Problem-based scenario generation by decomposing output distributions

Abstract

Scenario generation is required for most applications of stochastic programming to evaluate the expected effect of decisions made under uncertainty. We propose a novel and effective problem-based scenario generation method for two-stage stochastic programming that is agnostic to the specific stochastic program and kind of distribution. Our contribution lies in studying how an output distribution may change across decisions and exploit this for scenario generation. From a collection of output distributions, we find a few components that largely compose these, and such components are used directly for scenario generation. Computationally, the procedure relies on evaluating the recourse function over a large discrete distribution across a set of candidate decisions, while the scenario set itself is found using standard and efficient linear algebra algorithms that scale well. The method’s effectiveness is demonstrated on four case study problems from typical applications of stochastic programming to show it is more effective than its distribution-based alternatives. Due to its generality, the method is especially well suited to address scenario generation for distributions that are particularly challenging.