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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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    References listed on IDEAS

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    5. LOPARIC, Marko & MARCHAND, Hugues & WOLSEY, Laurence A., 2003. "Dynamic knapsack sets and capacitated lot-sizing," LIDAM Reprints CORE 1600, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

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    2. Nickel, Stefan & Saldanha-da-Gama, Francisco & Ziegler, Hans-Peter, 2012. "A multi-stage stochastic supply network design problem with financial decisions and risk management," Omega, Elsevier, vol. 40(5), pages 511-524.
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    4. 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.
    5. Jianqiu Huang & Kai Pan & Yongpei Guan, 2021. "Multistage Stochastic Power Generation Scheduling Co-Optimizing Energy and Ancillary Services," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 352-369, January.
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    7. 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).
    8. 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.
    9. İ. Esra Büyüktahtakın, 2022. "Stage-t scenario dominance for risk-averse multi-stage stochastic mixed-integer programs," Annals of Operations Research, Springer, vol. 309(1), pages 1-35, February.
    10. Franco Quezada & Céline Gicquel & Safia Kedad-Sidhoum, 2022. "Combining Polyhedral Approaches and Stochastic Dual Dynamic Integer Programming for Solving the Uncapacitated Lot-Sizing Problem Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1024-1041, March.
    11. Eyyüb Y. Kıbış & İ. Esra Büyüktahtakın & Robert G. Haight & Najmaddin Akhundov & Kathleen Knight & Charles E. Flower, 2021. "A Multistage Stochastic Programming Approach to the Optimal Surveillance and Control of the Emerald Ash Borer in Cities," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 808-834, May.
    12. Pimentel, Bruno S. & Mateus, Geraldo R. & Almeida, Franklin A., 2013. "Stochastic capacity planning and dynamic network design," International Journal of Production Economics, Elsevier, vol. 145(1), pages 139-149.
    13. 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.
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