Handling uncertainty in PERT and the critical path method

The program evaluation and review technique abbreviated as PERT is a valuable project management tool for determining various parameters related to project management, such as slack in the project, the critical path to execute the project, etc. PERT problem proceeds by determining Earliest Start Time, Earliest End Time, Latest Start Time, Latest End Time, etc., and plotting the dependencies between activities, etc.

Here very rarely can the predecessor relationship between activities be determined. Nor can you determine the pessimistic, optimistic, or most likely time to complete an activity. More on the formula for expected time to completion (or + 4m + p) / 6 involves discrete values, and will likely yield better estimates if a continuous distribution of the time required to complete the task is used. Or in other words, if you use a probability distribution of the expected completion time that would say that there is a 10 percent chance that the activity will be completed within 10 days, there is a 90 percent change that the activity it will be completed within 30 days. days, etc., will produce a solution with improved accuracy.

The discrete event simulation can be applied to the PERT network where the duration of the activities varies over some probability distribution and different initial PERT networks can be generated. Similarly, it is very difficult to accurately map predecessor dependencies between activities on a network. If one has a stochastic dependency matrix in which there is a possibility that A needs to precede B or that B may occur by itself or if there is a possibility that B itself occurs or not, etc., in such cases also if all initial If a network is simulated, one would find a large number of small initial networks and not just one.

Now the question arises which one to choose and solve. Which one will best fit among all these streams of network activities. Only one of the network of activities that has the highest percentage of occurrence in the output of the simulation model could be solved or all the initial simulated PERT networks could be solved.

Also, large PERT networks with a large number of activities can be divided into small networks, and each network can be solved as a subproblem. Subproblems or subnets can be assembled to provide the solution to a very large PERT network that has many activities. Sometimes when the number of activities is large, it can be difficult to draw all of these activities on a graph. In such cases, you can formulate subproblems and draw and link the corresponding diagrams.