Control Of Operations - Network Models - (pert, Cpm)
Program Evaluation and Review Technique (PERT) and the Critical Path Method (CPM) are two popular quantitative analysis techniques that help managers plan, schedule, monitor, and control large and complex projects.
After the Special Projects Office of the U.S. Navy introduced it on the Polaris missile project in 1958, PERT was widely credited with helping to reduce by two years the time for the completion of the missile's engineering and development programs.
Around the same time, Du Pont, with the help of Remington-Rand, created a similar network planning approach called the Critical Path Method (CPM). The result of their effort was a network model termed the critical path method.
There are six steps common to both PERT and CPM. The procedure is as follows:
- Define the project and all of its significant activities or tasks.
- Develop the relationships among the activities. Decide which activities must precede and follow others.
- Draw the network connecting all of the activities.
- Assign time and/or cost estimates to each activity.
- Compute the longest time path through the network; this is called the critical path.
- Use the network to help plan, schedule, monitor, and control the project.
Finding the critical path is a major part of controlling a project.
Although PERT and CPM are similar in their basic approach, they do differ in the way activity times are estimated. PERT is a probabilistic technique: it allows us to find the probability the entire project will be completed by any given data. CPM is called a deterministic approach. It uses two time estimates, the normal time (the time we estimates it will take under normal conditions to complete the activity) and the crash time (the shortest time it would take to finish an activity if additional funds and resources were allocated to the task) for each activity. Because of their similarity, only PERT will be discussed in detail.
PERT networks are developed around two key concepts: activities and events. An activity represents a task or subproject that uses time or resources. It is represented by an arrow. An event is an indication of the beginning and /or ending of activities in the network. It is denoted by a circle, which contains a number that helps identify its location.
In constructing a PERT network, manager must first develop a list of the major activities that are involved in the project and then determine which activities must precede others. The next step is constructing a network diagram, a graphic depiction of the interrelationship among activities.
Developing the diagram may also include providing initial time estimates for the duration of each activity. Providing activity time estimates is not always an easy task. For this reason, the developers of PERT employed a probability distribution based on three time estimates for each activity: optimistic time (a), most likely time (m), and pessimistic time (b).
A PERT network of eight events is depicted in Figure 7-1. The expected or average time for each activity is then calculated using the following formula:
To compute the dispersion and variance of this expected time estimate, we use the formula:
Computers software is increasingly being used to facilitate tasks. There are several good commercial software packages available that perform PERT analysis (e.g., Harvard Total Project Manager - HTPM).
PERT is especially useful for planning and controlling large projects, particularly if there are uncertainties about activity durations and/ or trade-offs between resource usage and projects completion times.