A new structural mechanism for reducibility of stochastic PERT networks

Abstract

In recent years, many techniques were developed to compute completion time distribution function of stochastic PERT networks. None of the existing techniques clearly consider the subject from structural viewpoint. In this paper a structural mechanism based on graph theory is presented. This mechanism changes structure of network to series–parallel network with contraction of some arcs. In contraction operation one arc is removed and its two nodes are changed to individual node. In this operation probably dependency between activities and number of existing paths in the network would be different from the original network. An algorithm is presented in correspondence with the developed structural mechanism. Through this algorithm, the mechanism acts as an effective approach to estimate F( t). The paper contains a comparative analysis. This comparison is made between the computational results of developed algorithm and those of Dodin’s and Kleindorfer’s approaches. The comparative analysis demonstrates that the mechanism has capability to be used for the networks with actual sizes. Also to show that the method works for practical problems in the real world, a real case from a car factory of Iran is considered. Again, for this case of the developed method, Dodin’s and Kleindorfer’s approaches are applied whose results approve the acceptability of proposed method completely.