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Network Flow Optimization with Minimum Quantities

In: Operations Research Proceedings 2010

Author

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  • Hans Georg Seedig

    (Technische Universität München)

Abstract

Economies of scale often appear as decreasing marginal costs, but may also occur as a constraint that at least a minimum quantity should be produced or nothing at all. Taking the latter into account can support decisions about keeping a production site, setting up a new one, establishing new routes in logistics network, and many more. In our work, we define the corresponding problem Minimum Cost Network Flow with Minimum Quantities and prove its computational hardness. Following that, we devise a tailored Branch-&-Bound algorithm with an efficient update step that usually affects only small parts of the network. Experiments are conducted on real problems and artificial networks. In our results, the update step made the inevitable but well-studied subproblem of the initial computation of a minimum cost network flow problem taking most of the actual total running time. As our method does also compare favorably with a heuristic algorithm that has been implemented before, we recommend it for practical use.

Suggested Citation

  • Hans Georg Seedig, 2011. "Network Flow Optimization with Minimum Quantities," Operations Research Proceedings, in: Bo Hu & Karl Morasch & Stefan Pickl & Markus Siegle (ed.), Operations Research Proceedings 2010, pages 295-300, Springer.
    • Handle: RePEc:spr:oprchp:978-3-642-20009-0_47
    DOI: 10.1007/978-3-642-20009-0_47
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    Cited by:

    1. Krumke, Sven O. & Thielen, Clemens, 2013. "The generalized assignment problem with minimum quantities," European Journal of Operational Research, Elsevier, vol. 228(1), pages 46-55.

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