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A New Lower Bound For Completion Time Distribution Function of Stochastic PERT Networks

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of duplicable arcs in this method differs from that of Dodin ʹs so that it must be considered a different method In this method, best duplicable arcs are adopted using a new mechanism. It is proved that duplicating numbers is minimized by this method The distribution function of this method Is a lower bound on exact network distribution function and an upper bound on distribution function of Dodinʹs and Kleindorferʹs methods. After the algorithm for the method is presented its efficiency is discussed and illustration examples will be used to Compare numerical results from this method with those from exact network distribution and Dodin ʹs method.