# Program Evaluation and Review Technique (PERT)

In the critical path method of scheduling projects, the duration of each activity is usually defined with a reasonable degree of certainty.   For some projects, it may be difficult to estimate a reasonable single duration for one more of the activities in the project schedule. The Program Evaluation and Review Technique or PERT method of project scheduling, uses three durations for each activity and the fundamental statistics to determine the probability of a project finishing earlier or later than expected.   Although the PERT method is not used extensively in engineering and construction projects, it provides valuable information for assessing the risks of a schedule slippage in a project.

Program Evaluation and Review Technique (PERT)  was first developed in 1958 by the U.S. Navy Special Projects Office on the Polaris missile system. Existing integrated planning on such a large scale was deemed inadequate, so the Navy pulled in the Lockheed Aircraft Corporation and the management consulting firm of Booz, Allen, and Hamilton. Traditional techniques such as line of balance, Gantt charts, and other systems were eliminated, and PERT evolved as a means to deal with the varied time periods it takes to finish the critical activities of an overall project. The Program Evaluation and Review Technique (PERT)  method uses an arrow network diagram to show the logical sequence of activities in a project, whereas the CPM uses a precedence diagram. In a PERT diagram, activities are represented by an arrow with circles at each end of the arrow.   The circles are called events that represent an instant in time.   The circle at the beginning of the activity represents the start of an activity, and the circle at the end of the arrow represents the finish of the activity.   The major difference between the PER method and CPM is the estimation of durations of activities.

Program Evaluation and Review Technique (PERT)  is applicable for projects where there is a high degree of uncertainty.   In PERT, three durations are assigned to each activity: a = optimistic time, b = pessimistic time, m = most likely time.   The optimistic time is the shortest possible time in which the activity could possibly completed, assuming that everything goes well. The pessimistic time is the longest time the activity could ever require, assuming that everything goes poorly. The most likely time is the time the activity could be accomplished if it could be repeated many times under exactly the same conditions.   a & b may not be symmetrical about m.

## Program Evaluation and Review Technique (PERT) Methodology

Program Evaluation and Review Technique (PERT) technique involves the following steps that are described below

1. Identify the specific activities and milestones. The activities are the tasks required to complete a project. The milestones are the events marking the beginning and the end of one or more activities. It is helpful to list the tasks in a table that in later steps can be expanded to include information on sequence and duration.

2. Determine the proper sequence of the activities. This step may be combined with the activity identification step since the activity sequence is evident for some tasks. Other tasks may require more analysis to determine the exact order in which they must be performed.

3. Construct a network diagram. Using the activity sequence information, a network diagram can be drawn showing the sequence of the serial and parallel activities. Each activity represents a node in the network, and the arrows represent the relation between activities. Software packages simplify this step by automatically converting tabular activity information into a network diagram.

4. Estimate the time required for each activity. Weeks are a commonly used unit of time for activity completion, but any consistent unit of time can be used. A distinguishing feature of PERT is its ability to deal with uncertainty in activity completion time. For each activity, the model usually includes three time estimates.  Three durations are assigned to each activity: a = optimistic time, b = pessimistic time, m = most likely time. PERT assumes a beta probability distribution for the time estimates. For a beta distribution, the expected time for each activity can be approximated using the following weighted average:    te  = (a + 4 m + b)/6, where  te is the  Expected time. This expected time may be displayed on the network diagram. To calculate the variance for each activity completion time, if three standard deviation times were selected for the optimistic and pessimistic times, then there are six standard deviations between them.  Variance is given by Î½ = Ïƒ2  = {(b — a)/6}2:   ÏƒTE  =   [Î½1-2 +  Î½2-3 +  Î½3-4 +  Î½4-5 +   ……  Î½i-j]0.5  , where ÏƒTE    is the standard deviation of the expected time,  Z = (Ts  – TE)/ ÏƒTE ;   The term TE  is the expected time of the event, which is calculated from the PERT diagram and TS  is the scheduled time.

5. Determine the critical path. The critical path is determined by adding the times for the activities in each sequence and determining the longest path in the project. The critical path determines the total calendar time required for the project. If activities outside the critical path speed up oe slow down (within limits), the total project time does not change. The amount of time that a non — critical path activity can be delayed without the project is referred to as a slack time. The variance in the project completion time can be calculated by summing the variances in the completion times of the activities in the critical path. Given this variance, one can calculate the probability that the project will be completed by the certain date assuming a normal probability distribution for the critical path. The normal distribution assumption holds if the number of activities in the path is large enough for the central limit theorem to be applied. Since the critical path determines the completion date of the project, the  project can be accelerated by adding the resources required to decrease the time for the activities in the critical path. Such a shortening of the project sometimes is referred to as project crashing.

6. Update the PERT chart as the project progresses. Make adjustments in the PERT chart as the project progresses. As the project unfolds, the estimated times can be replaced with actual times. In cases where there are delays, additional resources may be needed to stay on schedule and the PERT chart may be modified to reflect the new situation.

## Program Evaluation and Review Technique (PERT)  Terminology

• Activity – Activity or task to be accomplished as part of the total work to be done. Activities consume resources and/or time. They can be identified with starting and ending points. The network activities are represented by arrows and can be referred to by their endpoints and/or a letter assigned to the arrow.
• Event – An event is a point in time, a milestone in the total work to be accomplished. It marks the beginning and end of an activity. Events do not consume resources or time. Events are numbered with those at the tail of the activity having lower numbers than the events at the head of each activity arrow (left to right). Events are represented by circles (nodes).
• Precedence Relationships – Some activities can not begin until others have been completed. For example, a contractor cannot lay cement blocks until the foundation has been poured and cured. The foundation cannot be poured until the soil has been excavated and forms have been built. Precedence relationships must be defined in order to determine the sequence of activities in the network.
• Network – The set of all project activities graphically interrelated through precedence relationships. Networks should begin with one node and end with one node.
• Earliest Start Time(ES) – The earliest time an activity can start, assuming all preceding activities start as early as possible.
• Earliest Finish Time (EF) – The earliest time an activity can finish. EF = ES + t
• Latest Start Time(LS) – The latest time an activity can start and not delay the project. LS = LF – t
• Latest Finish Time (LF) – The latest time an activity can finish and not delay the project.
• Slack – The amount of play in the system. The slack associated with any path is simply the difference between the time required for the critical path and the time required for the given path. The amount of slack associated with each activity indicates the length of time an activity can be delayed without affecting the completion date for the entire project. The amount of slack for each activity is computed as follows: Slack = LS – ES or LF – EF
• Path  – A sequence of activities that leads from the starting node to the finishing node.
• Critical Path – The longest path through the network. The critical path is the minimum time for expected completion of the entire project. The amount of slack associated with the critical path is zero. Each of the activities on the critical path has zero slack. A network can have more than one critical path.
• Dummy – Dummy activities are not real activities and thus will not actually be performed during the project. A dummy activity has a time of zero. They are used primarily to maintain the precedence relationships required in the network.
• Crashing – Crashing involves reducing the overall time required to complete the project. This involves trading off costs of additional resources against the value of time saved to complete the project. Crashing is used with activities on the critical  path.

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