Resource-Constrained Critical Path Method - Revision history

GiorgiaS: /* Step 1: The Network Diagram */

2019-03-02T13:41:23Z

Step 1: The Network Diagram

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	The first step in CPM is constructing an arrow diagram that can show the precedence relationships among the project tasks.		The first step in CPM is constructing an arrow diagram that can show the precedence relationships among the project tasks.

	Generally, it starts by making a list of all the activities to be performed in the project, a list of the ~~precedences~~ and the relative duration. Based on this information, the network diagram can be constructed. As it can be seen in Figure 2, each arrow (capital letter) represents an activity; arrowheads show the order of each task. A node (number) indicates the beginning and the end of the activity, also called ''events''; circled numbers stand for the duration of the activities.		Generally, it starts by making a list of all the activities to be performed in the project, a list of the precedencies and the relative duration. Based on this information, the network diagram can be constructed. As it can be seen in Figure 2, each arrow (capital letter) represents an activity; arrowheads show the order of each task. A node (number) indicates the beginning and the end of the activity, also called ''events''; circled numbers stand for the duration of the activities.

	[[File:events.jpg\|thumb\|200px\|Figure 4: ETE and LTE values (''Inspired by <ref name=FEES />'')]]		[[File:events.jpg\|thumb\|200px\|Figure 4: ETE and LTE values (''Inspired by <ref name=FEES />'')]]

GiorgiaS: /* Step 2: Time Estimation */

2019-03-02T13:39:29Z

Step 2: Time Estimation

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	The LTE for each event can be found listed in the third column of Figure 4. After completing the forward and backward passes, it is possible to determine the earliest starting time '''ES''', latest starting time '''LS''', earliest finish time '''EF''', latest finish time '''LF''', and '''float times''' for each activity.		The LTE for each event can be found listed in the third column of Figure 4. After completing the forward and backward passes, it is possible to determine the earliest starting time '''ES''', latest starting time '''LS''', earliest finish time '''EF''', latest finish time '''LF''', and '''float times''' for each activity.

	By convention, ES(i, j) = 0 for any activity that has no ~~precedences~~, and LF(i, j) = project time for any activity that has no successors.		By convention, ES(i, j) = 0 for any activity that has no precedencies, and LF(i, j) = project time for any activity that has no successors.
	ES(i, j) = ETE(i) because the activity (i, j) may begin as soon as all of its ~~precedences~~ are completed, and LF(i, j) = LTE(j) because the activity (i, j) must finish before event j occurs<ref name=FEES />. Given these premises, EF(i,j) and LS(i,j) for each activity can be calculated with		ES(i, j) = ETE(i) because the activity (i, j) may begin as soon as all of its precedencies are completed, and LF(i, j) = LTE(j) because the activity (i, j) must finish before event j occurs<ref name=FEES />. Given these premises, EF(i,j) and LS(i,j) for each activity can be calculated with
	::::::::::EF(i, j) = ES(i, j) + D(i, j) = ETE(i) + D(i, j)		::::::::::EF(i, j) = ES(i, j) + D(i, j) = ETE(i) + D(i, j)
	::::::::::LS(i, j) = LF(i, j) - D(i, j) = LTE(j) - D(i, j)		::::::::::LS(i, j) = LF(i, j) - D(i, j) = LTE(j) - D(i, j)

GiorgiaS: /* What is Project Management? */

2019-03-02T13:29:25Z

What is Project Management?

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	[[File:I-Triangle.jpg\|thumb\|Figure 1: The Iron Triangle - Scope, Time, Cost (''autonomously created'')]]The definition of 'project' can be found in the Project Management Body of Knowledge: it ''is a temporary endeavor undertaken to create a unique product, service, or result''<ref name=PMI />. Ergo, a project is any series of activities and tasks having a specific objective to be completed within some specifications<ref name=CPA> Paing Hein Soe and Thein Min Htike, ''"Critical Path Analysis programming method without network diagram".'' MATEC Web Conference, Volume 192 (2018) </ref>, such as start and end dates, specific goals and limits, established implementers responsibilities, budget and schedule<ref name=estim> Rafik Nafkha and Artur Wilinski, ''"The Critical Path Method in estimating project duration".'' Information Systems in Management, Volume 5, No. 1, Pages 78−87 (2016) </ref>.		[[File:I-Triangle.jpg\|thumb\|Figure 1: The Iron Triangle - Scope, Time, Cost (''autonomously created'')]]The definition of 'project' can be found in the Project Management Body of Knowledge: it ''is a temporary endeavor undertaken to create a unique product, service, or result''<ref name=PMI />. Ergo, a project is any series of activities and tasks having a specific objective to be completed within some specifications<ref name=CPA> Paing Hein Soe and Thein Min Htike, ''"Critical Path Analysis programming method without network diagram".'' MATEC Web Conference, Volume 192 (2018) </ref>, such as start and end dates, specific goals and limits, established implementers responsibilities, budget and schedule<ref name=estim> Rafik Nafkha and Artur Wilinski, ''"The Critical Path Method in estimating project duration".'' Information Systems in Management, Volume 5, No. 1, Pages 78−87 (2016) </ref>.

	The management of a project can be defined as ''the application of knowledge, skills, tools, and techniques to project activities to meet the project requirements''<ref name=PMI />. Its success can be measured through the "iron triangle" model that includes time, scope, and cost. The success of a project should, therefore, be measured within project scope, scheduling, cost, quality, resource, and risk constraints in term of completing the project <ref name=aircraft> Arin Wulandari, M. Dachyar and Farizal, ''"Scheduling of Empennage Structure Design Project of Indonesia’s Aircraft with Critical Path Method (CPM)".'' MATEC Web Conferences, Volume 248 (2018) </ref>.		The management of a project can be defined as ''the application of knowledge, skills, tools, and techniques to project activities to meet the project requirements''<ref name=PMI />. Its success can be measured through the "iron triangle" model that includes time, scope, and cost (Figure 1). The success of a project should, therefore, be measured within project scope, scheduling, cost, quality, resource, and risk constraints in term of completing the project <ref name=aircraft> Arin Wulandari, M. Dachyar and Farizal, ''"Scheduling of Empennage Structure Design Project of Indonesia’s Aircraft with Critical Path Method (CPM)".'' MATEC Web Conferences, Volume 248 (2018) </ref>.

	Scheduling is an important and difficult task during project planning since it helps to monitor the project duration and resource utilization. The challenge is about the scheduling complexity and dynamism: in fact, plans can change before the start but even during the implementation<ref name=estim />. In order to better manage projects and face the changes that may occur over time, a lot of methods were created, and among them, the Critical Path Method (CPM) is one of the better-known planning and control techniques in project scheduling.		Scheduling is an important and difficult task during project planning since it helps to monitor the project duration and resource utilization. The challenge is about the scheduling complexity and dynamism: in fact, plans can change before the start but even during the implementation<ref name=estim />. In order to better manage projects and face the changes that may occur over time, a lot of methods were created, and among them, the Critical Path Method (CPM) is one of the better-known planning and control techniques in project scheduling.

GiorgiaS: /* The Benefits of Resource-constrained Critical Path Method */

2019-02-28T11:45:04Z

The Benefits of Resource-constrained Critical Path Method

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	In a CPM schedule, activities are sharing total float only if they are on the same chain. In the RCPM schedule, due to sharing of resources, some parallel activities, not in the same chain, can share floats, and these can be consumed by any activity that needs them first (an additional resource link is required to reflect the condition)<ref name= PF />.		In a CPM schedule, activities are sharing total float only if they are on the same chain. In the RCPM schedule, due to sharing of resources, some parallel activities, not in the same chain, can share floats, and these can be consumed by any activity that needs them first (an additional resource link is required to reflect the condition)<ref name= PF />.

	Undoubtedly, other studies need to be conducted to improve the RCPM technique explained in this article. The dynamic features of resource links related to schedule updates and shared floats need to be studied further to provide a better rationale for scheduling, control, and time impact analysis. In addition, effects on resource links from variable resource requirements and availability should also be investigated<ref name= PF />.		Undoubtedly, other studies need to be conducted to improve the RCPM technique explained in this article. The dynamic features of resource links related to schedule updates and shared floats need to be studied further to provide a better rationale for scheduling, control, and time impact analysis. In addition, effects on resource links from variable (and not static, as the ones presented in this article) resource requirements and availability should also be investigated<ref name= PF />.

	==References==		==References==

GiorgiaS at 11:43, 28 February 2019

2019-02-28T11:43:27Z

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	According to Project Management Body of Knowledge (PMBOK), CPM ''is a method used to estimate the minimum project duration and determine the amount of scheduling ﬂexibility on the logical network paths within the schedule model''<ref name=PMI> Project Management Institute, ''"A guide to the project management body of knowledge (PMBOK® guide) - Fifth edition".'' (2013) </ref>.		According to Project Management Body of Knowledge (PMBOK), CPM ''is a method used to estimate the minimum project duration and determine the amount of scheduling ﬂexibility on the logical network paths within the schedule model''<ref name=PMI> Project Management Institute, ''"A guide to the project management body of knowledge (PMBOK® guide) - Fifth edition".'' (2013) </ref>.
	Given scheduled activities for a project that need to be completed in a specific order, multiple task sequences can be defined. CPM helps us to determine the longest sequence of tasks in the project, which will be also the shorter possible project duration. Thus, the main steps of CPM will be described ~~through the use of an example~~, providing a brief guidance on how to apply the method so to obtain the optimal project duration.		Given scheduled activities for a project that need to be completed in a specific order, multiple task sequences can be defined. CPM helps us to determine the longest sequence of tasks in the project, which will be also the shorter possible project duration. Thus, through a specific example, the main steps of CPM will be described, providing a brief guidance on how to apply the method so to obtain the optimal project duration.

	However, a traditional CPM schedule is not realistic, because it assumes unlimited resources, some of which are highly limited in practice<ref name=PF> Kyunghwan Kim and Jesùs M. de la Garza, ''"Phantom Float".'' Journal of Construction Engineering and Management, Volume 129, No. 5 (October 1, 2003) </ref>.		However, a traditional CPM schedule is not realistic, because it assumes unlimited resources, some of which are highly limited in practice<ref name=PF> Kyunghwan Kim and Jesùs M. de la Garza, ''"Phantom Float".'' Journal of Construction Engineering and Management, Volume 129, No. 5 (October 1, 2003) </ref>.

GiorgiaS at 11:41, 28 February 2019

2019-02-28T11:41:21Z

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	According to Project Management Body of Knowledge (PMBOK), CPM ''is a method used to estimate the minimum project duration and determine the amount of scheduling ﬂexibility on the logical network paths within the schedule model''<ref name=PMI> Project Management Institute, ''"A guide to the project management body of knowledge (PMBOK® guide) - Fifth edition".'' (2013) </ref>.		According to Project Management Body of Knowledge (PMBOK), CPM ''is a method used to estimate the minimum project duration and determine the amount of scheduling ﬂexibility on the logical network paths within the schedule model''<ref name=PMI> Project Management Institute, ''"A guide to the project management body of knowledge (PMBOK® guide) - Fifth edition".'' (2013) </ref>.
	Given scheduled activities for a project that need to be completed in a specific order, multiple task sequences can be defined. CPM helps us to determine the longest sequence of tasks in the project, which will be also the shorter possible project duration. Thus, the main steps of CPM will be described, providing a brief guidance on how to apply the method so to obtain the optimal project duration.		Given scheduled activities for a project that need to be completed in a specific order, multiple task sequences can be defined. CPM helps us to determine the longest sequence of tasks in the project, which will be also the shorter possible project duration. Thus, the main steps of CPM will be described through the use of an example, providing a brief guidance on how to apply the method so to obtain the optimal project duration.

	However, a traditional CPM schedule is not realistic, because it assumes unlimited resources, some of which are highly limited in practice<ref name=PF> Kyunghwan Kim and Jesùs M. de la Garza, ''"Phantom Float".'' Journal of Construction Engineering and Management, Volume 129, No. 5 (October 1, 2003) </ref>.		However, a traditional CPM schedule is not realistic, because it assumes unlimited resources, some of which are highly limited in practice<ref name=PF> Kyunghwan Kim and Jesùs M. de la Garza, ''"Phantom Float".'' Journal of Construction Engineering and Management, Volume 129, No. 5 (October 1, 2003) </ref>.
	Therefore, a different approach of the same technique, called '''Resource-constrained Critical Path Method (RCPM)''', will be presented. By providing a step-by-step RCPM procedure, the article will focus on the advantages that this method can offer compared to the traditional Critical Path Method.		Therefore, a different approach of the same technique, called '''Resource-constrained Critical Path Method (RCPM)''', will be presented. By providing a step-by-step RCPM procedure applied to another example, the article will focus on the advantages that this method can offer compared to the traditional Critical Path Method.
	The paper will then conclude with observations about the benefits and limitations of both CPM and RCPM, highlighting differences and similarities between the two techniques.		The paper will then conclude with observations about the benefits and limitations of both CPM and RCPM, highlighting differences and similarities between the two techniques.

GiorgiaS: /* The Resource-constrained Critical Path Method */

2019-02-27T21:04:50Z

The Resource-constrained Critical Path Method

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	[[File:Step2.jpg\|thumb\|left\|250px\|Figure 9: Resource links are created based on the CPM results (''Inspired by <ref name=PF />'')]]		[[File:Step2.jpg\|thumb\|left\|250px\|Figure 9: Resource links are created based on the CPM results (''Inspired by <ref name=PF />'')]]
	====Step 1====		====Step 1: The CPM technique====
	Based on the steps described earlier, the Critical Path Method can be performed in order to find the earliest and latest times of each activity of a project. These can be found written in Figure 8 around the activity (follow the legend). Moreover, the total float can be calculated by using the formula explained before in this article.		Based on the steps described earlier, the Critical Path Method can be performed in order to find the earliest and latest times of each activity of a project. These can be found written in Figure 8 around the activity (follow the legend). Moreover, the total float can be calculated by using the formula explained before in this article.

	====Step 2====		====Step 2: The RCS technique - forward pass====

	Having the CPM results of the first step, it is possible to apply an RCS technique. During this process, the activity that is currently being evaluated in the process is named as ''current activity''. If there are enough resources, the current activity can be scheduled at its earliest possible time according to relationships with precedent activities. However, if there are not enough resources for the current activity, it should be delayed until it acquires available resources. After being delayed, the current activity is to encounter a certain date from which enough resources are available throughout its whole duration.		Having the CPM results of the first step, it is possible to apply an RCS technique. During this process, the activity that is currently being evaluated in the process is named as ''current activity''. If there are enough resources, the current activity can be scheduled at its earliest possible time according to relationships with precedent activities. However, if there are not enough resources for the current activity, it should be delayed until it acquires available resources. After being delayed, the current activity is to encounter a certain date from which enough resources are available throughout its whole duration.
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	As a result (Figure 9), resource links are created and the scheduled start and end times of the activity automatically become ES and EF, and since this step can be described as a forward step, it is necessary to apply a backward step in order to identify LS and LF.		As a result (Figure 9), resource links are created and the scheduled start and end times of the activity automatically become ES and EF, and since this step can be described as a forward step, it is necessary to apply a backward step in order to identify LS and LF.

	====Step 3====		====Step 3: The RCS technique - backward pass====

	Considering then both the original relationships between activities and the resource links found in ''Step 2'', LS and LF for each activity can be identified (Figure 10).		Considering then both the original relationships between activities and the resource links found in ''Step 2'', LS and LF for each activity can be identified (Figure 10).
	[[File:Step4.jpg\|thumb\|left\|250px\|Figure 11: Schedule in ''Step 4'', showing a new resource link added due to a resource dependency (''Inspired by <ref name=PF />'')]]		[[File:Step4.jpg\|thumb\|left\|250px\|Figure 11: Schedule in ''Step 4'', showing a new resource link added due to a resource dependency (''Inspired by <ref name=PF />'')]]
	[[File:Finalstep.jpg\|thumb\|left\|250px\|Figure 12: Schedule in ''Step 5'' (''Inspired by <ref name=PF />'')]]		[[File:Finalstep.jpg\|thumb\|left\|250px\|Figure 12: Schedule in ''Step 5'' (''Inspired by <ref name=PF />'')]]
	====Step 4====		====Step 4: Finding unidentified resource links====

	In the result of step 3, the TF of a critical activity, which is calculated using the formula		In the result of step 3, the TF of a critical activity, which is calculated using the formula
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	At this point, there are no resource links between activities if the completion of the prescheduled activities does not immediately affect the delayed activity’s start, although the released resources are transferred to the delayed activity. In order to find those unidentified resource dependencies, every activity of nonzero TF will be checked by delaying the completion time day by day, and a resource link will be created between activities that have resource dependency (Figure 11).		At this point, there are no resource links between activities if the completion of the prescheduled activities does not immediately affect the delayed activity’s start, although the released resources are transferred to the delayed activity. In order to find those unidentified resource dependencies, every activity of nonzero TF will be checked by delaying the completion time day by day, and a resource link will be created between activities that have resource dependency (Figure 11).

	====Step 5====		====Step 5: Alternative schedule====

	The schedule resulted after ''Step 4'' may be acceptable, but, due to the characteristics of the resource link, an activity that has successors by resource links may be delayed beyond its TF period without affecting the project completion time. Therefore, in this step, those activities will be checked to propose an alternative schedule.		The schedule resulted after ''Step 4'' may be acceptable, but, due to the characteristics of the resource link, an activity that has successors by resource links may be delayed beyond its TF period without affecting the project completion time. Therefore, in this step, those activities will be checked to propose an alternative schedule.

GiorgiaS: /* Step 3 */

2019-02-27T21:02:36Z

Step 3

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	::::::::::2 (B) + 8 (G) + 5 (K) = 15.		::::::::::2 (B) + 8 (G) + 5 (K) = 15.

	===Step 3===		===Step 3: Scheduling===

	The third step is about constructing a time chart that can display start and finish times for each activity and the associated floats. It may also show the relationships between activities, therefore presenting a possible project schedule. A schedule is possible in the sense that, if available resources are unlimited, the project could be completed at the scheduled time<ref name=FEES />.		The third step is about constructing a time chart that can display start and finish times for each activity and the associated floats. It may also show the relationships between activities, therefore presenting a possible project schedule. A schedule is possible in the sense that, if available resources are unlimited, the project could be completed at the scheduled time<ref name=FEES />.

GiorgiaS: /* Step 2 */

2019-02-27T21:02:06Z

Step 2

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	By applying these rules, the precedence-relationship diagram can be designed, and it will represent the master plan or working model of the entire project<ref name=martino> R.L. Martino, ''"Applying Critical Path Method to System Design and Installation".'' Control Engineering, Volume 10, Issue 2, pp. 93-98 (1963) </ref>.		By applying these rules, the precedence-relationship diagram can be designed, and it will represent the master plan or working model of the entire project<ref name=martino> R.L. Martino, ''"Applying Critical Path Method to System Design and Installation".'' Control Engineering, Volume 10, Issue 2, pp. 93-98 (1963) </ref>.

	===Step 2===		===Step 2: Time Estimation===
	[[File:times.jpg\|thumb\|200px\|Figure 5: ES, EF, LS and LF (''Inspired by <ref name=FEES />'')]]		[[File:times.jpg\|thumb\|200px\|Figure 5: ES, EF, LS and LF (''Inspired by <ref name=FEES />'')]]
	[[File:floats.jpg\|thumb\|200px\|Figure 6: Total float and Free float (''Inspired by <ref name=FEES />'')]]		[[File:floats.jpg\|thumb\|200px\|Figure 6: Total float and Free float (''Inspired by <ref name=FEES />'')]]

GiorgiaS: /* Step 1 */

2019-02-27T21:01:36Z

Step 1

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	# Actual scheduling, checking the dependencies among activities and taking into account both ''necessary'' resources and ''available'' resources;		# Actual scheduling, checking the dependencies among activities and taking into account both ''necessary'' resources and ''available'' resources;

	===Step 1===		===Step 1: The Network Diagram===

	[[File:dummy.jpg\|thumb\|400px\|Figure 3: Dummy activity example (''Inspired by <ref name=FEES />'')]]		[[File:dummy.jpg\|thumb\|400px\|Figure 3: Dummy activity example (''Inspired by <ref name=FEES />'')]]