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Solving the Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem by Dynamic Programming

Author

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  • Tue R. L. Christensen

    (Department of Economics and Business, Aarhus University, 8210 Aarhus V, Denmark)

  • Kim Allan Andersen

    (Department of Economics and Business, Aarhus University, 8210 Aarhus V, Denmark)

  • Andreas Klose

    (Department of Mathematics, Aarhus University, 8000 Aarhus C, Denmark)

Abstract

This paper considers a minimum-cost network flow problem in a bipartite graph with a single sink. The transportation costs exhibit a staircase cost structure because such types of transportation cost functions are often found in practice. We present a dynamic programming algorithm for solving this so-called single-sink, fixed-charge, multiple-choice transportation problem exactly. The method exploits heuristics and lower bounds to peg binary variables, improve bounds on flow variables, and reduce the state-space variable. In this way, the dynamic programming method is able to solve large instances with up to 10,000 nodes and 10 different transportation modes in a few seconds, much less time than required by a widely used mixed-integer programming solver and other methods proposed in the literature for this problem.

Suggested Citation

  • Tue R. L. Christensen & Kim Allan Andersen & Andreas Klose, 2013. "Solving the Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem by Dynamic Programming," Transportation Science, INFORMS, vol. 47(3), pages 428-438, August.
    • Handle: RePEc:inm:ortrsc:v:47:y:2013:i:3:p:428-438
    DOI: 10.1287/trsc.1120.0431
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    References listed on IDEAS

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    Cited by:

    1. Bertazzi, Luca & Maggioni, Francesca, 2018. "A stochastic multi-stage fixed charge transportation problem: Worst-case analysis of the rolling horizon approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 555-569.
    2. Amir Ardestani-Jaafari & Erick Delage, 2018. "The Value of Flexibility in Robust Location–Transportation Problems," Transportation Science, INFORMS, vol. 52(1), pages 189-209, January.

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