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Multi-depot traveling salesmen location problems on networks with special structure

Author

Listed:
  • Igor Averbakh

    (University of Toronto Scarborough)

  • Wei Yu

    (East China University of Science and Technology)

Abstract

Suppose that on any day, calls for service are generated by nodes of a transportation network independently with known probabilities. The calls are allocated to p service units that visit the allocated customers on shortest closed tours. That is, each service unit performs an optimal traveling salesman tour on its set of allocated calls (customers). We need to find optimal locations for the service units to minimize the expected travel distance. For this problem on a path, we present an $$O(n^4)$$O(n4) algorithm, where n is the number of nodes of the network. We also present an $$O(n^5)$$O(n5) algorithm for the problem on a tree with $$p=2$$p=2.

Suggested Citation

  • Igor Averbakh & Wei Yu, 2020. "Multi-depot traveling salesmen location problems on networks with special structure," Annals of Operations Research, Springer, vol. 286(1), pages 635-648, March.
    • Handle: RePEc:spr:annopr:v:286:y:2020:i:1:d:10.1007_s10479-018-2812-4
    DOI: 10.1007/s10479-018-2812-4
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    References listed on IDEAS

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    1. Kien Nguyen & Lam Anh, 2015. "Inverse $$k$$ k -centrum problem on trees with variable vertex weights," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 19-30, August.
    2. Igor Averbakh & Oded Berman, 1995. "Probabilistic Sales-Delivery Man and Sales-Delivery Facility Location Problems on a Tree," Transportation Science, INFORMS, vol. 29(2), pages 184-197, May.
    3. David Simchi-Levi & Oded Berman, 1988. "A Heuristic Algorithm for the Traveling Salesman Location Problem on Networks," Operations Research, INFORMS, vol. 36(3), pages 478-484, June.
    4. Nagy, Gabor & Salhi, Said, 2007. "Location-routing: Issues, models and methods," European Journal of Operational Research, Elsevier, vol. 177(2), pages 649-672, March.
    5. Berman, O. & Simchi-Levi, D., 1988. "Minisum location of a travelling salesman on simple networks," European Journal of Operational Research, Elsevier, vol. 36(2), pages 241-250, August.
    6. Robert C. Burness & John A. White, 1976. "The Traveling Salesman Location Problem," Transportation Science, INFORMS, vol. 10(4), pages 348-360, November.
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