(A) stochastic shortest path problem with arc failure

Abstract

This thesis deals with the problem of finding an optimal shortest path in a stochastic path network where each arc weight is a random variable and some arcs are fixed at positive failure probabilites. In order to consider the risk attitude of a decision maker, a quadratic utility function is introduced. The problem is handled in a subpath comparison rule approach based on some dominant properties such that we may not have to enumerate all paths. Then an algorithm is exploited and illustrated with a numerical example. A stochastic shortest path problem is also considered without arc failures and shown that it can be solved by a linear programming approach.