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Minmax p-Traveling Salesmen Location Problems on a Tree

Author

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  • Igor Averbakh
  • Oded Berman

Abstract

Suppose that p traveling salesmen must visit together all points of a tree, and the objective is to minimize the maximum of the lengths of their tours. The location–allocation version of the problem (where both optimal home locations of the salesmen and their optimal tours must be found) is known to be NP-hard for any p≥2. We present exact polynomial algorithms with a linear order of complexity for location versions of the problem (where only optimal home locations must be found, without the corresponding tours) for the cases p=2 and p=3. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Igor Averbakh & Oded Berman, 2002. "Minmax p-Traveling Salesmen Location Problems on a Tree," Annals of Operations Research, Springer, vol. 110(1), pages 55-68, February.
    • Handle: RePEc:spr:annopr:v:110:y:2002:i:1:p:55-68:10.1023/a:1020759332183
    DOI: 10.1023/A:1020759332183
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    Cited by:

    1. Ahmadi-Javid, Amir & Amiri, Elahe & Meskar, Mahla, 2018. "A Profit-Maximization Location-Routing-Pricing Problem: A Branch-and-Price Algorithm," European Journal of Operational Research, Elsevier, vol. 271(3), pages 866-881.
    2. Fusheng Wang, 2013. "A hybrid algorithm for linearly constrained minimax problems," Annals of Operations Research, Springer, vol. 206(1), pages 501-525, July.
    3. Xu, Liang & Xu, Zhou & Xu, Dongsheng, 2013. "Exact and approximation algorithms for the min–max k-traveling salesmen problem on a tree," European Journal of Operational Research, Elsevier, vol. 227(2), pages 284-292.
    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.

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