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Critical Path Method
The Critical Path Method (CPM) is one of the Activity-On-Arrow (AOA) project management network procedures applied in project management to establish the sequence of the longest path and shortest duration for project finish.
The Principles of Critical Path Method
The principles of the Critical Path Method (CPM) are described below.
Activity
An activity in a project schedule is defined as a unique task with a start date, finish date, and duration. A project is split into activities at the lowest Work Breakdown Structure (WBS) level. The activities consume duration and resources within a project. In the CPM network diagram, a project’s activities are shown by arrows pointing in the progressing direction.
Dependency
Dependency is the affiliation between activities that are linked with each other with predecessors and successors. The start or finish of an activity depends on the progress of the predecessor activity.
Sequence
The sequence is the logical arrangement of the planned performance of activities. The sequence of activities is illustrated by arrows in a CPM network diagram.
Activity Duration
Activity duration is the time needed to complete an activity. This can be estimated using data from the completed projects that are of similar type, PERT, or other techniques.
Critical Path
The critical path is the longest in a project schedule. The activities in the critical path are termed critical activities. If there is any delay in critical activities, it will adversely impact the project finish date.
Total Float/ Total Slack
Total float/ total slack is the time by which an activity can be delayed without delaying the successor activity and the project finish date. The critical activities in the longest path have zero total float/ total slack and any delay in these activities will delay the project’s completion. The non-critical activities in the CPM network have a total float/ total slack of more than 0 days. The positive total float available for the non-critical activities provides flexibility and with any delay less than the available total float will not delay the project completion.
Methodologies of Critical Path Method
The methodologies for Critical Path Method (CPM), Network Diagram critical path, and computation of total float/ slack for the activities are explained below.
Network Diagram
A Network Diagram in CPM is a graphical representation of tasks, dependencies, and the order for the occurrence of planned tasks in a project schedule. CPM scheduling consultants often rely on these diagrams to illustrate the sequence and dependencies of activities in a project. The activities and the order of occurrence are illustrated using arrows in the network diagram. The start and finish of each event/node are joined as per the logic by an arrow. In addition, dummy activities are introduced to maintain the logic of the sequence of activities.
For instance, we will consider a simple CPM network for easy understanding, as shown in Figure 1 below. The network consists of 6 activities named: A, B, C, D, E, and F. The duration of the previously mentioned activities is 2, 3, 2, 1, 3, and 2 days, respectively.
Figure 1: CPM Network Diagram
Logic of the CPM network
The logic of the CPM network illustrated above is as follows.
- Activity A, B, and C are independent activities and start at the same time.
- Activity D starts after activities A, and B are finished.
- Activity E starts after activities C and D are finished.
- Activity F starts Activity after activity C is finished.
- Activities E and F are to be completed before the project finishes.
The points to be noted in the above-mentioned CPM network diagram are as follows.
- Activities A and B are concurrent as shown in the network diagram.
- The dummy activities are shown as dotted lines in the above CPM network.
- The dummy activity G is used to provide a logical relationship between Activity B and D. (Activity B is to be completed before the start of Activity D)
- The dummy activity H is introduced to illustrate the logical relationship between Activities C and E.
Longest Path
The longest path of the above CPM network and total project duration shall be determined as follows. There are 4 possible paths based on the logical sequence of the above CPM network which are tabulated below.
| Sl. No | Activity path | Calculated duration | Remarks |
| 1 | A, D, E | 2 days + 1 days + 3 days = 6 days | |
| 2 | B, D, E | 3 days + 1 day + 3 days = 7 days | Longest Path |
| 3 | C, E | 2 days + 3 days = 5 days | |
| 4 | C, F | 2 days + 2 days = 4 days |
Table 1: Calculation of the longest path
The longest path of the network runs through activities B, D, and E and the total project duration is 7 days. The critical activities in the network are Activity B, D, and E which are in the longest path of the network.
Calculation of Total Float/ Total Slack
The total float/total slack for the activities in the above CPM network shall be calculated as follows.
| Activity | Total float/ Total slack | Remarks |
| A | 1 day | (Duration of B- Duration of A). Non-critical activity |
| B | 0 day | Critical activity |
| C | 2 days | (Duration of B + Duration of D)- Duration of C, non-critical activity |
| D | 0 days | Critical activity |
| E | 0 days | Critical activity |
| F | 3 days | (Duration of the longest path)- (Duration of C+ Duration of F), Non-critical activity |
Table 2: Calculation of total float/total slack
Summary
The critical path method is useful for developing a realistic project schedule with a logical sequence of activities. Critical and non-critical activities shall be observed using this technique which will be helpful for effective resource management, and time management, and to ensure the project is completed on time and within the budget.
