Critical Path Method (CPM) is a one of the tool used to identify the paths through the project and the other way is through PERT tool which is also called as program evaluation review technique. The critical path uses one time estimate when the duration of the task is solid, whereas PERT uses three time estimates and uses probabilistic activity times. The three time estimates for each activity are the most likely time (m), the optimistic time (a), and the pessimistic time (b) (Russell and Taylor, 2014). These three time estimates are used to estimate the mean and variance of a beta distribution, as follows:
We start with the calculation for the given problem using a block that is shown in the legend of the below diagram "Figure - Probabilistic activity time estimates for a CPM/PERT network". The block consists of an activity in the middle representing a task, down at the bottom represent ting duration of the task, top left representing early start and top right representing early finish, the bottom left representing late start and the bottom right representing late finish.
Earliest Start and Finish Times is defined as
Latest Start and Finish Times is defined as
The slack represent the difference between Late Finish minus Early Finish or Late Start minus Early Start. Activity Slack is defined as
The calculation of critical path needs an activity, a predecessor and the time needed for completing each task. We have the list of tasks, the dependency and completion time in days. We have constructed a precedence network diagram that gives the pictorial diagram the given network.
Figure - Probabilistic activity time estimates for a CPM/PERT network
Determining a Critical Path
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...nish and Early Finish or the difference between the Late Start and Early Start. Any task that has zero slack time becomes critical path task and cannot be reassigned.
Activities representing the critical path
As we can see from the above diagram the activities 1, 3, 7, 8, 10 and 12 do not have any slack time which indicates that these activities represent the critical path. The expected project completion time is the sum of the each critical path task duration in days.
= activity duration for 1 + activity duration for 3 +activity duration for 7 +
activity duration for 8 + activity duration for 10 + activity duration for 12
= 2 +5 +1 +3+ 3+1
= 15 days
The above calculated table shows each for Expected activity times, Earliest start and finish times, Latest start and finish times, Activity Slack and Expected Project completion duration which is 15 days.
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