A New Approach to Approximate Completion Time Distribution Function of Stochastic Pert Networks

The classical PERT approach uses the path with the largest expected duration as the critical path to estimate the probability of completing a network by a given deadline. However, in general, such a path is not the most critical path (MCP) and does not have the smallest estimate for the probability of completion time. The main idea of this paper is derived from the domination structure between paths that was presented by Soroush for the first time. This paper develops this domination structure and its properties, which make Soroush’s algorithm work faster in some cases. Then a labeling algorithm is presented that is able to compute the MCP from starting node of the network to any node of the network. Also, suitable and practical completion time distribution function estimation is defined. In many cases, the estimation is obtained by the developed method is better than that of Soroush’s. To clarify the point, some examples are given. Finally, conclusions are presented.