Using influence diagrams for PERT

Summary form only given. We describe a new method for explicit modeling of decisions that bear on activity times in a project. This method extends the PERT belief network (PBN) model to include decisions variables. The resulting network is called PERT Influence Diagram (PID). A PID is a PBN that includes decision variables, where arrows into decision nodes mean that the decision maker knows the value at each of the decision node´s predecessors. A PBN uses belief networks (BNs) to model dependence between completion and duration times, where a BN is a directed acyclic graph in which nodes represent variables, and arrows represent probabilistic dependencies which are quantified by conditional distributions. A PBN extends the traditional PERT network model to include not only duration times, but also other chance variables that affect duration and completion times. We assume that the product of all marginal and conditional distributions specifies the joint density of all variables in a PID. We use a combination of stochastic dynamic programming and Gibbs sampling, an iterative Monte Carlo method, to solve PIDs. We solve PIDs by determining the decision strategy that minimizes the expected completion time of the project. We also compute, for every strategy, the mean completion time of the project and the probability of completing the project within a specified time. We illustrate our ideas with an example of a software development project. In summary, PIDs enhance managerial decision making by allowing project managers to explicitly model decision and chance variables that bear on activity times in a project