Each arc (i,j) of the network has capacity ξij where ξij is a non-negative random variable. The capacity of any arc may be reduced or increased by an amount uij≥0 at a cost of cijuij. The objective is to maximize v-KΣcijuij where v is the expected maximum flow. This problem is formulated as a two-stage linear program under uncertainty. Each feasible nu=||nuij|| generates a constraint ¸-Σ;ij(nu)uij+θ•ρ(nu) where ;ij(nu) is the probability arc (i,j) is in the minimum cut set and ρ(nu) the expected value of the maximum flow under u=nu. The formulation is later generalized to include certain conditions under which the increase in capacity of an arc may be a non-deterministic function of the investment cijuij.
