Using belief networks for PERT

Summary form only given. This paper describes a new method for explicit modeling of dependence between activity times in a project. This method improves on existing methods by taking into account (1) the probabilistic dependencies between duration and completion times of different activities, and (2) the different ways a project may be delayed. We take account of these complications by using advances in artificial intelligence and statistics, namely belief networks (BNs) and Gibbs sampling. We model dependence between completion and duration times using BNs, where a BN is a directed acyclic graph in which nodes represent variables, and arrows represent probabilistic dependencies which are quantified by conditional probability distributions. This allows us to extend the PERT network model to include not only duration times, but also other variables that affect duration and completion times. We call the resulting network PERT belief network (PBN). We describe iterative Monte Carlo algorithms (forward and conditional) to estimate the marginal density of the completion time of the project. We use forward Monte Carlo to solve PBNs without observations. We use a conditional Monte Carlo method known as Gibbs sampling to solve PBNs with observations. Gibbs sampling takes advantage of the factorization of the joint density to estimate posterior distributions for any subset of variables in a PBN, given observations. Thus we can estimate the mean completion time of the project and the probability of completing the project within a specified time. We illustrate our ideas using an example of a software development project