The Sample Average Approximation Method for Stochastic Programs with Integer Recourse Shabbir Ahmed * and Alexander Shapiro † School of Industrial & Systems Engineering Georgia Institute of Technology 765 Ferst Drive, Atlanta, GA 30332 February 5, 2002 Abstract This paper develops a solution strategy for two-stage stochastic pro- grams with integer recourse. The proposed methodology relies on ap- proximating the underlying stochastic program via sampling, and solving the approximate problem via a specialized optimization algorithm. We show that the proposed scheme will produce an optimal solution to the true problem with probability approaching one exponentially fast as the sample size is increased. For fixed sample size, we describe statistical and deterministic bounding techniques to validate the quality of a candidate optimal solution. Preliminary computational experience with the method is reported. Keywords: Stochastic programming, integer recourse, sample average ap- proximation, branch and bound. 1 Introduction In the two-stage stochastic programming approach for optimization under un- certainty, the decision variables are partitioned into two sets. The first stage variables are those that have to be decided before the actual realization of the uncertain parameters becomes available. Subsequently, once the random events have presented themselves, further design or operational policy improvements can be made by selecting, at a certain cost, the values of the second stage or recourse variables. The objective is to choose the first stage variables in a way that the sum of first stage costs and the expected value of the random second stage or recourse costs is minimized. * Supported in part by the National Science Foundation under Grant No. DMII-0099726. † Supported in part by the National Science Foundation under Grant No. DMS-0073770. 1