## Probabilistic network planning PERT

PERT allows three estimates for the duration of an activity to be provided: a most pessimistic estimate (p), a most likely estimate (m) and a most optimistic estimate (o). When using PERT, it is usually assumed that activity times follow the beta probability distribution (Fig. 3.8).

Probability of 1 in 100 of < o occurring

Most Optimistic Time (o)

Most Likely Time (m)

Probability of 1 in 100 of > p occurring

Probability of 1 in 100 of < o occurring

Probability of 1 in 100 of > p occurring

Activity Time

Most Optimistic Time (o)

Most Likely Time (m)

Most Pessimistic Time (p)

Figure 3.8 Beta probability distribution with three estimates

Most Pessimistic Time (p)

Activity Time

Figure 3.8 Beta probability distribution with three estimates

With two more assumptions — total project completion times follow a normal distribution and activity times are stochastically independent — answers can then be given to questions regarding the probability of finishing the project on time. For more detailed information on CPM and PERT, reference is made to Render et al. (2003) Chapter 7 and Hargitay and Yu (1993) Chapter 8.

The probabilistic approach of PERT constitutes an improvement compared to the deterministic CPM approach, but it brings along a fundamental shortcoming: it only provides information on activities on the Critical Path that was established using the expected mean times (m) of the activities the project is composed of. It may very well be, that the Critical Path for achieving, say, a 90% probability of completion before the end date of that path, is different from the one calculated with the estimated means of the activities.

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