What is PERT?

The Program Evaluation Review Technique (PERT) was originally developed for the U.S. Navy`s Polaris submarine project. The primary purpose of PERT is to plan, schedule, and coordinate the sequential activities required in one time complex project. The PERT model develops a graphical depiction of the sequential activities required to complete a project. It then determines the total anticipated time needed for the project`s completion. PERT is considered a network method of project scheduling since activities are depicted as arrows while intermediate goals, or events, are depicted as circles. There are four steps necessary in developing a PERT network project schedule:

1. A comprehensive project analysis is performed.
2. All of the required project activities are categorized according to their order of precedence.
3. A PERT chart is drawn where all the activities preceding an event are shown using a lettered arrow and events are numbered using circles.
4. Time and/or cost estimates are assigned to each activity.


It is necessary for a manager to develop a PERT network using the following information listing activities and their respective predecessors.

Preceding Activity
B --

A PERT chart is drawn as in Figure 1.14, where all the activities are lettered using arrows and the events are numbered using circles.


Activities can also be designated by their beginning and ending events.
For example:

Beginning Event Ending Event Activity
1 2 1-2
2 3 2-3
2 4 2-4
3 4 3-4
4 5 4-5
4 6 4-6
5 7 5-7

What is the critical path method (CPM)?

The critical path method was originally developed to schedule the startup and shutdown of major production plants. It is based on developing three activity time estimates for calculating project completion time with variances. The three time estimates are an optimistic time (a), pessimistic time (b), and most likely time (m).

What are the optimistic, pessimistic, and most likely times?

1. Optimistic time (a). This is an estimate of the least, or minimum, time an activity will take to complete.
2. Pessimistic time (b). This is an estimate of the most, or maximum, time an activity will take to complete.
3. Most Likely time (m). This is an estimate of the average or normal amount of time an activity would take assuming it were to be repeated several times.

In arriving at an expected time (te) for a given project activity, a beta probability distribution is employed in PERT. The three time estimates are combined and averaged to calculate a time estimate. Normally, in PERT applications the most likely time (m) is given a weight of 4 while the optimistic time (a) and pessimistic time (b) are each given a weight of 1. The variance (v) for each activity is also calculated:

te = a + 4m + b / 6

v = b - a / 6

The expected times (te) and variance (v) are calculated for each activity after the network for the PERT analysis is completed.


There are five activities in a project. It is necessary to compute the expected times and variances for the project:

What is critical path analysis?

Critical path analysis consists of analyzing the sequence of activities from the beginning event to the ending event. The critical path is the longest path through a network. It is critical because any increase in time for an activity on this path will delay the entire project. Moreover, any decrease in time for an activity not on the critical path will not shorten the project. To calculate the critical path, data must be obtained on the earliest start and finish times, the latest start and finish times, and the available slack time:

1. ES-Earliest activity start time. The time when all preceding activities are finished; the earliest an activity can commence.

2. LS-Latest activity start time. The time when all successor activities have to be finished without delaying the entire project. The latest activity start time is calculated by subtracting the expected time of the activity (t) from the latest finish time (LF) and then subsequently subtracting (t) for the slowest (longest (t) path(s).

3. EF-Earliest activity finish time. The earliest activity finish time equals the earliest activity start time (ES) of the activity plus expected time (t) for the activity.

4. LF-Latest finish time. The time when the project must be finished. The latest activity finish time equals the latest start time (LS) plus the expected time (t) of the activity.

5. S-Slack time. An activity`s total slack is the difference between the latest and earliest activity start times (LS - ES) or the latest and earliest activity finish times (LF-EF). Slack is the free time associated with each activity. In other words, paths that are not critical have slack time. Slack represents unused resources that can be diverted to the critical path.

After calculating the preceding data for each activity, the overall project can be analyzed. This includes:

1. The critical path. The time it takes to finish all the project`s activities without any slack time.


Using the PERT chart in Figure 1.15, calculate ES and EF for each activity.


Now the earliest start (ES) and earliest activity finish times (EF) are determined. In order for an activity to begin, all of the preceding activities must be finished. EF is calculated by adding expected time (te) to ES for each activity.

Activity t ES EF
(t + ES)
1-2 3 0 3
1-3 6 0 6
1-4 5 0 5
2-5 4 3 7
3-5 5 6 11
4-5 2 5 7

The latest activity finish time (LF) of the project is 11 since the earliest activity finish time (EF) for activity 3-5 is 11.
In order to calculate a project`s critical path, it is necessary to determine the latest start time (LS) by subtracting the expected time (t) of the activity from the latest finish time (LF). It is also necessary to determine the slack time for each activity by subtracting the earliest activity start time (ES) from the latest activity start time (LS).


Using the above data, what is the project`s slack time and critical path?

The critical path is the activity with 0 slack time, or activity 3-5. The total completion time of the project is 11 since activity 3-5 is the longest path to completion. Figure 1.16 presents the critical path.


1. If the project duration (length of critical path) exceeds the allowable deadline, options include (1) changing the deadline or (2) "crashing" the project. Crashing means speeding up one or more activities along the critical path. This may involve shifting more resources (money) to those activities or perhaps outsourcing some of the work. The critical path method (CPM) model, also known as pert/cost, argues that most activities can be reduced in duration if extra resources (men, machines, money, and so on) are assigned to them. The cost for getting the job done may increase, but if other advantages outweigh this added cost, the job should be expedited or crashed. When making a cost/time trade-off, the first activity to be crashed (have its completion time accelerated) is one on the critical path. To select and activity on another path would not reduce the total time of completion. The activity chosen should be the one whose completion time can be accelerated at the lowest possible cost per unit of time saved.
2. The primary difference between PERT and CPM is that. CPM considers activity costs and PERT does not.

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