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A branch-and-cut algorithm for the single commodity uncapacitated fixed charge network flow problem

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  • ORTEGA, Francisco
  • WOLSEY, Laurence
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    Abstract

    We present a branch-and-cut algorithm to solve the single commodity uncapacitated fixed charge network flow problem, which includes the Steiner tree problem, uncapacitated lot-sizing problems, and the fixed charge transportation problem as special cases. The cuts used are simple dicut inequalities and their variants. A crucial problem when separating these inequalities is to find the right cut set on which to generate the inequalities. The prototype branch-and-cut system, bc-nd includes a separation heuristic for the dicut inequalities, and problem specific primal heuristics, branching and pruning rules. Computational results show that bc-nd is competitive compared to a variety of special purpose algorithms for problems with explicit flow costs. We also examine how general purpose MIP systems perform on such problems when provided with formulations that have been tightened a priori with dicut inequalities.

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    Bibliographic Info

    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2000049.

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    Date of creation: 00 Oct 2000
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    Handle: RePEc:cor:louvco:2000049

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    Related research

    Keywords: Network Design; Fixed Charge; Branch and Cut; Dicut Inequalities; Branching; Heuristics; Minimum cost flow.;

    References

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    1. Schaffer, Joanne R. & O'Leary, Daniel E., 1989. "Use of penalties in a branch and bound procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 43(3), pages 305-312, December.
    2. Sun, Minghe & Aronson, Jay E. & McKeown, Patrick G. & Drinka, Dennis, 1998. "A tabu search heuristic procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 441-456, April.
    3. GüNLüCK, Oktay & POCHET, Yves, 1998. "Mixing mixed-integer inequalities," CORE Discussion Papers 1998011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. repec:fth:louvco:9953 is not listed on IDEAS
    5. MARCHAND, Hugues & MARTIN, Alexander & WEISMANTEL, Robert & WOLSEY, Laurence, 1999. "Cutting planes in integer and mixed integer programming," CORE Discussion Papers 1999053, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Rardin, Ronald L. & Wolsey, Laurence A., 1993. "Valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems," European Journal of Operational Research, Elsevier, vol. 71(1), pages 95-109, November.
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    Cited by:
    1. VAN VYVE, Mathieu & POCHET, Yves, 2001. "A general heuristic or production planning problems," CORE Discussion Papers 2001056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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