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Cutting planes in integer and mixed integer programming

Author

Listed:
  • MARCHAND, Hugues

    (Department of Operational Research London School of Economics Houghton Street, London WC2A 2AE, United Kingdom)

  • MARTIN, Alexander

    (Konrad-Zuse-Zentrum Berlin Takustr. 7 D-14195 Berlin Germany)

  • WEISMANTEL, Robert

    (Fakultat fur Mathematik, IMO Otto-von-Guericke Universitat Magdeburg Universit?atsplatz 2 D-39106 Magdeburg Germany)

  • WOLSEY, Laurence

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

Abstract

This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints, and iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally the use of valid inequalities for classes of problems with structure, such as network design, is explored.

Suggested Citation

  • 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).
    • Handle: RePEc:cor:louvco:1999053
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1999.html
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    References listed on IDEAS

    as
    1. 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).
    2. M. W. Padberg & T. J. Van Roy & L. A. Wolsey, 1985. "Valid Linear Inequalities for Fixed Charge Problems," Operations Research, INFORMS, vol. 33(4), pages 842-861, August.
    3. Padberg, M.W. & Van Roy, T.J. & Wolsey, L.A., 1985. "Valid linear inequalities for fixed charge problems," LIDAM Reprints CORE 656, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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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).

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    More about this item

    Keywords

    Mixed Integer Programming; Cutting Planes;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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