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An extension of the Christofides heuristic for the generalized multiple depot multiple traveling salesmen problem

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  • Xu, Zhou
  • Rodrigues, Brian

Abstract

We study a generalization of the classical traveling salesman problem, where multiple salesmen are positioned at different depots, of which only a limited number (k) can be selected to service customers. For this problem, only two 2-approximation algorithms are available in the literature. Here, we improve on these algorithms by showing that a non-trivial extension of the well-known Christofides heuristic has a tight approximation ratio of 2−1/(2k). In doing so, we develop a body of analysis which can be used to build new approximation algorithms for other vehicle routing problems.

Suggested Citation

  • Xu, Zhou & Rodrigues, Brian, 2017. "An extension of the Christofides heuristic for the generalized multiple depot multiple traveling salesmen problem," European Journal of Operational Research, Elsevier, vol. 257(3), pages 735-745.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:3:p:735-745
    DOI: 10.1016/j.ejor.2016.08.054
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    References listed on IDEAS

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    1. Gilbert Laporte & Yves Nobert & Serge Taillefer, 1988. "Solving a Family of Multi-Depot Vehicle Routing and Location-Routing Problems," Transportation Science, INFORMS, vol. 22(3), pages 161-172, August.
    2. Prodhon, Caroline & Prins, Christian, 2014. "A survey of recent research on location-routing problems," European Journal of Operational Research, Elsevier, vol. 238(1), pages 1-17.
    3. Mina, Hokey & Jayaraman, Vaidyanathan & Srivastava, Rajesh, 1998. "Combined location-routing problems: A synthesis and future research directions," European Journal of Operational Research, Elsevier, vol. 108(1), pages 1-15, July.
    4. William Cook & André Rohe, 1999. "Computing Minimum-Weight Perfect Matchings," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 138-148, May.
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    Cited by:

    1. Henan Liu & Huili Zhang & Yi Xu, 2021. "The m-Steiner Traveling Salesman Problem with online edge blockages," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 844-860, May.
    2. Bérczi, Kristóf & Mnich, Matthias & Vincze, Roland, 2023. "Approximations for many-visits multiple traveling salesman problems," Omega, Elsevier, vol. 116(C).
    3. Xiaofan Lai & Liang Xu & Zhou Xu & Yang Du, 2023. "An Approximation Algorithm for k -Depot Split Delivery Vehicle Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1179-1194, September.
    4. Yong Wang, 2019. "Sufficient and Necessary Conditions for an Edge in the Optimal Hamiltonian Cycle Based on Frequency Quadrilaterals," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 671-683, May.

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