## Using PERT to evaluate the effects of uncertainty

PERT was developed to take account of the uncertainty surrounding estimates of task durations. It was developed in an environment of expensive, high-risk and

PERT (program evaluation and review technique) was published in the same year as CPM. Developed for the Fleet Ballistic Missiles Program it is said to have saved considerable time in development ol the Polaris missile.

state-of-the-art projects - not that dissimilar to many of today's large software projects.

The method is very similar to the CPM technique (indeed many practitioners use the terms PERT and CPM interchangeably) but. instead of using a single estimate for the duration of each task. PERT requires three estimates.

• Most likely time - the time we would expect the task to take under normal circumstances. We shall denote this by the letter m.

• Optimistic time - the shortest time in which we could expect to complete the activity, barring outright miracles. We shall use the letter a to denote this.

• Pessimistic time - the worst possible time allowing for all reasonable eventualities but excluding 'acts of (iod and warfare' (as they say in most insurance exclusion clauses). We shall denote this by b.

PERT then combines these three estimates to form a single expected duration. tt, using the formula t, =

Exercise 7.4 Table 7.3 provides additional activity duration estimates for the network shown in

Figure 6.17. There are new estimates for a and b and the original activity duration estimates have been used as the most likely times, m. Calculate the expected duration. for each activity.

### Using expected durations

The expected durations are used to carry out a forward pass through a network; using the same method as the CPM technique. In this case, however, the calculated event dates are not the earliest possible dates but arc the dates by w hich we expect to achieve those events.

Exercise 7.5 Before reading further, use your calculated expected activ ity durations to carry out a forward pass through the network (Figure 6.17) and verify that the project duration is 13.5 weeks.

What does an expected duration of 13.5 weeks mean in terms of the completion date for the project?

The PERT network illustrated in Figure 7.3 indicates that we expect the project to take 13.5 weeks - unlike CPM. this does not indicate the earliest date by w hich we could complete the project but the expected (or most likely) dale. An adv antage of this approach is that it places an emphasis on the uncertainty of the real world.

Table 7.3 PERT activity time estimates

Activity durations (weeks) Activity Optimistic (a) Most likely (m) Pessimistic (b)

 A 5 6 8 B 3 4 5 C 2 3 3 D 3.5 4 5 E 1 3 4 F 8 10 15 (» 2 3 4 II 2 2 2.5

Rather than being tempted to say 'the completion date lor the project is we are lead to say 'we expect to complete the project by

It also focuses attention on the uncertainty of the estimation of activity durations. Requesting three estimates for each activity emphasizes the fact that we are not certain w hat w ill happen - we are forced to take into account the fact that estimates are approximate.

Figure 7 J The PERT network after the forward pass.

Event Target number date

### Expected Standard date

The PERT event labelling convention adopted here indicates event number and its target date along with the calculated values tor expected time and standard deviation.

deviation.

Figure 7 J The PERT network after the forward pass.

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