Clustering of sample average approximation for stochastic program

Abstract

We present an improvement to the Sample Average Approximation (SAA) method for two-stage stochasticprogram. Although the SAA has nice theoretical properties, such as convergence in probability and consistency,as long as the sample is large enough, the requirement on the sample size is always a concern forboth academia and practitioners. Our clustering method employs the Maximum Volume Inscribed Ellipsoid(MVIE) to approximate the feasible set of each scenario and calculates a measure of similarity. The scenariosare clustered based on such a measure of similarity and our clustering method reduces the sample size considerably.Moreover, the clustering method will offer managerial implications by highlighting the matteringscenarios. The clustering method would be implemented in a distributed computational infrastructure withlow-cost computers.