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Using branch-and-price approach to solve the directed network design problem with relays

  • Li, Xiangyong
  • Aneja, Y.P.
  • Huo, Jiazhen
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    We present node-arc and arc-path formulations, and develop a branch-and-price approach for the directed network design problem with relays (DNDR). The DNDR problem can be used to model many network design problems in transportation, service, and telecommunication system, where relay points are necessary. The DNDR problem consists of introducing a subset of arcs and locating relays on a subset of nodes such that in the resulting network, the total cost (arc cost plus relay cost) is minimized, and there exists a directed path linking the origin and destination of each commodity, in which the distances between the origin and the first relay, any two consecutive relays, and the last relay and the destination do not exceed a predefined distance limit. With the node-arc formulation, we can directly solve small DNDR instances using mixed integer programming solver. With the arc-path formulation, we design a branch-and-price approach, which is a variant of branch-and-bound with bounds provided by solving linear programs using column generation at each node of the branch-and-bound tree. We design two methods to efficiently price out columns and present computational results on a set of 290 generated instances. Results demonstrate that our proposed branch-and-price approach is a computationally efficient procedure for solving the DNDR problem.

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    Article provided by Elsevier in its journal Omega.

    Volume (Year): 40 (2012)
    Issue (Month): 5 ()
    Pages: 672-679

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    Handle: RePEc:eee:jomega:v:40:y:2012:i:5:p:672-679
    DOI: 10.1016/
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    1. Ehrgott, Matthias & Tind, Jørgen, 2009. "Column generation with free replicability in DEA," Omega, Elsevier, vol. 37(5), pages 943-950, October.
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    5. Aneja, Y.P. & Chandrasekaran, R. & Li, Xiangyong & Nair, K.P.K., 2010. "A branch-and-cut algorithm for the strong minimum energy topology in wireless sensor networks," European Journal of Operational Research, Elsevier, vol. 204(3), pages 604-612, August.
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    9. Caramia, M. & Guerriero, F., 2009. "A heuristic approach to long-haul freight transportation with multiple objective functions," Omega, Elsevier, vol. 37(3), pages 600-614, June.
    10. Lee, Der-Horng & Dong, Meng & Bian, Wen, 2010. "The design of sustainable logistics network under uncertainty," International Journal of Production Economics, Elsevier, vol. 128(1), pages 159-166, November.
    11. Cabral, Edgar Alberto & Erkut, Erhan & Laporte, Gilbert & Patterson, Raymond A., 2007. "The network design problem with relays," European Journal of Operational Research, Elsevier, vol. 180(2), pages 834-844, July.
    12. Tempelmeier, Horst, 2011. "A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint," Omega, Elsevier, vol. 39(6), pages 627-633, December.
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