Evaluating the reliability of a stochastic distribution network in terms of minimal cuts

This paper presents a d-minimal cut based algorithm to evaluate the performance index Rd+1 of a distribution network, defined as the probability that a specified demand d + 1 can be successfully distributed through stochastic arc capacities from the source to the destination. To improve the efficiency of solving d-minimal cuts, a novel technique is developed to determine the minimal capacities of arcs. Also, two new judging criteria are proposed to detect duplicate d-minimal cuts. Both theoretical and computational results indicate that our algorithm outperforms the existing methods. Furthermore, a real case study is provided to illustrate the application of the algorithm.