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A New Approximation Algorithm for the Capacitated Vehicle Routing Problem on a Tree

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  • Tetsuo Asano

    (JAIST)

  • Naoki Katoh

    (Kyoto University)

  • Kazuhiro Kawashima

    (JAIST)

Abstract

This paper presents a new approximation algorithm for a vehicle routing problem on a tree-shaped network with a single depot. Customers are located on vertices of the tree, and each customer has a positive demand. Demands of customers are served by a fleet of identical vehicles with limited capacity. It is assumed that the demand of a customer is splittable, i.e., it can be served by more than one vehicle. The problem we are concerned with in this paper asks to find a set of tours of the vehicles with minimum total lengths. Each tour begins at the depot, visits a subset of the customers and returns to the depot without violating the capacity constraint. We propose a 1.35078-approximation algorithm for the problem (exactly, $$\left( {\sqrt {41} - 1} \right)/4$$ ), which is an improvement over the existing 1.5-approximation.

Suggested Citation

  • Tetsuo Asano & Naoki Katoh & Kazuhiro Kawashima, 2001. "A New Approximation Algorithm for the Capacitated Vehicle Routing Problem on a Tree," Journal of Combinatorial Optimization, Springer, vol. 5(2), pages 213-231, June.
    • Handle: RePEc:spr:jcomop:v:5:y:2001:i:2:d:10.1023_a:1011461300596
    DOI: 10.1023/A:1011461300596
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    References listed on IDEAS

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    1. Kemal Altinkemer & Bezalel Gavish, 1990. "Technical Note—Heuristics for Delivery Problems with Constant Error Guarantees," Transportation Science, INFORMS, vol. 24(4), pages 294-297, November.
    2. Desrochers, M. & Lenstra, J. K. & Savelsbergh, M. W. P., 1990. "A classification scheme for vehicle routing and scheduling problems," European Journal of Operational Research, Elsevier, vol. 46(3), pages 322-332, June.
    3. M. Haimovich & A. H. G. Rinnooy Kan, 1985. "Bounds and Heuristics for Capacitated Routing Problems," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 527-542, November.
    4. Martine Labbé & Gilbert Laporte & Hélène Mercure, 1991. "Capacitated Vehicle Routing on Trees," Operations Research, INFORMS, vol. 39(4), pages 616-622, August.
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    Cited by:

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    4. Yuanxiao Wu & Xiwen Lu, 2022. "Capacitated vehicle routing problem on line with unsplittable demands," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1953-1963, October.

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