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Network design and flow problems with cross-arc costs

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  • Cohn, Amy
  • Davey, Melinda
  • Schkade, Lisa
  • Siegel, Amanda
  • Wong, Caris

Abstract

Network design and flow problems appear in a wide variety of transportation applications. We consider a new variation to this important class of problems, in which the cost associated with an arc depends not only on the amount of flow moving across that arc, but on the amount of flow on other arcs in the network as well. We formulate an integer program to address this problem, discuss a real-world application in which cross-arc costs are found, and conduct computational experiments on a broad class of problems to analyze how the model performs as network characteristics vary.

Suggested Citation

  • Cohn, Amy & Davey, Melinda & Schkade, Lisa & Siegel, Amanda & Wong, Caris, 2008. "Network design and flow problems with cross-arc costs," European Journal of Operational Research, Elsevier, vol. 189(3), pages 890-901, September.
  • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:890-901
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    1. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    2. Daeki Kim & Cynthia Barnhart & Keith Ware & Gregory Reinhardt, 1999. "Multimodal Express Package Delivery: A Service Network Design Application," Transportation Science, INFORMS, vol. 33(4), pages 391-407, November.
    3. Keely L. Croxton & Bernard Gendron & Thomas L. Magnanti, 2003. "A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems," Management Science, INFORMS, vol. 49(9), pages 1268-1273, September.
    4. Cynthia Barnhart & Christopher A. Hane & Pamela H. Vance, 2000. "Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems," Operations Research, INFORMS, vol. 48(2), pages 318-326, April.
    5. Kaj Holmberg & Johan Hellstrand, 1998. "Solving the Uncapacitated Network Design Problem by a Lagrangean Heuristic and Branch-and-Bound," Operations Research, INFORMS, vol. 46(2), pages 247-259, April.
    6. LeBlanc, Larry J. & Boyce, David E., 1986. "A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows," Transportation Research Part B: Methodological, Elsevier, vol. 20(3), pages 259-265, June.
    7. Rina R. Schneur & James B. Orlin, 1998. "A Scaling Algorithm for Multicommodity Flow Problems," Operations Research, INFORMS, vol. 46(2), pages 231-246, April.
    8. Klaus Büdenbender & Tore Grünert & Hans-Jürgen Sebastian, 2000. "A Hybrid Tabu Search/Branch-and-Bound Algorithm for the Direct Flight Network Design Problem," Transportation Science, INFORMS, vol. 34(4), pages 364-380, November.
    9. Andrew P. Armacost & Cynthia Barnhart & Keith A. Ware, 2002. "Composite Variable Formulations for Express Shipment Service Network Design," Transportation Science, INFORMS, vol. 36(1), pages 1-20, February.
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    8. SteadieSeifi, M. & Dellaert, N.P. & Nuijten, W. & Van Woensel, T. & Raoufi, R., 2014. "Multimodal freight transportation planning: A literature review," European Journal of Operational Research, Elsevier, vol. 233(1), pages 1-15.

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