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

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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.

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Authors and Affiliations

  1. School of Information Science, JAIST, Asahidai, Tatsunokuchi, 923-1292, Japan

    Tetsuo Asano & Kazuhiro Kawashima

  2. Department of Architecture and Architectural Systems, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto, 606-8501, Japan

    Naoki Katoh

Authors
  1. Tetsuo Asano
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  2. Naoki Katoh
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  3. Kazuhiro Kawashima
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Asano, T., Katoh, N. & Kawashima, K. A New Approximation Algorithm for the Capacitated Vehicle Routing Problem on a Tree. Journal of Combinatorial Optimization 5, 213–231 (2001). https://doi.org/10.1023/A:1011461300596

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  • DOI: https://doi.org/10.1023/A:1011461300596

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