Sensitivity Analysis of ARC Criticalities in Stochastic Activity Networks

Abstract

Using Monte Carlo simulation, this paper proposes a new algorithm for estimating the arc criticalities of stochastic activity networks. The algorithm is based on the following result: given the length of all arcs in a network except for the one arc of interest, which is on the critical path (longest path) if and only if its length is greater than a threshold. Therefore, the new algorithm is named Threshold Arc Criticality (TAC). By applying Infinitesimal Perturbation Analysis (IPA) to TAC, an unbiased estimator of the stochastic derivative of the arc criticalities with respect to parameters of arc length distributions can be derived. With a valid estimator of stochastic derivative of arc criticalities, sensitivity analysis of arc criticalities is carried out via simulation of a small test network.