39 Project Planning: Critical Path Method (CPM)

Vikas Singla

  • 39.1 OBJECTIVES

This chapter would help students to understand:

  • Importance of project planning
  • Rules of network construction
  • Importance of CPM in project planning
  • Application of CPM in estimating trade-off between time and cost of project

39.2 INTRODUCTION

Building of a house requires carrying out numerous activities sequentially as well as simultaneously. It is necessary to identify type of activities and resources required to carry out such activities. Some of such activities might be creating foundation, construction, wood work, electric work, interior designing etc. Each activity can be further broken down into number of activities. Thus, a project in this example construction of house involves combination of number of activities arranged in such a sequence so as to achieve completion of project in significant period of time. Definition of project involves following important aspects:

  • Identification of activities: which activities need to be performed for completion of project?
  • Sequence of activities: which activities are to be performed in what sequence and can some of them be performed simultaneously or can some of them be combined?
  • Resources required: each activity requires certain resources in terms of man, machine, material, time and effort. How many individuals are required to perform a particular activity? Can they be used for
  • performance of other activities? How much time does each activity take? What is the cost required to perform each activity?
  • Critical activities: which are the most important activities and what is the time required to complete those activities? Can these activities be delayed and if yes what would be the effect on project completion time? Which are non-critical activities or activities which can be delayed without delaying the project?

Thus, a project involves number of aspects and its successful completion requires a scientific and systematic approach. PERT and CPM are two of the such approaches which answers above mentioned questions. These two methods are network oriented techniques used primarily to determine project completion time. This chapter discusses CPM in detail with illustrations. CPM is used to find out critical and non-critical activities. The identification of such activities helps a manager to evaluate which activities can be delayed and which cannot with an effect on project completion time. Also, chapter discusses time-cost model of project which provides the effect of change in time of activity on total cost of completion of project.

 

39.3 PROJECT MANAGEMENT: IMPORTANCE

 

Project management primarily involves following three managerial functions:

·         Planning: involves identification and breaking down of activities into viable and feasible tasks that must be performed for completion of project. It also involves determination and allocation of resources to each activity. It requires estimation of number of man hours, amount of material required, cost that would be incurred etc. for each activity.

·        Scheduling: involves arranging activities in a logical sequence that would help in converting allocated resources to desired outputs in most productive manner.  It is important  to note that identified activities can be arranged in different ways to obtain certain outputs. But it is important to find out the most productive way of arranging activities. Such approach would also require identification of critical activities and estimation of available idle time for which activities can be delayed.

·        Control: function involves review of project progress. This function determines whether each activity is performed in estimated duration, uses allocated resources or is deviating from planned schedule. This function allows controlling any difference between planned and actual schedule. The reasons for such a difference are analyzed and remedial measures adopted.

PERT and CPM methods of project management helps management to achieve these functions effectively as these methods identifies and estimates time for performance of activities, arranges them in most efficient sequence and provides data regarding any deviation from planned schedule.

Application of these methods requires understanding of construction of network diagrams representing arrangement of project activities. This has been discussed in following section.

39.1 NETWORK CONSTRUCTION: SOME DEFINITIONS

Network is a web of identified activities showing their arrangement or sequence in a diagrammatic fashion. Construction of network diagram requires understanding of following terms:

Activity: An activity is a task that requires certain resource such as time, money and labor for its completion. In a network diagram it is represented by an arrow. An activity occurs over a period of time.

Event: An event indicates start or finish of an activity. It is represented by a circle called as node. An event does not consume any resource and it occurs at a point in time.

If in a network diagram an activity is represented by arrow and an event by node then such a diagram is called as activity on arrow (A-o-A) network diagram. Whereas if in a network diagram an activity is represented by a node and an event by an arrow then such a diagram is called as activity on node (A-o-N) network diagram.

Predecessor: An activity which has to be completed before the start of another activity is called as predecessor to start of new activity.

Successor: An  activity  which starts  after or succeeds the finish of another activity is called successor  or succeeding activity.

Concurrent activity: An activity which can be performed simultaneously with some other activity is called as concurrent or parallel activities.

These activities are illustrated in figure 39.3.1. This is an activity on arrow network diagram. A is preceding activity to C which is preceding to E. Similarly, B is preceding to D which is preceding to F. Activities can also be explained in successor terms. E activity will start after finish of C i.e. it succeeds C which succeed .Similarly, F succeeds D which succeeds B. Events are depicted by circles called as nodes. They indicate the start and finish of an activity. It is important to note that A and B start from same node at same time making them concurrent or parallel activities.

 

39.5 CRITICALPATHMETHOD (CPM)

CPM is a deterministic approach of network technique where duration of each activity involved in completion of project is known with certainty. Certain activity times would be known in cases of projects which are repetitive or are not new for an organization. For example an IT firm specializing in creating software for different banks would apply CPM for a new banking project. As company has already created software for other banks so creating software for new bank would involve similar tasks for which completion time is known with high certainty.

The purpose of CPM technique is to:

  • Find scheduled project completion time.
  • Scheduled start and finish times for each activity.
  • Identification of most important or critical activities which should be completed within scheduled time without delaying the project.
  • Identification of non-critical activities which can be delayed by specific time without delaying the completion of project from its scheduled time.

To achieve objectives of CPM certain terms have to be understood:

Earliest Start Time (EST) of an activity indicates the time at which an activity can start as soon as possible. Earliest  Finish  Time  (EFT)  of  an  activity  indicates  the  earliest  possible  time  at  which  an  activity  can  be completed. It is the sum of EST and duration of that activity.

Calculation of EST is governed by forward path rule. This rule states that for calculating EST we should move forward from first event to the last event in a network diagram. As an activity cannot start until all preceding activities have been completed so EST of an activity is equal to the largest EFT of immediate preceding activity. Latest Finish Time (LFT) of an activity indicates finish of an activity as late as possible without having an effect on scheduled finish of entire project.

Latest Start Time (LST) of an activity indicates start of an activity as late as possible without having an effect on scheduled finish of entire project. LST is the difference of LFT and duration of particular activity.

Calculation of LFT is governed by backward path rule. This rule states that for calculating LFT we should move backwards from last event to the first event in a network diagram. As purpose is to finish an activity as early as possible so LFT for an activity is the smallest of latest start time of immediate succeeding activities.

Slack is determined after finding out all earliest and latest times by moving forward and backward in a network diagram. Slack indicates idle time of an activity with which it can be delayed without increasing the project completion time. It can be computed as: LFT – EFT or LST – EST.

 

LFT is calculated by moving backwards from last event in the network diagram. E6 indicates finish of all the paths. Now E6 can be reached by moving along A—C—F, A—D—G and B—E—G. Total time for each of the path would be 19 days, 22 days and 20 days respectively. As project cannot be finished till all activities are completed so LFT of E6 would be 22 days. Moving backwards C finishes at E4. Its LFT would be 22-5 = 17 days and so on. Interestingly, finish of E2 can be achieved by moving backwards from F to C or from G to D. For F to C LFT would be 22-5-5 = 12 days and for G to D LFT would be 22-5-8 = 9 days. As an activity should be finished as early as possible so by moving backwards minimum LFT should be considered. So finish of E2 or LFT of activity A would be 9 days. All other times are calculated and shown in table.

 

Step 3: Calculation of slack:

Zero slack of an activity would indicate that such an activity cannot be delayed or it has to be completed within scheduled time. Such activities are most important activities in a project and constitute critical path. In this case A—D—G constitute critical path which would take 22 days. This would also be the project completion time i.e. project comprising of above mentioned activities would take minimum of 22 days. Activities with some slack are called as non-critical activities. For instance, activity B with a slack of two days implies that even if start of this activity is delayed by two days then also project would be completed in 22 days

 

 

39.6 CRASHING

The major application of CPM is to estimate the impact on total cost associated with project if project completion time is reduced. The knowledge of scheduled start and finish times of each activity, slack of each activity and identification of critical and non-critical activities obtained from application of CPM is used in estimating cost of project with change in project completion time. In network techniques of PERT and CPM the resource used with each activity is the duration of that activity. But performance of each activity also uses other resources such as labor, materials etc. which incur cost. Crashing method uses this information of cost associated with performance of each activity to achieve the objective of estimating project time. It is important to understand that with reduction in activity time more resources would be required for its completion thus, increasing its cost. That is why there would always be a trade-off between time and cost.

So, question that a project manager faces:

·         Which activities to be crashed i.e. duration time of which activities should be reduced so that project time gets reduced?

  • What is  the  increase  in  cost  of  project  completion  with  reduction  in  time  period  of  identified activities?
  • For how much time period an activity can be crashed?

Crashing should not be done indefinitely. A stage will come when further crashing of activities will not reduce total project completion time but it would increase cost significantly. As illustration discussed below would show that with decrease in time of an activity it increases direct cost such as cost of machinery, labor etc. and reduces indirect cost such as cost of lighting, rent, security etc. At first total cost would reduce with reduction in project time because proportion of increase in direct cost is less than decrease in indirect cost. But after certain reductions in time period proportion of increase in direct cost would outweigh reduction in indirect cost thus increasing total cost. This is an indication that further crashing would not result in optimal results. Thus objective of crashing gets defeated. So, a project manager should stop crashing when all the paths in network diagram become critical or total cost starts increasing.

Following are certain terms that must be understood in application of crashing:

  • Normal time: It is the expected time of completion of an activity.
  • Crash time: It is the reduced time of completion of an activity.
  • Normal cost: is the cost of performance of an activity when performed under normal conditions.

Crash cost: is the cost of performance of an activity when performed under reduced time.

  • Following are the steps to be used in crashing of a project:

Step 1: Draw network diagram

Step 2: Find cost slope of each activity. Cost slope is the increase in direct cost of an activity when its duration is reduced by one day. Cost slope = change in cost / change in time

Step 3: Find critical path. As discussed critical path is found by calculating EST, EFT, LST and LFT. By definition critical path is the longest path in the network diagram. In example shown under critical path is estimated by finding the longest path in diagram.

Step 4: In the critical path find an activity with least cost slope because aim is to reduce project time with least increase in cost.

Step 5: Estimate the time for which selected activity can be crashed. For this a general rule that is followed is that activity should be crashed for so much time that it does not result in change of critical path.

Step 6: Keep on repeating the process till further reduction in time period leads to increase in cost or when all paths in network diagram have become critical.

 

Example: For the following project estimate total project cost under normal times and crash times. Indirect cost is Rs.100 per day.

 

 

39.7 SUMMARY

Project is a combination of activities arranged in a sequence to achieve objective of completion of project. Planning of project becomes increasingly difficult if it involves numerous activities. Thus, need of managing project arises which involves arranging activities in a sequence which would help in completing the project most productively. Management of project can be done by using two time oriented network techniques namely PERT and CPM. These techniques are similar to each other in fulfilling objectives of finding project completion time and identifying critical and non-critical activities. They differentiate from each other in a manner that CPM is a deterministic approach used for projects which have been carried out earlier also. Whereas PERT is a probabilistic technique used for finding out probability of completion of project within scheduled time of those projects which are new and project manager has little experience for their conduct. Crashing is a time-cost trade-off technique used to find minimum possible time in which project can be completed with minimal impact on cost.

39.1 GLOSSARY

  • Project: is a non-repetitive combination of activities arranged in a logical sequence.
  • Critical Path Method (CPM): is a deterministic time oriented network technique used to determine critical and non-critical activities.
  • Forward pass: is a procedure that involved moving forward in network diagram for determining earliest start and finish times.
  • Backward pass: is a procedure that involved moving backwards in network diagram for determining latest start and finish times.
  • Crashing: is a method of shortening of activity times by adding resources leading to increase in costs.

39.1 REFERENCES/ SUGGESTED READINGS

  • Chase, B.R., Shankar, R., Jacobs, F.R. and Aquilano, N.J., Operations & Supply Chain Management, 12thEdition, McGraw Hill.
  • Stevenson, W.J., Operations Management, 9thEdition, Tata McGraw Hill.
  • Lee J. Krajewski, Operations Management, Prentice-Hall of India, New Delhi, 8th Edition.