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An Exact Algorithm for IP Column Generation

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  • VANDERBECK, François

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

  • WOLSEY, Laurence

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

Abstract

An exact column generation algorithm for integer programs with a large (implicit) number of columns is presented. The family of problems that can be treated includes not only standard partitioning problems such as bin packing and certain vehicle routing problems in which the columns generated have 0 - 1 components and a right hand side vector of 1 's, but also the cutting stock problem in which the columns and right hand side are nonnegative integer vectors. We develop a combined branching and subproblem modification scheme that generalizes existing approaches, and also describe the use of lower bounds to reduce tailing-off effects.

Suggested Citation

  • VANDERBECK, François & WOLSEY, Laurence, 1994. "An Exact Algorithm for IP Column Generation," LIDAM Discussion Papers CORE 1994019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1994019
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1994.html
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    Cited by:

    1. Aardal, K. & van Hoesel, C.P.M., 1995. "Polyhedral techniques in combinatorial optimization," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Jaumard, Brigitte & Semet, Frederic & Vovor, Tsevi, 1998. "A generalized linear programming model for nurse scheduling," European Journal of Operational Research, Elsevier, vol. 107(1), pages 1-18, May.
    3. Aardal, K.I. & van Hoesel, S., 1995. "Polyhedral Techniques in Combinatorial Optimization," Other publications TiSEM ed028a07-eb6a-4c8d-8f21-d, Tilburg University, School of Economics and Management.
    4. Aardal, K.I. & van Hoesel, S., 1995. "Polyhedral Techniques in Combinatorial Optimization," Discussion Paper 1995-57, Tilburg University, Center for Economic Research.

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