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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

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.

Suggested Citation

  • 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).
    • Handle: RePEc:cor:louvco:2000049
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    References listed on IDEAS

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    Cited by:

    1. VAN VYVE, Mathieu & POCHET, Yves, 2001. "A general heuristic or production planning problems," LIDAM Discussion Papers CORE 2001056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Alper Atamtürk & Simge Küçükyavuz, 2005. "Lot Sizing with Inventory Bounds and Fixed Costs: Polyhedral Study and Computation," Operations Research, INFORMS, vol. 53(4), pages 711-730, August.

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