Solving Stochastic Programs with Complete Integer Recourse: A Framework Using Gröbner Bases

Rüdiger Schultz, Leen Stougie and Maarten van der VLERK
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Rüdiger Schultz: Konrad-Zuse-Zentrum für Informationstechnik Berlin
Leen Stougie: Institut for Actuarial Sciences and Econometrics, University of Amsterdam
Maarten van der VLERK: CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

No 1995062, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Grabner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the integer expected recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest possible improvements to economize on the number of function evalutations needed.

Date: 1995-11-01
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