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Mixing mixed-integer inequalities

Author

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  • GüNLüCK, Oktay

    (School of ORIE, Cornell University, Ithaca, New York)

  • POCHET, Yves

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

Abstract

Mixed-integer rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixed-integer programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities. Given a mixed-integer region S and a collection of valid 'base' mixed-integer inequalities, we develop a procedure for generating new valid inequalities for S. The starting point of our procedure is to consider the MIR inequalities related with the base inequalities. For any subset of these MIR inequalities, we generate two new inequalities by combining or "mixing" them. We show that the new inequalities are strong in the sense that they fully describe the convex hull of a mixed integer region associated with the base inequalities. We also study some extensions of this mixing procedure, and discuss how it can be used to obtain new classes of strong valid inequalities for various mixed-integer programming problems. In particular, we present examples for production planning, capacitated facility location, capacitated network design, and multiple knapsack problems.

Suggested Citation

  • GüNLüCK, Oktay & POCHET, Yves, 1998. "Mixing mixed-integer inequalities," LIDAM Discussion Papers CORE 1998011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1998011
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1998.html
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    Cited by:

    1. ORTEGA, Francisco & WOLSEY, Laurence, 2000. "A branch-and-cut algorithm for the single commodity uncapacitated fixed charge network flow problem," LIDAM Discussion Papers CORE 2000049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. BELVAUX, Gaetan & WOLSEY, Laurence A., 1998. "Lot-sizing problems: modelling issues and a specialized branch-and-cut system BC-PROD," LIDAM Discussion Papers CORE 1998049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. MARCHAND, Hugues & MARTIN, Alexander & WEISMANTEL, Robert & WOLSEY, Laurence, 1999. "Cutting planes in integer and mixed integer programming," LIDAM Discussion Papers CORE 1999053, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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