Fast Scenario Reduction by Conditional Scenarios in Two-Stage Stochastic MILP Problems

Abstract

A common approach to model stochastic programming problems is based on scenarios. An option to manage the difficulty of these problems corresponds to reduce the original set of scenarios. In this paper we study a new fast scenario reduction method based on Conditional Scenarios (CS). We analyse the degree of similarity between the original large set of scenarios and the small set of conditional scenarios in terms of the first two moments. In our numerical experiment, based on the stochastic capacitated facility location problem, we compare two fast scenario reduction methods: the CS method and the Monte Carlo (MC) method. The empirical conclusion is twofold: On the one hand, the achieved expected costs obtained by the two approaches are similar, although the MC method obtains a better approximation to the original set of of scenarios in terms of the moment matching criterion. On the other hand, the CS approach outperforms the MC approach with the same number of scenarios in terms of solution time