This paper concentrates on a multicommodity stochastic-flow network in which each arc has both the capacity and cost attributes. We utilize this network to model the supply chain with several factories. Different from the single-commodity case, the system capacity is a pattern for multicommodity case. We propose a new performance index, the probability that the system capacity is less than or equal to a given pattern under the budget constraint. A simple algorithm based on minimal cuts is presented to generate all (d,B)-MCs that are the maximal capacity vectors meeting the demand d and budget B. The proposed performance index, which is evaluated in terms of (d,B)-MCs, is applied to evaluate the performance of a supply chain.