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. 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. We propose a 1.35078-approximation algorithm for the problem (exactly, \( (\sqrt {41} - 1)/4) \) , which is an improvement over the existing 1.5-approximation.
Research of this paper is partly supported by the Grant-in-Aid for Scientific Research on Priority Areas (B) by the Ministry of Education, Science, Sports and Culture of Japan.
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© 1999 Springer-Verlag Berlin Heidelberg
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Asano, T., Kawashima, K., Katoh, N. (1999). A New Approximation Algorithm for the Capacitated Vehicle Routing Problem on a Tree. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_32
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DOI: https://doi.org/10.1007/3-540-46632-0_32
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