Insert figure of time numbers for PND
For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure …
Figure med ES og EF indsat
As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.
After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see figure …
Figur med alle LS og LF udfyldt.
Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF indsæt mathligning evt

This formula is applied to every task, and the results are shown above the crosses for every task, on figure …
Figur med TS’er (5’eren)

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more.

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017
[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146
[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research
[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-22T19:08:45Z

S124052: /* Work Breakdown Structure (WBS) */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in figure….

[[File:WBSExample.PNG|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in figure ….
INDSÆT tabellen her

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In figure … (reference) it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.
After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in figure…. and the explanation follows.
Figure før tal indsættes
The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in figure …
Insert figure of time numbers for PND
For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure …
Figure med ES og EF indsat
As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.
After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see figure …
Figur med alle LS og LF udfyldt.
Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF indsæt mathligning evt

This formula is applied to every task, and the results are shown above the crosses for every task, on figure …
Figur med TS’er (5’eren)

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more.

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017
[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146
[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research
[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-22T19:07:32Z

S124052: /* Work Breakdown Structure (WBS) */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in figure….

[[WBSExample.PNG|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in figure ….
INDSÆT tabellen her

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In figure … (reference) it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.
After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in figure…. and the explanation follows.
Figure før tal indsættes
The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in figure …
Insert figure of time numbers for PND
For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure …
Figure med ES og EF indsat
As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.
After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see figure …
Figur med alle LS og LF udfyldt.
Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF indsæt mathligning evt

This formula is applied to every task, and the results are shown above the crosses for every task, on figure …
Figur med TS’er (5’eren)

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more.

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017
[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146
[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research
[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-22T19:06:43Z

S124052: /* Work Breakdown Structure (WBS) */

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in figure….

[[File:WBSExample.png|0|Figure 1]]

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in figure ….
INDSÆT tabellen her

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In figure … (reference) it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.
After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in figure…. and the explanation follows.
Figure før tal indsættes
The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in figure …
Insert figure of time numbers for PND
For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure …
Figure med ES og EF indsat
As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.
After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see figure …
Figur med alle LS og LF udfyldt.
Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF indsæt mathligning evt

This formula is applied to every task, and the results are shown above the crosses for every task, on figure …
Figur med TS’er (5’eren)

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more.

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017
[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146
[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research
[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

File:WBSTABLE.PNG

2017-09-22T19:03:33Z

S124052:

File:WBSExample.PNG

2017-09-22T19:03:21Z

S124052:

File:PND MAP7.PNG

2017-09-22T19:03:09Z

S124052:

File:PND MAP6.PNG

2017-09-22T19:03:01Z

S124052:

File:PND MAP5.PNG

2017-09-22T19:02:53Z

S124052:

File:PND MAP4.PNG

2017-09-22T19:02:45Z

S124052:

File:PND MAP3.PNG

2017-09-22T19:02:29Z

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File:PND MAP2.PNG

2017-09-22T19:02:19Z

S124052:

File:PND MAP1.PNG

2017-09-22T19:02:01Z

S124052:

Project Network Diagram

2017-09-22T19:00:28Z

S124052:

==Abstract==
This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the necessary processes one should work through, to arrive at the PND. These processes involve the Work Breakdown Structure (WBS) and a time-estimate on the different bodies of the WBS. After arriving at the PND, the article will explain how to find slack areas, so the project manager will get a clearer vision of how to prioritize resources for the project. Finally, it explains how the critical path of the project is deduced from the PND.

==Pre-processes for the Project Network Diagram (PND)==
In order to define the PND for a specific project, the project manager need inputs. These inputs are the Work Breakdown Structure (WBS) as well as a time estimation for the different bodies on the WBS.

==Work Breakdown Structure (WBS)==
The WBS should be formulated in a top-down box order. That means, that the highest level of the WBS is the overall project. From there, the next level beneath confines deliverables in order to reach the project goal. These deliverables are confined in the second level boxes. Deliverables are things as they shall be defined by nouns and not verbs. Now to the third level, where all the deliverables can be broken into items. This procedure continues until one reaches the lowest level, being the action level, where direct actions in order to reach the level above is defined. [1]
An example of such a WBS is given in figure….

WBS figure here.....

The WBS shown in the figure illustrates an example with a project, where a new building is to be built. Of course, for the sake of simplicity, the project components are confined to only a few, in comparrison to what a real such project would include as components.

It is seen that the overall goal is to build a new building. This is the project. The second level describes some areas of deliverables. The architects have deliverables for the project, and same goes for the Engineers and e.g. Finance (who is going to pay for the building, how should the contracts be defined etc.). To make the WBS foreseeable in this example, only the lower levels for the architect group are defined. One deliverable from the architects could be the entire design of the building. To make a design, the architects should know what their client wishes are, so they meet ends with regard to mutual satisfaction for the project stakeholders. The last level defined in the example is a level of action. This level is pretty intuitive, as it can be interpreted in the same way, that many people use post-it notes at work every day – it is simply things one needs to do, described in keywords.

==Time estimation of the WBS==

When having defined a functional and rational WBS, a time estimation of each component should be determined, in order to eventually estimate a project overall duration and critical path. The idea here is to formulate the time estimates as realistic as possible. For many projects, the primary key factors are time and economy. The more conservative time estimates will often be aligned with the more successful projects. [2] It is very different for individual projects, how time estimation is handled. For smaller firms, it is often the experienced senior managers that drives their estimates on heuristics. They apply their experience and realistic estimates to agree on a good time interval for processes in the project. Sometimes, the time estimates are based on a best case scenario, an average scenario and a worst case scenario, regarding the time needed for a process. This can lead to the usage of a Monte Carlo method, to estimate the probable time intervals. This is a widely used method when the data simulated has a large number of samples, or historical examples. [4] In all, time estimations can be built on a large variety of validating foundations, and by all means, the statistical method will always be the most meaningful with regard to realistic results, but the necessary amount of samples to complete it is not always at hand. Besides, completing a Monte Carlo simulation requires that the analyst has an insight in order to differentiate for correlation between key factors, why it can be a somewhat cumbersome process. [5]

==Defining the Project Network Diagram==
After the process of formulating a rational WBS, and good time estimates on the different bodies of the WBS, a Project Network Diagram can be constructed. The following will give an example of such a PND. [6] First off, see the table shown in figure ….
INDSÆT tabellen her

The table shows an example of how one can establish a WBS on table form. The activities are the different bodies of the WBS, and the time is estimated and allocated to each individual body/activity. The Immediate Predecessors is a list of dependencies. This is the new object to include. In figure … (reference) it is shown as the last column, at an activity row. This means, that when coming to activity C, activity A and B must be completed beforehand. In other words, task C can start solely when A and B are done. Where the cells of Immediate Predecessors are empty, the connecting activity can be started whenever the project starts. They do not depend on other activities. In this example, the project manager could potentially start activity A, B and D at the same time, at the beginning of the project.
After having formulated this table with immediate predecessors, built upon the WBS and time estimation for each activity, the PND can finally be constructed. The project manager can do this by making a start point, and visualize the start off possibilities. An example of this is shown in figure…. and the explanation follows.
Figure før tal indsættes
The arrows in the diagram shows the dependencies. For example, activity C depends both of activity A and B, why C is connected to these mentioned activities. Activity F depends only on activity D, why this activity is solely connected by D. This diagram now shows the flow of activities. Now, the time estimates of the different tasks should be implemented. This is done by inserting numbers in every circle, corresponding to the time the activity takes. This can be seen in figure …
Insert figure of time numbers for PND
For example, it is seen that task C takes 5 days, why 5 is inserted into the C circle and so forth. The crosses that now show above all circles are for the further calculation of the overall duration and critical path. Now, numbers are to be filled into the crosses, and the way they should are as follows: Top left corner is ES, which stands for Earliest Start. This will indicate when is the earliest time the activity can start. Top right corner is called EF, which stands for Earliest Finnish. This is intuitively the time it would take to complete the task in the fastest scenario possible. Task A, B and D can all start at the beginning, why the number 0 is put into the place of ES. Then, the EF would be 4 days, 3 days and 1 day for A, B and D respectively. Then, if one looks at task C, the ES should be filled out. Now there are two tasks that are linked to task C (being task A and B). The ES will then be the highest value, of the EF for the previous tasks. Since A and B can be done simultaneously, the highest required number of days for the respective tasks will determine the value of the beginning time foor the next task. That means that task C can be completed after task A is finished, being the highest number of days, four days. Task C itself takes 5 days, so the earliest finnish time for task C will be the previous 4 days plus its own duration of 5 days, meaning 9 days in the time schedule. To visualize and comprehend the method, see figure …
Figure med ES og EF indsat
As it is seen, task G can again only start when the corresponding previous tasks are finished, which is determined by the longest task line, being the one including task E, which makes it 14 days until task G can begin. It is also seen, that the last task can begin the earliest after 19 days, and that it takes 6 days itself, why the overall earliest finish of the project will be 25 days.
After having done this, the time has come to declare what the latest start (LS) is for each task. The LS value maintains, that the project will still finish in the firstly calculated overall duration (being 25 days). The LS value will be in the bottom left corner of the cross. To the bottom right, the latest finish (LF) time is introduced. Here, the question is when is the latest possible time the tasks can finish in order to maintain the overall duration. The trick to this is to go “backwards” in the PND. You start with the last task, being task H here, and fill out the LF in the bottom right corner. It is of course the 25 days that should be put in the LF for task H, since this is the latest finish we demanded for our project. In the LS field, the latest start should be the latest finish minus the duration of the task, meaning (25-6) days = 19 days. To see the principle, see figure …
Figur med alle LS og LF udfyldt.
Take task G for example, here the latest finish must match the earliest start for the next task (task H) why task G must finish latest at day 19. The duration of G is 5 days, so the latest start must be (19 – 5) days = 14 days. When there are 2 tasks connecting to a point, as in task E and F connecting to task G, the approach is to take the latest start of G, and find the latest start of either E or F by subtracting their individual duration from this mutual requirement. This means that task F must latest be finished at day 14, where task G has to start, but since F is only a 2 day task, it can start at day (14-2) days = day 12. Another example is for task A, where the latest start for task C is 4 days, so the latest finish for task A is 4 days. Then, since A takes 4 days, it must start at day 0 (LS = 0) in order to finish on time.

==Slack==

The total slack on a project can be measured through the PND. The reader is suggested to read the previous section “Defining the Project Network Diagram” in order to follow the guidelines coming. The total slack on a project is not about how many workers that fall asleep on their desktop. Neither is it about how slow people are. The total slack is a measure of “time buffers” being the difference between the latest finish and earliest finish. This means that a task can be done as the manager wishes, freely between these boundaries of time. The formula is:

TS (Total Slack)=LF-EF indsæt mathligning evt

This formula is applied to every task, and the results are shown above the crosses for every task, on figure …
Figur med TS’er (5’eren)

As it is seen, there will be 0 slack on the last task. Often, the slack is also referred to as slippage. This might be a bit more of an intuitive name, since the number will show the allowed slippage, in number of days, that a task can slip, while the project still finishes on time. This can also be a tool for a project manager, during the project, to reallocate workers or other recourses from one task to another, where there is less slack. Basically, this will give a total visualization on where the manager should prioritize, and how resources should be located.

==Critical path and overall duration of project==

The critical path is the path with the least allowed slippage. This is the path that for all sake should be respected to maintain the overall duration of the project. Therefore, the critical path for this project example would be: A, C, E, G, H. This is the line with 0 slack indeed. This tool is a very powerful tool for project managers, and it can be used during the project as an active measuring tool of how the project is progressing, amongst much more.

==References==
[1] IEEE ENGINEERING MANAGEMENT REVIEW, VOL. 45, NO. 2, SECOND QUARTER, JUNE 2017
[2] https://www.inloox.com/company/blog/articles/the-importance-of-time-management-aspects-of-project-management-part-1/
[3] POLISH JOURNAL OF MANAGEMENT STUDIES, Manole A.L., Grabara I, 2016, Vol. 14, No.2, pp. 146
[4] Montecinos, J., Ouhimmou M., Chauhan, S. – Waiting-time estimation in clinics – 2016 International Transactions in Operational Research
[5] http://quantmleap.com/blog/2009/10/monte-carlo-simulation-for-dummies/
[6] https://www.youtube.com/watch?v=URdxhl_8qIE&t=5s

Project Network Diagram

2017-09-20T17:29:30Z

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Project Network Diagram

2017-09-20T17:21:05Z

S124052:

Project Network Diagram

2017-09-20T17:19:56Z

S124052:

Project Network Diagram

2017-09-20T17:12:45Z

S124052: /* Table of Content */

Project Network Diagram

2017-09-20T17:12:32Z

S124052: /* Abstract */

Project Network Diagram

2017-09-20T17:09:38Z

S124052: /* Abstract */

Articles Fall Term 2017

2017-09-20T17:08:52Z

S124052: /* Overview of 2017 Wiki articles */

{| class="wikitable"
|+ '''Disclaimer!
|-
|''The requirements for the articles written in previous Terms (2014, 2015, 2016, Jun 2017) were not the same as for Fall Term 2017. Please make sure you read the requirements for your own fall term carefully before starting your wiki article.''
|}

Please complete this table with your group number, full name, username and the title of your article.

To create more lines in the table click '''Edit''' and use the following code to create more lines in the table and replace the example text with your own information:

<pre style="white-space: pre-wrap;
white-space: -moz-pre-wrap;
white-space: -pre-wrap;
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word-wrap: break-word;">
|-
|Group Number
|First Name
|Last Name
|Username
|Link to Article
|-
</pre>
Create a direct link by making square brackets ([[ ]]) around the title such as [[Title]]

The straight lines ( | ) create columns and the straight line with a dash ( |- ) creates a new row in the table.

( |} ) is only used at the very end to finish the coding for the table.

=Overview of 2017 Wiki articles=

{| class="wikitable sortable"
|+June 2017 Wiki Articles
|-
!Group number
!First name
!Second name
!User name
!Link to article
|-
|8
|Malyn
|Jørgensen
|Malyn
|[[Construction Contract Management Guidelines and Administration]]
|-
|4
|Javier
|Durá María
|Jaduma
|[[Delphi Method (expert for identification)]]
|-
|2
|Cornelis Johannes
|Jongenelen
|CJJongenelen
|[[Stage-Gate Process]]
|-
|4
|Waqas
|Khalid
|waqaskhld
|[[Risk Quantification]]
|-
|9
|Thomas
|Reigstad
|Thomas Reigstad
|[[Quality Control and Safety During Construction]]
|-
|GN
|Karlotta
|Thorhallsdóttir
|S162285
|[[Impact vs. Probability]]
|-
|GN
|Guillermo
|Altuna Faus
|Galtunaf
|[[RAPID Outcome Mapping Approach (ROMA)]]
|-
|4
|Bjarke
|Schjødt Rasmussen
|Schjodt92
|[[Adjusted Balanced Scorecard (ABSC)]]
|-
|8
|Marion
|Chambon
|s172284
|[[HAZOP method, deviation analysis]]
|-
|8
|Davide
|Morbin
|Davide
|[[Kaizen Week]]
|-
|GN
|Ignacio
|López Cabañas
|S161357
|[[PERT]]
|-
|GN
|Leon David
|Schleer
|LeonS
| [[Project Manager Competencies and Personality Types]]
|-
|GN
|Pascal
|Trebin
|Pascal
|[[Kano model]]
|-
|2
|Michael Kirkeby
|Hansen
|Mikirkeby
|[[Scenario Analysis]]
|-
|7
|Julian
|Ofenstein
|Bekis
|[[Waterfall vs. Agile Methodology]]
|-
|GN
|Kamma
|Christensen
|Kamma
|[[Change order]]
|-
|5
|Alexandra
|Darmaraki
|s162578
|[[Scenario Planning Strategy]]
|-
|3
|Eyðbjørg Amanda
|Petersen
|EAP
|[[Feasibility Study]]
|-
|5
|Iason
|Divanis
|Iason Divanis
|[[Dynamic Systems Development Method(DSDM)]]
|-
|2
|Signe
|Risager
|s163071
|[[Teamweek (virtual resource management tool)]]
|-
|11
|Erik A.
|Heggstad
|Erikheggstad
|[[Stage-Gate Model]]
|-
|GN
|Philip
|van Berkom
|PA
|[[Contingency]]
|-
|GN
|Apostolos
|Bougas
|S162469
|[[Decision Tree]]
|-
|GN
|Paolo
|Meneghini
|Paolo M
|[[Reporting]]
|-
|GN
|Ragnheidur
|Ragnarsdottir
|S161269
|[[Benefit map analysis]]
|-
|3
|Thorunn Sif
|Ingimundardottir
|Thorunn
|[[MBTI]]
|-
|2
|Sophie Emilie
|Smietana
|SophieEmilie
|[[Agile Methodology]]
|-
|5
|Thomas
|Engelhart
|Engelhart
|[[DICE Framework]]
|-
|3
|Nathalie Lückstädt
|Nielsen
|S130038
|[[Scope creep]]
|-
|11
|Eleni
|Pagoni
|Ele
|[[The Stage-Gate Model]]
|-
|11
|Konstantinos
|Vontas
|Konstantinos
|[[Project Control]]
|-
|5
|Emmanouil
|Psomas
|Manolis
|[[Decision making skills]]
|-
|GN
|Ingvild Reine
|Assmann
|Ingvild Assmann
|[[Muda, Mura and Muri]]
|-
|-
|GN
|Javier
|Gumà
|S161631
|[[Simon's four levels of control]]
|-
|-
|GN
|Christina Diget
|Christiansen
|S160541
|[[Lean Construction on Bispebjerg Bakke]]
|-
|-
|10
|Nikoleta
|Kolitsopoulou - Maridaki
|Nikoletta
|[[Roles and responsibilities]]
|-
|-
|7
|Matthis
|Hanstein
|Matthis
|[[Communication with public stakeholders on the femern link project in Germany]]
|-
|-
|6
|Patrick
|Grimm
|S161459
|[[SMART goals in project planning and performance management]]
|-
|-
|7
|John
|Gomes
|S161001
|[[Application of Alignment Matrix in Project Coordination and Communication]]
|-
|-
|6
|Hani
|Selim
|s135278
|[[Project Scope Control]]
|-
|-
|9
|Anders Stig
|Pedersen
|S124052
|[[Project Network Diagram]]
|-
|-
|GN
|Timokleia
|Orfanidou
|S155592
|[[Sponsorship of a project, programme or portfolio]]
|-
|-
|4
|Gudmann
|Tommy
|tg_dk
|[["Interpersonal skills of a Project Manager"]]
|-
|-
|4
|Gudjon
|Arngrimsson
|Gudjon
|[[Expectations Management]]
|-
|-
|6
|Victor
|Aguasca Lloberes
|S161321
|[[Performance Measurement and Performance Management]]
|-
|3
|Asger
|Fuhr Høyer
|Asger
|[[Antifragility]]
|-
|1
|Klavs
|Skovby
|Klask
|[[Decision Tree: Risk & Opportunities]]
|-
|1
|Nicolaj J. B.
|Thomsen
|Kittymaumau
|[[Pro-active: Risk and Opportunity Management]]
|-
|-
|7
|Laurens M.
|van der Schaft
|s172077
|[[Implementation of BIM as communication tool for construction site operations]]
|-
|-
|8
|Thuritha
|Ravindran
|s123252
|[[Role of a project sponsor]]
|-
|-
|GN
|Rune
|Nedergaard
|RRN
|[[Case Study: Updating Airplane Tracking Systems in the Australian Defense Force]]
|-
|11
|Ioanna-Eleni
|Vasilopoulou
|Ioanna-Eleni Vasilopoulou
|[[Balanced Scorecard]]
|-
|6
|Maria
|Barba Garcia
|MariaB
|[[Omnichannel strategy]]
|-
|1
|Frederik Lybek
|Lind
|Frederik Lind
|[[Decision tree]]
|-
|1
|Alisha
|Patnaik
|Alisha.patnaik
|[[Critical Path Method (CPM)]]
|-
|6
|Patricia
|Máñez Aleixandre
|Patriciamanez
|[[Schein culture]]
|-
|4
|Niels
|Mikkelsen
|Niels
|[[Servant Leadership]]
|-
|GN
|Einar
|Loktu
|ELoktu
|[[Lean construction, takt time planning]]
|-
|-
|12
|Edvinas
|Zamaratskis
|Edvinas
|[[Risk tolerances]]
|-
|-
|2
|Lea
|Glahn Christiansen
|LeaGlahn
|http://apppm.man.dtu.dk/index.php/Jung%27s_personality_Theory
|-
|2
|Karoline
|Holm Hansen
|Karoline
|[[Fishbone diagram]]
|-
|9
|Thomas
|Sotiriadis
|ThomasSot
|https://en.wikipedia.org/wiki/Theory_of_Constraints_in_streamline_manufacturing
|-
|9
|Rick
|Kool
|Rick Kool
|http://apppm.man.dtu.dk/index.php/Collaborative_Tendering
|-

Project Network Diagram

2017-09-20T17:08:04Z

S124052: Created page with "==Abstract== This article is an application oriented in-depth description of the Project Network Diagram tool (PND tool). Firstly, the article will explain and visualize the n..."

Network Plan and Monte Carlo Method

2017-09-19T15:09:23Z

S124052:

==Abstract==

Gantt Chart --> Network Schedule (Plan) --> organizing resources

This article is an application oriented in-depth description of a Network Plan, in regards to project planning. The Network Plan diagram is a visualization of the time plan, after having formulated an ideal WBS, which can reveal the Critical Path for the project time plan. Furthermore, the Network Plan diagram will reveal which WBS areas has time buffers, which ideally can be utilized to redirect human resources, in case of time critical situations. There exists software to create time plans, e.g. “Microsoft Project” and many more. In practice, the project time plan is often determined from rough estimates or experience of needed time in different WBS areas. This article will describe the functionality of a Network Plan Diagram and how the diagram is created. Furthermore, the article will describe how more realistic estimates of time consumption in different WBS areas could be obtained, by the use of the statistical tool called Monte Carlo method.

==Table of Content==
• Network Plan from decided WBS

• Network Plan Diagram

• Limitations of the diagram

• Buffers and relocation of human resources

• Critical Path

• The process of estimating needed time in different WBS areas

• Monte Carlo Method for realistic time estimates

• Limitations of the Monte Carlo Method

==Network Plan from decided WBS==

List of activities to evaluate

When having formulated a Work Breakdown Structure (WBS) for a given project, the WBS needs to be logical in regard to defining what processes in the project can run side by side, and which processes are dependant on each other. When knowing this, the project stages can be mapped logically. For an example, one can think of producing a car. There are many aspects that needs to be handled, and in order to not confuse the overall goal, it is necesary to break the process up in structures like e.g. "Design", "Motor", "Interiour", "Satisfying Safety Requirements" and finally "Integrating all aspects into producing the car". The Network Plan could look like shown in the following picture:

[[File:AP_WBS-PLAN.jpg]]

Network Plan and Monte Carlo Method

2017-09-19T14:16:50Z

S124052:

==Abstract==

This article is an application oriented in-depth description of a Network Plan, in regards to project planning. The Network Plan diagram is a visualization of the time plan, after having formulated an ideal WBS, which can reveal the Critical Path for the project time plan. Furthermore, the Network Plan diagram will reveal which WBS areas has time buffers, which ideally can be utilized to redirect human resources, in case of time critical situations. There exists software to create time plans, e.g. “Microsoft Project” and many more. In practice, the project time plan is often determined from rough estimates or experience of needed time in different WBS areas. This article will describe the functionality of a Network Plan Diagram and how the diagram is created. Furthermore, the article will describe how more realistic estimates of time consumption in different WBS areas could be obtained, by the use of the statistical tool called Monte Carlo method.

==Table of Content==
• Network Plan from decided WBS

• Network Plan Diagram

• Limitations of the diagram

• Buffers and relocation of human resources

• Critical Path

• The process of estimating needed time in different WBS areas

• Monte Carlo Method for realistic time estimates

• Limitations of the Monte Carlo Method

==Network Plan from decided WBS==

When having formulated a Work Breakdown Structure (WBS) for a given project, the WBS needs to be logical in regard to defining what processes in the project can run side by side, and which processes are dependant on each other. When knowing this, the project stages can be mapped logically. For an example, one can think of producing a car. There are many aspects that needs to be handled, and in order to not confuse the overall goal, it is necesary to break the process up in structures like e.g. "Design", "Motor", "Interiour", "Satisfying Safety Requirements" and finally "Integrating all aspects into producing the car". The Network Plan could look like shown in the following picture:

[[File:AP_WBS-PLAN.jpg]]

File:AP WBS-PLAN.jpg

2017-09-19T14:16:02Z

S124052: