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On a Level-Set Characterization of the Value Function of an Integer Program and Its Application to Stochastic Programming

Author

Listed:
  • Andrew C. Trapp

    (School of Business, Worcester Polytechnic Institute, Worcester, Massachusetts 01609)

  • Oleg A. Prokopyev

    (Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261)

  • Andrew J. Schaefer

    (Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261)

Abstract

We propose a level-set approach to characterize the value function of a pure linear integer program with inequality constraints. We study theoretical properties of our characterization and show how they can be exploited to optimize a class of stochastic integer programs through a value function reformulation. Specifically, we develop algorithmic approaches that solve two-stage multidimensional knapsack problems with random budgets, yielding encouraging computational results.

Suggested Citation

  • Andrew C. Trapp & Oleg A. Prokopyev & Andrew J. Schaefer, 2013. "On a Level-Set Characterization of the Value Function of an Integer Program and Its Application to Stochastic Programming," Operations Research, INFORMS, vol. 61(2), pages 498-511, April.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:2:p:498-511
    DOI: 10.1287/opre.1120.1156
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    References listed on IDEAS

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    1. Antonio Alonso-Ayuso & Laureano Escudero & Monique Guignard & Martín Quinteros & Andres Weintraub, 2011. "Forestry management under uncertainty," Annals of Operations Research, Springer, vol. 190(1), pages 17-39, October.
    2. WOLSEY, Laurence A., 1981. "Integer programming duality: price functions and sensitivity analysis," LIDAM Reprints CORE 431, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Lewis Ntaimo, 2010. "Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse," Operations Research, INFORMS, vol. 58(1), pages 229-243, February.
    4. Yang Yuan & Suvrajeet Sen, 2009. "Enhanced Cut Generation Methods for Decomposition-Based Branch and Cut for Two-Stage Stochastic Mixed-Integer Programs," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 480-487, August.
    5. Robert G. Jeroslow, 1978. "Some Basis Theorems for Integral Monoids," Mathematics of Operations Research, INFORMS, vol. 3(2), pages 145-154, May.
    6. Alonso-Ayuso, Antonio & Escudero, Laureano F. & Teresa Ortuno, M., 2003. "BFC, A branch-and-fix coordination algorithmic framework for solving some types of stochastic pure and mixed 0-1 programs," European Journal of Operational Research, Elsevier, vol. 151(3), pages 503-519, December.
    7. Klabjan, Diego, 2007. "Subadditive approaches in integer programming," European Journal of Operational Research, Elsevier, vol. 183(2), pages 525-545, December.
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    Cited by:

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