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

Author

Listed:
  • SCHULTZ, Rüdiger

    (Konrad-Zuse-Zentrum für Informationstechnik Berlin)

  • STOUGIE, Leen

    (Institut for Actuarial Sciences and Econometrics, University of Amsterdam)

  • van der VLERK, Maarten

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

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.

Suggested Citation

  • SCHULTZ, Rüdiger & STOUGIE, Leen & van der VLERK, Maarten, 1995. "Solving Stochastic Programs with Complete Integer Recourse : A Framework Using Gröbner Bases," LIDAM Discussion Papers CORE 1995062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1995062
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1995.html
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    Cited by:

    1. Aardal, K. & van Hoesel, C.P.M. & Lenstra, J.K. & Stougie, L., 1997. "A decade of combinatorial optimization," Research Memorandum 023, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Georg Pflug & Andrzej Ruszczyński & Rüdiger Schultz, 1998. "On the Glivenko-Cantelli problem in stochastic programming: Mixed-integer linear recourse," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 39-49, February.
    3. Caroe, Claus C. & Tind, Jorgen, 1997. "A cutting-plane approach to mixed 0-1 stochastic integer programs," European Journal of Operational Research, Elsevier, vol. 101(2), pages 306-316, September.
    4. Samer Takriti & John R. Birge, 2000. "Lagrangian Solution Techniques and Bounds for Loosely Coupled Mixed-Integer Stochastic Programs," Operations Research, INFORMS, vol. 48(1), pages 91-98, February.

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