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## Handling Uncertainty in PERT and Critical Path Method

Program Evaluation and Review Technique abbreviated as PERT is a valuable project management tool for determining several project management related parameters such as slack in the project, critical path to execute the project etc., The solution to the PERT problem proceeds by determining Earliest Start time, Earliest Finish time, Latest Start time, Latest Finish time etc., and plotting dependencies amongst activities etc.,

Here very seldom can one determine predecessor relationship between activities. Neither can one determine pessimistic, optimistic or most likely time to complete an activity. More over the formula for expected time for completion (o+4m+p)/6 involves discrete values, and will probably yield better estimates if a continuous distribution of time taken to complete the task is used. Or in other words if a probability distribution of expected time of completion is used which would say that there is a 10 percent chance that the activity will be completed within 10 days’ time, there is 90 percent change that the activity will be completed within 30 days’ time etc., will yield a solution with improved accuracy.

Discrete event simulation can be applied to the PERT network where the duration of activities range over some probability distribution and different initial PERT networks can be generated. Similarly it is very difficult to accurately chart out predecessor dependencies between activities of a network. If one has a stochastic dependency matrix in which there is a chance that A needs to precede B or B can occur by itself or if there is a chance that B itself may occur or not etc., In such cases as well if the entire initial network is simulated then one would encounter a large number of small initial networks and not just one.

Now the question arises as to which one to choose and solve. Which will be best fit amongst all these network flows of activities. One could just solve only one of the network of activities which has the highest percentage of occurrence in the output of the simulation model or one can solve all the PERT simulated initial networks.

Also large PERT networks with large number of activities can be broken down into small networks and each network can be solved as a sub problem. The sub problems or sub networks can be assembled to yield the solution to a very large PERT network which has a lot of activities. Sometimes when the number of activities is large it may be difficult to draw all these activities in one chart. In such cases sub problems can be formulated and corresponding diagrams can be plotted and linked.

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