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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
I. Averbakh and O. Berman, Sales-delivery man problems on treelike networks, Networks, 25 (1995), 45–58.
J.P. Crouzeix, J.A. Ferland and S. Schaible, An algorithm for generalized fractional programs, J. of Optimization Theory and Applications, 47 (1985), 35–49.
M.L. Fischer. Vehicle Routing. in Network Routing, Handbooks in Operations Research and Management Science, 8, Ball, M. O., T. L. Magnanti, C. L. Monma and G. L. Nemhauser (Eds.), Elsevier Science, Amsterdam, 1–33, 1995.
G. Frederickson, Notes on the complexity of a simple transportation problem, SIAM J. Computing, 22-1 (1993), 57–61.
B.L. Golden and A. A. Assad (Eds.). Vehicle Routing: Methods and Studies, Studies in Manag. Science and Systems 16, North-Holland Publ., Amsterdam, 1988.
S. Hamaguchi and N. Katoh. A Capacitate Vehicle Routing Problem on a Tree, Proc. of ISAAC’98, LNCS 1533, Springer-Verlag 397–406, 1998.
Y. Karuno, H. Nagamochi, T. Ibaraki, Vehicle Scheduling on a Tree with Release and Handling Times, Proc. of ISAAC’93, LNCS 762, Springer-Verlag 486–495, 1993.
Y. Karuno, H. Nagamochi, T. Ibaraki, Vehicle Scheduling on a Tree to Minimize Maximum Lateness, Journal of the Operations Research Society of Japan, Vol. 39, No.3 (1996) 345–355.
M. Labbé, G. Laporte and H. Mercure. Capacitated Vehicle Routing Problems on Trees, Operations Research, Vol. 39 No. 4 (1991) 616–622.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-46632-0_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66916-6
Online ISBN: 978-3-540-46632-1
eBook Packages: Springer Book Archive