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Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs

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Abstract

We consider a class of two-stage stochastic integer programs with binary variables in the first stage and general integer variables in the second stage. We develop decomposition algorithms akin to the \(L\)-shaped or Benders’ methods by utilizing Gomory cuts to obtain iteratively tighter approximations of the second-stage integer programs. We show that the proposed methodology is flexible in that it allows several modes of implementation, all of which lead to finitely convergent algorithms. We illustrate our algorithms using examples from the literature. We report computational results using the stochastic server location problem instances which suggest that our decomposition-based approach scales better with increases in the number of scenarios than a state-of-the art solver which was used to solve the deterministic equivalent formulation.

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Acknowledgments

We thank the referees for their suggestions on previous versions of this paper.

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Authors and Affiliations

  1. Integrated Systems Engineering, The Ohio State University, 210 Baker Systems, 1971 Neil Avenue, Columbus, OH, 43210, USA

    Dinakar Gade, Simge Küçükyavuz & Suvrajeet Sen

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  1. Dinakar Gade
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  2. Simge Küçükyavuz
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  3. Suvrajeet Sen
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Correspondence to Simge Küçükyavuz.

Additional information

This work is supported in part by NSF-CMMI Grant 1100383.

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Gade, D., Küçükyavuz, S. & Sen, S. Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs. Math. Program. 144, 39–64 (2014). https://doi.org/10.1007/s10107-012-0615-y

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