A Stochastic Flow Problem

If the demand/supply values at the nodes of a given graph are assumed to be random variables standard flow theory is no longer meaningful. A two stage stochastic programming approach can be used to yield an optimal “quasi”-flow Solution which minimizes “quasi”-flow costs and expected costs for compensating nonconformity with the actual realizations of the demand/supply. A special case of this formulation is shown to be the well-known stochastic transportation problem. An example is included for illustration.