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

  • ORTEGA, Francisco
  • WOLSEY, Laurence
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    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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    File URL: http://alfresco.uclouvain.be/alfresco/download/attach/workspace/SpacesStore/096d460a-0bad-4ff1-a2ae-8cd42c0c231f/coredp_2000_49.pdf
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    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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    1. 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.
    2. 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).
    3. 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.
    4. 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.
    5. GüNLüCK, Oktay & POCHET, Yves, 1998. "Mixing mixed-integer inequalities," CORE Discussion Papers 1998011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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