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Operations Research Proceedings pp 42–48Cite as

Cost Flow Improvement by Upgrading Costs and Capacities

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Part of the book series: Operations Research Proceedings ((ORP,volume 2000))

Abstract

We examine a network upgrade problem for cost flows. A budget can be distributed among the arcs of the network. An investment on a single arc can be used either to decrease the arc flow cost, or to increase the arc capacity, or both. The goal is to maximize the flow through the network while not exceeding bounds on the budget and on the total flow cost.

The problems are NP-hard even on series-parallel graphs. We provide an approximation algorithm on series- parallel graphs which, for arbitrary δ, ε > 0, produces a solution which exceeds the bounds on the budget and the flow cost by factors of at most 1 + δ and 1 + ε, respectively, while the amount of flow is at least that of an optimum solution. The running time of the algorithm is polynomial in the input size and 1/(δε).

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Würzburg, D-97074, Würzburg, Germany

    I. Demgensky & H.-C. Wirth

Authors
  1. I. Demgensky
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  2. H.-C. Wirth
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Produktion und Logistik, Universität Augsburg, Universitätsstraße 16, D-86135, Augsburg, Germany

    Bernhard Fleischmann

  2. Lehrstuhl für Betriebswirtschaftslehre, insbesondere Logistik, Technische Universität Dresden, Mommsenstraße 13, D-01062, Dresden, Germany

    Rainer Lasch

  3. Seminar für Wirtschaftsinformatik und Operations Research, Universität zu Köln, Pohligstraße 1, D-50969, Köln, Germany

    Ulrich Derigs

  4. Institut für Betriebswirtschaftslehre, Fachgebiet Operations Research, Technische Universität Darmstadt, Hochschulstraße 1, D-64289, Darmstadt, Germany

    Wolfgang Domschke

  5. Abteilung Mathematik VII, Universität Ulm, D-89069, Ulm, Germany

    Ulrich Rieder

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© 2001 Springer-Verlag Berlin Heidelberg

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Demgensky, I., Wirth, HC. (2001). Cost Flow Improvement by Upgrading Costs and Capacities. In: Fleischmann, B., Lasch, R., Derigs, U., Domschke, W., Rieder, U. (eds) Operations Research Proceedings. Operations Research Proceedings, vol 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56656-1_7

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  • DOI: https://doi.org/10.1007/978-3-642-56656-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41587-9

  • Online ISBN: 978-3-642-56656-1

  • eBook Packages: Springer Book Archive

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