The algorithm presented here makes exact computations of characteristics of the probability distribution of project duration for a stochastic project network. Given discrete independent probability distributions for task durations, the algorithm will compute either moments of the project duration distribution or values of the cumulative distribution function of project duration. The algorithm can be used for sensitivity analysis on probability weights since several task duration distributions having the same range can be handled simultaneously with no great increase in computation time requirements.
1. Introduction
This section introduces the problem under consideration and establishes notation and terminology. A general background in project scheduling can be obtained from Elmaghraby [ 6 ] . Graph theoretic terms used here are consistent with Even [7], except that we use the term arc instead of edge.
We will consider a project as represented by an activity-on-arc network. Figure 1 represents a project in which tasks have deterministic durations. Each arc of the network corresponds to a task. All tasks directed into a vertex must be completed before any task directed out of it may be started. The vertices in Figure 1 have been labeled with a precedence numbering, so that if there is an arc from i to j , then i < j .