A simple heuristic for reducing the number of scenarios in two-stage stochastic programming

In this work we address the problem of solving multiscenario optimization models that are deterministic equivalents of two-stage stochastic programs. We present a heuristic approximation strategy where we reduce the number of scenarios and obtain an approximation of the original multiscenario optimization problem. In this strategy, a subset of the given set of scenarios is selected based on a proposed criterion, and probabilities are assigned to the occurrence of scenarios in the reduced set. The original stochastic programming model is converted into a deterministic equivalent using the reduced set of scenarios. A mixed-integer linear program (MILP) is proposed for the reduced scenario selection. We apply this practical heuristic strategy to four numerical examples and show that reformulating and solving the stochastic program with the reduced set of scenarios yields an objective value close to the optimum of the original multiscenario problem.