Study on the multicommodity reliability of a capacitated-flow network

Traditionally, many researchers solved the multicommodity maximum Row problem by assuming that the area of the flow network are deterministic. When the arcs: are stochastic (i.e., the capacity of each are has several values), this article studies how to calculate the probability that a capacitated-Row network with a unique source node satisfies a demand (d(1), d(2),..., d(P)) at the unique sink node, where d(k) is the demand of commodity k. Such a probability is named the multicommodity reliability and is dependent on capacities of nrcs. One solution procedure is proposed to evaluate the multicommodity reliability, which includes two parts: an algorithm to generate all (d(1), d(2),...,d(p))-MPs and a method to calculate the multicommodity reliability in terms of (d(1), d(2),..., d(P))-MPs. Two illustrative examples are given. (C) 2001 Elsevier Science Ltd. All rights reserved.