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Two-stage integer programs with stochastic right-hand sides: a superadditive dual approach

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Abstract

We consider two-stage pure integer programs with discretely distributed stochastic right-hand sides. We present an equivalent superadditive dual formulation that uses the value functions in both stages. We give two algorithms for finding the value functions. To solve the reformulation after obtaining the value functions, we develop a global branch-and-bound approach and a level-set approach to find an optimal tender. We show that our method can solve randomly generated instances whose extensive forms are several orders of magnitude larger than the extensive forms of those instances found in the literature.

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, Pittsburgh, PA, 15261, USA

    Andrew J. Schaefer & Brady Hunsaker

  2. Department of Industrial and Management Systems Engineering, University of South Florida, 4202 E. Fowler Avenue, ENB 118, Tampa, FL, 33620, USA

    Nan Kong

Authors
  1. Nan Kong
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  2. Andrew J. Schaefer
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  3. Brady Hunsaker
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Correspondence to Nan Kong.

Additional information

This work is supported by National Science Foundation grants DMI-0217190 and DMI-0355433.

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Kong, N., Schaefer, A. & Hunsaker, B. Two-stage integer programs with stochastic right-hand sides: a superadditive dual approach. Math. Program. 108, 275–296 (2006). https://doi.org/10.1007/s10107-006-0711-y

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