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The Capacitated Traveling Salesman Location Problem

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  • David Simchi-Levi

    (Columbia University, New York, New York)

Abstract

The capacitated traveling salesmen location problem is the problem of locating one service station with servers, each having a limited capacity, q . The service units must visit each day all the calls that are registered in a service list. Each call is generated with a given probability and the service list contains at most n calls. In the paper we present an O ( n 3 ) time heuristic for the problem on networks. This heuristic finds a solution whose relative worst-case error equals 3 /2−3/(2 q ). We also show how one can use this heuristic to solve the problem on the plane with rectilinear or Euclidean distances with the same worst-case error. In the latter case the heuristic is proved to be asymptotically optimal.

Suggested Citation

  • David Simchi-Levi, 1991. "The Capacitated Traveling Salesman Location Problem," Transportation Science, INFORMS, vol. 25(1), pages 9-18, February.
    • Handle: RePEc:inm:ortrsc:v:25:y:1991:i:1:p:9-18
    DOI: 10.1287/trsc.25.1.9
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    Cited by:

    1. Nagy, Gabor & Salhi, Said, 2007. "Location-routing: Issues, models and methods," European Journal of Operational Research, Elsevier, vol. 177(2), pages 649-672, March.
    2. Martin Schwardt & Kathrin Fischer, 2009. "Combined location-routing problems—a neural network approach," Annals of Operations Research, Springer, vol. 167(1), pages 253-269, March.
    3. Luca Bertazzi & Francesca Maggioni, 2015. "Solution Approaches for the Stochastic Capacitated Traveling Salesmen Location Problem with Recourse," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 321-342, July.
    4. Weijun Xie & Yanfeng Ouyang & Sze Chun Wong, 2016. "Reliable Location-Routing Design Under Probabilistic Facility Disruptions," Transportation Science, INFORMS, vol. 50(3), pages 1128-1138, August.

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