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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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    3. NEMHAUSER, George L. & WOLSEY, Laurence A., 1990. "A recursive procedure to generate all cuts for 0-1 mixed integer programs," LIDAM Reprints CORE 894, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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