PERT Charts

What is PERT?

Program Evaluation Review Technique Also known as the Critical Path Method PERT is a planning and control tool which can be used to define and control tasks necessary to complete a project. Can be graphically represented in a network diagram 

1. Identifying activities and milestones

Activities are the tasks of the project. Milestones are the events that mark the beginning or end of one or more of the activities.

Milestone 2445523 960 720 (binary/octet-stream)

2. Identify the sequence of activites

For some activities this may be obvious, and can be completed as part of step one. Other tasks may require some analysis to determine the appropriate order in which they should be performed

3. Construct a Network diagram

A visual representation of the sequence of successive and parallel activites Arrowed lines represent activites Circles or "bubbles" represent milestones

405px 5n Pert Graph With Critical Path.Svg (binary/octet-stream)

4. Estimate times for activites

This involves estimating three times for each activity: Optimistic time: How long it would take to complete the task in the best case scenario Pessimistic time: How long it would take to complete the task in the worst case scenario Most likely time: The highest probability time that the activity could take This times are used to calculate the expected time using the following equation: \[\text{ Expected time = } \frac{\text{(Optimistic time + (4 x Most likely time) + Pessimistic time)}}{6}\] Usually times are calculated in weeks, but other units can be used if it is more appropriate for the project in question.

5.1 Calculate start and finish times

The following times for each activity should be calculated: Earliest Start Time Earliest Finish Time Latest Start Time Latest Finish Time Earliest Start and Finish Times: Determined by working forward through the network and determining the earliest time at which an activity can start and finish considering its predecessor activities Latest Start and Finish Times: Latest times that an activity can start and finish without delaying the project. LS and LF are found by working backward through the network

5.2 Determine the Critical Path

The Critical Path is determined by adding the time for the activities in each sequence, in order to determine the longest path Slack time: The amount of time non-critical path activity can be delayed for without delaying the overall project The difference in the latest and earliest finish of each activity is that activity's slack. The critical path then is the path through the network in which none of the activities have slack.

The variance in each activity can be calculated by \(Variance = (\frac{Pessimistic - Optimistic}{6})^2\) 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 a 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.

5.3 Calculate Variance in Completion Time

6. Updating chart as project progresses

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.

Pert Chart Example (binary/octet-stream)

Caption: : Example of Network Diagram: The Critical Path is marked in red. Each activity is assign an expected time. measured in days.

Limitations of PERT

Project activities must be clearly defined, independent and stable in their relationships   Precedence relationships must be specified and networked together   Time estimates are subjective and open for manipulation by managers   There is a risk that too much emphasis might be placed on the critical path