Computing bounds on project duration distributions for stochastic PERT networks

We consider the PERT model with activities whose durations are random variables with known discrete independent distributions. We develop an algorithm to compute lower and upper bounds for the distribution function of the project duration of the stochastic PERT network. The algorithm is based on conditioning on the longest distances to nodes in the network. In addition, we develop an extension of the Kleindorfer's upper bound. We evaluate the method developed in this paper with some numerical examples.