The Stochastic Shortest Route Problem

The problem addressed in this paper is the selection of the shortest path through a directed, acyclic network where the arc lengths are independent random variables. This problem has received little attention although the deterministic version of the problem has been studied extensively. The concept of a path optimality index is introduced as a performance measure for selecting a path of a stochastic network. A path optimality index is defined as the probability a given path is shorter than all other network paths. This paper presents an analytic derivation of path optimality indices for directed, acyclic networks. A new network concept, Uniformly Directed Cutsets (UDCs), is introduced. UDCs are shown to be important to the efficient implementation of the prescribed analytic procedure. There are strong indications that stochastic shortest route analysis has numerous applications in operations research and management science. Potential application areas include, equipment replacement analysis, reliability ...