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Cutting Planes for Integer Programs with General Integer Variables

Author

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  • CERIA, Sebastian

    (Graduate School of Business, Columbia University, New York)

  • CORDIER, Cecile

    (Graduate School of Business, Columbia University, New York)

  • MARCHAND, Hugues

    (CORE and FSA, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • WOLSEY, Laurence

    (CORE and FSA, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

Abstract

We investigate the use of cutting planes for integer programs with general integer variables. We show how cutting planes arising from knapsack inequalities can be generated and lifted as in the case of 0-1 variables. We also explore the use of Gomory's mixed integer cuts. We address both theoretical and computational issues and show how to embed these cutting planes in a branch-and-bound framework. We compare results obtained by using our cut generation routines in two existing systems with a commercially available branch-and-bound code on a range of test problems arising from practical applications

Suggested Citation

  • CERIA, Sebastian & CORDIER, Cecile & MARCHAND, Hugues & WOLSEY, Laurence, 1995. "Cutting Planes for Integer Programs with General Integer Variables," LIDAM Discussion Papers CORE 1995075, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1995075
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1995.html
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    Cited by:

    1. MARCHAND, Hugues & WOLSEY, Laurence A., 1997. "The 0-1 knapsack problem with a single continuous variable," LIDAM Discussion Papers CORE 1997020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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