Stochastic bounds on distributions of optimal value functions with applications to pert, network flows and reliability

Meilijson and Nadas [1979] have obtained stochastic bounds in the convex majorisation sense to the critical path length of a project network with random activity durations. In this paper we present those results in a more general framework and, using similar techniques, obtain bounds for shortest route, maximal flow and reliability system lifetime. Subject classification: #488 Bounds for stochastic networks #672 Convex majorisation of project critical path length. #725 Stochastic majorisation of reliability system lifetime. Consider a set I = {,..., n} of n nodes, the base set. Let Ii. ... , I be subsets whose union is I, and no two of which are ordered by k inclusion; (11 1 4 j 4 k is a clutter over I. The blocking clutter to 4 J [I} is a clutter J1 ,..., J zsuch that I r J pfor all r, s, and J are minimal sets with this property, cf. Edmonds and Fulkerson [1970]. In a directed acyclic graph or in a two terminal network, the paths and co qcuts are an example of a pair of blocking clutters. We call I a system,