A new, stochastic programming model of PERT

In this paper we give a new, stochastic programming based solution method to the PERT model. The main drawback of the conventional solution techniques is that the activities of the project are supposed to be started promptly when all predecessor activities are finished at a random time point. However in many applications this can not be guaranteed. In our new stochastic programming method there are provided deterministic starting times in advance to all of the activities and these starting times (and so the finishing time of the whole project) are guaranteed to be kept with prescribed reliability. A further advantage of the new approach is that it makes possible to model the random activity duration times with Dirichlet distribution. The one dimensional marginals of the Dirichlet distribution are known to be beta distributed so the Dirichlet distribution may become as popular in PERT modelling as beta distribution is. The results of the two solution methods are compared on numerical test problems.