Abstract
In this paper, we consider the single vehicle scheduling problem (SVSP) on networks. Each job, located at some node, has a release time and a handling time. The vehicle starts from a node (depot), processes all the jobs, and then returns back to the depot. The processing of a job cannot be started before its release time, and its handling time indicates the time needed to process the job. The objective is to find a routing schedule of the vehicle that minimizes the completion time. When the underlying network is a path, we provide a simple 3/2-approximation algorithm for SVSP where the depot is arbitrarily located on the path, and a 5/3-approximation algorithm for SVSP where the vehicle’s starting depot and the ending depot are not the same. For the case when the network is a tree network, we show that SVSP is polynomially approximable within 11/6 of optimal. All these results are improvements of the previous results [2,4]. The approximation ratio is improved when the tree network has constant number of leaf nodes. For cycle networks, we propose a 9/5-approximation algorithm and show that SVSP without handling times can be solved exactly in polynomial time. No such results on cycle networks were previously known.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Augustine, J.E., Seiden, S.: Linear time approximation schemes for vehicle scheduling problems. Theoretical Comput. Sci. 324(2-3), 147–160 (2004)
Gaur, D.R., Gupta, A., Krishnamurti, R.: A 5/3-approximation algorithm for scheduling vehicles on a path with release and handling times. Inform. Proc. Let. 86(2), 87–91 (2003)
Karuno, Y., Nagamochi, H., Ibaraki, T.: A 1.5-approximation for single vehicle scheduling problem on a line with release and handling times. In: Proc. ISCIE/ASME, vol. 3, pp. 1363–1368 (1998)
Karuno, Y., Nagamochi, H., Ibaraki, T.: Vehicle scheduling on a tree with release and handling time. Ann. Oper. Res. 69, 193–207 (1997)
Karuno, Y., Nagamochi, H.: An approximability result of the multi-vehicle scheduling problem on a path with release and handling times. Theoretical Comput. Sci. 312, 267–280 (2004)
Karuno, Y., Nagamochi, H.: 2-approximation algorithms for the multi-vehicle scheduling problem on a path with release and handling times. Discrete Appl. Math. 129, 433–447 (2003)
Nagamochi, H., Mochizuki, K., Ibaraki, T.: Complexity of the single vehicle scheduling problem on graphs. Inform. Systems Oper. Res. 35(4), 256–276 (1997)
Psaraftis, H., Solomon, M., Magnanti, T., Kim, T.-U.: Routing and scheduling on a shoreline with release times. Management Sci. 36, 212–223 (1990)
Tsitsiklis, J.: Special cases of traveling salesman and repairman problems with time windows. Networks 22(3), 263–282 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bhattacharya, B., Carmi, P., Hu, Y., Shi, Q. (2008). Single Vehicle Scheduling Problems on Path/Tree/Cycle Networks with Release and Handling Times. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_70
Download citation
DOI: https://doi.org/10.1007/978-3-540-92182-0_70
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92181-3
Online ISBN: 978-3-540-92182-0
eBook Packages: Computer ScienceComputer Science (R0)