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.
• 

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
• 

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.

5.3 Calculate Variance in Completion Time

• 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.

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.

Folie 10

• 
• Bildunterschrift: 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