Some insights regarding selecting sets of scenarios in combinatorial stochastic problems

Stochastic combinatorial problems are inherently difficult to solve. In this paper the authors explore the use of a relatively small subset of all the possible random scenarios, thus drastically reducing the size of such problems. Two different methods of selecting the sample scenarios are investigated. Encouraging results are found for two variations of multi-item newsvendor problems used for testing purposes. In particular, the cost penalties associated with using one of the sampling methods are very small even with a low number of scenarios.