# Project Evaluation and Review Technique (PERT)

CPM uses a fixed time estimate for each project activity. While easy to understand and use, it does not take account of the time variations that can impact on the completion time of a complex project. The *Program Evaluation and Review Technique* (PERT) is a network model that allows for variations in activity completion times. In a PERT network model, each activity is represented by a line (or *arc*), and each milestone (i.e. the completion of an activity) is represented by a *node*. A simple example is shown below.

A simple PERT network

Milestones are numbered so that the end node of an activity has a higher number than the start node. Incrementing the numbers by 10 allows for additional nodes to be inserted without modifying the numbering of the entire network. The activities are labelled alphabetically, and the expected time required for each activity is also indicated. The *critical path* is the pathway through the project network that takes the longest to complete, and will determine the overall time required to complete the project. Bear in mind that for a complex project with many activities and task dependencies, there can be more than one critical path through the network, and that the critical path can change.

PERT planning involves the following steps:

*Identify activities and milestones*- the tasks required to complete the project, and the events that mark the beginning and end of each activity, are listed in a table.*Determine the proper sequence of the activities*- this step may be combined with step 1, if the order in which activities must be performed is relatively easy to determine.*Construct a network diagram*- using the results of steps 1 and 2, a network diagram is drawn which shows activities as arrowed lines, and milestones as circles. Software packages are available that can automatically produce a network diagram from tabular information.*Estimate the time required for each activity*- any consistent unit of time can be used, although days and weeks are a common.*Determine the critical path*- the critical path is determined by adding the activity times for each sequence and determining the longest path in the project. If the activity time for activities in other paths is significantly extended, the critical path may change. The amount of time that a non-critical path activity can be extended without delaying the project is referred to as its slack time.*Update the PERT chart as the project progresses*- as the project progresses, estimated times can be replaced with actual times.

Because the critical path determines the completion date of the project, the project can be completed earlier by allocating additional resources to the activities on the critical path. PERT also identifies activities that have slack time, and which can therefore lend resources to critical path activities. One drawback of the model is that if there is little experience in performing an activity, the activity time estimate may simply be a guess. Another more serious problem is that, because another path may become the critical path if one or more of its associated activities are delayed, PERT often tends to underestimate the to time required to complete the project.

PERT incorporates uncertainty by making it possible to schedule a project while not knowing precise details and durations of all activities. The time shown for each project activity when creating the network diagram is the time that the task is *expected* to take based on a range of possibilities that can be defined as:

*The optimistic time*- the minimum time required to complete a task*The pessimistic time*- the maximum time required to complete a task*The most likely time*- an estimate of how long the task will actually take

The expected time (the time that will appear on the network diagram) is defined as the average time the task would require if it were repeated a number of times over a period of time, and can be calculated using the following formula:

expected time = (optimistic time + (4 x most likely time) + pessimistic time) / 6

The information included on the network diagram for each activity may include:

- the activity name
- the expected duration
- the earliest start (ES)
- the earliest finish (EF)
- the latest start (LS)
- the latest finish (LF)
- the slack

In order to determine these parameters, the project activities must have been identified and the expected duration of each calculated. The *earliest start* (ES) for any activity will depend on the maximum *earliest finish* (EF) of all predecessor activities (unless the activity is the first activity, in which case the ES is zero). The *earliest finish* for the activity is the *earliest start* plus the *expected duration*. The *latest start* (LS) for an activity will be equal to the maximum *earliest finish* of all predecessor activities. The *latest finish* (LF) is the *latest start* plus the *expected duration*. The *slack* in any activity is defined as the difference between the *earliest finish* and the *latest finish*, and represents the amount of time that a task could be delayed without causing a delay in subsequent tasks or the project completion date. Activities on the critical path by definition have zero slack.

A PERT chart provides a realistic estimate of the time required to complete a project, identifies the activities on the critical path, and makes dependencies (precedence relationships) visible. It can also identify the earliest and latest start and finish dates for a task, and any slack available. Resources can thus be diverted from non-critical activities to those that lie on the critical path should the need arise, in order to prevent project slippage. Variance in the project completion time can be calculated by summing the variances in the completion times of the activities in the critical path, allowing the probability of the project being completed by a certain date to be determined (this will depend on the number of activities in the critical path being great enough to allow a meaningful normal distribution to be derived).PERT charts can become unwieldy, however, if the number of tasks is too great. The accuracy of the task duration estimates will also depend on the experience and judgment of the individual or group that make them.