The "Best" Algorithm for Solving Stochastic Mixed Integer Programs / Proceedings of the 2006 Winter Simulation Conference

Abstract

We present a new algorithm for solving two-stage stochastic mixed-integer programs (SMIPs) having discrete first-stage variables, and continuous or discrete second-stage variables. For a minimizing SMIP, the BEST algorithm (1) computes an upper Bound on the optimal objective value (typically a probabilistic bound), and identifies a deterministic lowerbounding function, (2) uses the bounds to Enumerate a set of first-stage solutions that contains an optimal solution with pre-specified confidence, (3) for each first-stage solution, Simulates second-stage operations by repeatedly sampling random parameters and solving the resulting model instances, and (4) applies statistical Tests (e.g., “screening procedures”) to the simulated outcomes to identify a nearoptimal first-stage solution with pre-specified confidence. We demonstrate the algorithm’s performance on a stochastic facility-location problem.