Computing the reliability of a stochastic distribution network subject to budget constraint

Abstract

Reliability and delivery cost are two crucial indicators to show whether a distribution network is in the stable and high-quality operation. This paper develops a (d, b)-minimal path ((d, b)-MP) based algorithm to compute the reliability R(d,b) of a stochastic distribution network as the probability that a prescribed demand d can be successfully delivered from the source to the destination subject to the constraint that the total delivery cost is not above b. Specifically, this paper focuses two aspects to facilitate the solution of (d, b)-MPs. Firstly, by transforming a large Diophantine system into several small Diophantine systems, a modified model is constructed to promote the efficiency of searching for (d, b)-MP candidates and narrow the scope of duplicate (d, b)-MPs. Secondly, a novel technique is devised to identify all duplicate (d, b)-MPs, and its efficiency advantage is theoretically proven. Finally, it is demonstrated through numerical experiments that the developed algorithm compares favorably with the existing ones in the literature, and a case study is provided to display the application of the algorithm.