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Cutting Planes for Multistage Stochastic Integer Programs

Author

Listed:
  • Yongpei Guan

    () (School of Industrial Engineering, University of Oklahoma, Norman, Oklahoma 73019)

  • Shabbir Ahmed

    () (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • George L. Nemhauser

    () (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

This paper addresses the problem of finding cutting planes for multistage stochastic integer programs. We give a general method for generating cutting planes for multistage stochastic integer programs based on combining inequalities that are valid for the individual scenarios. We apply the method to generate cuts for a stochastic version of a dynamic knapsack problem and for stochastic lot-sizing problems. We give computational results, which show that these new inequalities are very effective in a branch-and-cut algorithm.

Suggested Citation

  • Yongpei Guan & Shabbir Ahmed & George L. Nemhauser, 2009. "Cutting Planes for Multistage Stochastic Integer Programs," Operations Research, INFORMS, vol. 57(2), pages 287-298, April.
  • Handle: RePEc:inm:oropre:v:57:y:2009:i:2:p:287-298
    DOI: 10.1287/opre.1080.0535
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    File URL: http://dx.doi.org/10.1287/opre.1080.0535
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    References listed on IDEAS

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    1. NEMHAUSER, George L. & WOLSEY, Laurence A., 1990. "A recursive procedure to generate all cuts for 0-1 mixed integer programs," CORE Discussion Papers RP 894, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Matthias Nowak & Werner Römisch, 2000. "Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty," Annals of Operations Research, Springer, vol. 100(1), pages 251-272, December.
    3. BARANY, Imre & VAN ROY, Tony & WOLSEY, Laurence A., 1984. "Uncapacitated lot-sizing: the convex hull of solutions," CORE Discussion Papers RP 605, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Guglielmo Lulli & Suvrajeet Sen, 2004. "A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems," Management Science, INFORMS, vol. 50(6), pages 786-796, June.
    5. MILLER, Andrew J. & WOLSEY, Laurence A., 2003. "Tight formulations for some simple mixed integer programs and convex objective integer programs," CORE Discussion Papers RP 1653, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. LOPARIC, Marko & MARCHAND, Hugues & WOLSEY, Laurence A., 2003. "Dynamic knapsack sets and capacitated lot-sizing," CORE Discussion Papers RP 1600, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Citations

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    Cited by:

    1. Correia, Isabel & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2018. "A stochastic multi-period capacitated multiple allocation hub location problem: Formulation and inequalities," Omega, Elsevier, vol. 74(C), pages 122-134.
    2. Ward Romeijnders & Niels van der Laan, 2020. "Pseudo-Valid Cutting Planes for Two-Stage Mixed-Integer Stochastic Programs with Right-Hand-Side Uncertainty," Operations Research, INFORMS, vol. 68(4), pages 1199-1217, July.
    3. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    4. Mahmutoğulları, Ali İrfan & Çavuş, Özlem & Aktürk, M. Selim, 2018. "Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR," European Journal of Operational Research, Elsevier, vol. 266(2), pages 595-608.
    5. Sakine Batun & Brian T. Denton & Todd R. Huschka & Andrew J. Schaefer, 2011. "Operating Room Pooling and Parallel Surgery Processing Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 220-237, May.
    6. Qipeng Zheng & Jianhui Wang & Panos Pardalos & Yongpei Guan, 2013. "A decomposition approach to the two-stage stochastic unit commitment problem," Annals of Operations Research, Springer, vol. 210(1), pages 387-410, November.
    7. Kai Pan & Yongpei Guan, 2016. "Strong Formulations for Multistage Stochastic Self-Scheduling Unit Commitment," Operations Research, INFORMS, vol. 64(6), pages 1482-1498, December.

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