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Generalized Chvátal-Gomory closures for integer programs with bounds on variables

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Abstract

Integer programming problems that arise in practice often involve decision variables with one or two sided bounds. In this paper, we consider a generalization of Chvátal-Gomory inequalities obtained by strengthening Chvátal-Gomory inequalities using the bounds on the variables. We prove that the closure of a rational polyhedron obtained after applying the generalized Chvátal-Gomory inequalities is also a rational polyhedron. This generalizes a result of Dunkel and Schulz on 0–1 problems to the case when some of the variables have upper or lower bounds or both while the rest of them are unbounded.

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Acknowledgements

The authors would like to thank two anonymous referees for their detailed comments on the first manuscript. This research is supported, in part, by the Institute for Basic Science (IBS-R029-C1).

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Authors and Affiliations

  1. IBM Research, Yorktown Heights, NY, 10598, USA

    Sanjeeb Dash

  2. School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, 14850, USA

    Oktay Günlük

  3. Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, 34126, Republic of Korea

    Dabeen Lee

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  1. Sanjeeb Dash
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  2. Oktay Günlük
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  3. Dabeen Lee
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Correspondence to Dabeen Lee.

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Dash, S., Günlük, O. & Lee, D. Generalized Chvátal-Gomory closures for integer programs with bounds on variables. Math. Program. 190, 393–425 (2021). https://doi.org/10.1007/s10107-020-01539-5

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  • DOI: https://doi.org/10.1007/s10107-020-01539-5

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