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Finding Disjoint Routes in Telecommunications Networks with Two Technologies

Author

Listed:
  • Anne de Jongh

    (Université Libre de Bruxelles, Bruxelles, Belgium)

  • Michel Gendreau

    (Université de Montréal, Montréal, Québec, Canada)

  • Martine Labbé

    (Université Libre de Bruxelles, Bruxelles, Belgium)

Abstract

We consider networks in which a cost is associated with each arc or edge and a transition cost is associated with each node. This last cost is related to the presence of two technologies on the network and is incurred only when a flow enters and leaves the corresponding node on arcs of different types. The problem we consider consists in finding two node disjoint paths with minimum total cost. We show that it is strongly NP-complete. Then we propose two heuristics, study their worst case behavior, provide a lower bounding procedure based on Lagrangean relaxation, and finally embed those elements in a branch and bound procedure.

Suggested Citation

  • Anne de Jongh & Michel Gendreau & Martine Labbé, 1999. "Finding Disjoint Routes in Telecommunications Networks with Two Technologies," Operations Research, INFORMS, vol. 47(1), pages 81-92, February.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:1:p:81-92
    DOI: 10.1287/opre.47.1.81
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    References listed on IDEAS

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    1. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
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    Cited by:

    1. Costa, Alysson M. & França, Paulo M. & Lyra Filho, Christiano, 2011. "Two-level network design with intermediate facilities: An application to electrical distribution systems," Omega, Elsevier, vol. 39(1), pages 3-13, January.

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