Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis |
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| Authors: | Rüdiger Schultz Leen Stougie Maarten H. van der Vlerk |
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| Affiliation: | (1) Mathematical Institute, University of Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany;(2) Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB, Eindhoven, The Netherlands;(3) Department of Econometrics, University of Groningen, P.O. Box 800, NL-9700 AV Groningen, The Netherlands |
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| Abstract: | In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer 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 improvements to reduce the number of function evaluations needed. |
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| Keywords: | Stochastic programming Integer recourse Algorithm Gr?bner basis |
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