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

Francisco Ortega and Laurence Wolsey

No 2000049, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: Network Design; Fixed Charge; Branch and Cut; Dicut Inequalities; Branching; Heuristics; Minimum cost flow. (search for similar items in EconPapers)
Date: 2000-10
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Citations: View citations in EconPapers (2)

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