A Capacitated Vehicle Routing Problem on a Tree

Authors:
Shin-ya Hamaguchi;Naoki Katoh
Affiliations:
-;-
Venue:
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Year:
1998

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Abstract

In this paper we deal with 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 show that the problem is NP-complete and propose a 1.5-approximation algorithm for the problem. We also give some computational results.