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

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  • 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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    Cited by:

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