The "BEST" algorithm for solving stochastic mixed integer programs

Authors:
Susan M. Sanchez;R. Kevin Wood
Affiliations:
Naval Postgraduate School, Monterey, CA;Naval Postgraduate School, Monterey, CA
Venue:
Proceedings of the 38th conference on Winter simulation
Year:
2006

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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 lower-bounding 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 near-optimal first-stage solution with pre-specified confidence. We demonstrate the algorithm's performance on a stochastic facility-location problem.