Sensitivity analysis with regard to capacity expansion in network flow simulation

In the design of flow networks it is desirable to assess the incremental gain in network flow permitted by increasing the flow capacities of one or more components of the system. Probing this question for a stochastic flow network encounters many problems not present in the deterministic case. The authors provide a Monte Carlo sampling plan for investigating this issue. This plan allows one to conduct a sensitivity analysis for a variable upper bound on the flow capacity of a specified arc where the individual arc flow capacities are all random. The plan permits estimation of the probabilities of a feasible flow for many values of the upper bound on the arc capacity from a single data set generated by the Monte Carlo method at a single value of the upper bound. Also, the resulting estimators have considerably smaller variances than crude Monte Carlo sampling would produce in the same setting. The success of the technique follows from the use of lower and upper bounds on each probability of interest where the bounds are generated from an established method of decomposing the capacity state space