Abstract
The single vehicle scheduling problems based on tree/cycle networks are studied in this paper. Each customer, assumed as a vertex on the given network, has a release time and a service time requirement. The single vehicle starts from the depot and aims to serve all the customers. The objective of the problem is to find the optimal routing schedule so as to minimize the makespan. We provide a \(\frac{16}{9}\)-approximation algorithm and a \(\frac{48}{25}\)-approximation algorithm for the tour-version and path-version of single vehicle scheduling problem on a tree, respectively. For the tour-version and path-version of single vehicle scheduling problem on a cycle, we present a \(\frac{5}{3}\)-approximation algorithm and a \(\frac{29}{17}\)-approximation algorithm, respectively.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Augustine JE, Seiden SS (2004) Linear time approximation schemes for vehicle scheduling problems. Theor Comput Sci 324:147–160
Bao X, Liu Z (2012) Approximation algorithms for single vehicle scheduling problems with release and service times on a tree or cycle. Theor Comput Sci 434:1–10
Bhattacharya B, Hu Y (2010) Approximation algorithms for the muti-vehicle scheduling problems. Lect Notes Comput Sci 6507:192–205
Bhattacharya B, Carmi P, Hu Y, Shi Q (2008) Single vehicle scheduling problems on path/tree/cycle networks with release and handling times. Lect Notes Comput Sci 5369:800–811
Gaur DR, Gupta A, Krishnamurti R (2003) A \(\frac{5}{3}\)-approximation algorithm for scheduling vehicles on a path with release and handling times. Inf Process Lett 86:87–91
Karuno Y, Nagamochi H (2003) \(2\)-approximation algorithms for the multi-vehicle scheduling problem on a path with release and handling times. Discrete Appl Math 129:433–447
Karuno Y, Nagamochi H, Ibaraki T (1997) Vehicle scheduling on a tree with release and handling times. Ann Oper Res 69:193–207
Karuno Y, Nagamochi H, Ibaraki T (2002) Better approximation ratios for the single-vehicle scheduling problems on line-shaped networks. Networks 39(4):203–209
Nagamochi H, Mochizuki K, Ibaraki T (1997) Complexity of the single vehicle scheduling problem on graphs. Inf Syst Oper Res 35:256–276
Psaraftis HN, Solomon MM, Magnanti TL, Kim T-U (1990) Routing and scheduling on a shoreline with release times. Manag Sci 36:212–223
Tsitsiklis JN (1992) Special cases of traveling salesman and repairman problems with time windows. Networks 22:263–282
Yu W, Liu Z (2009) Vehicle routing problems on a line-shaped network with release time constraints. Oper Res Lett 37:85–88
Yu W, Liu Z (2011) Single vehicle scheduling problems with release and service times on a line. Networks 57:128–134
Acknowledgements
The authors would like to thank the associated editor and the anonymous referees for their constructive comments and kind suggestions. This research was supported by the National Natural Science Foundation of China under Grant Nos. 11871213, 71431004 and 11371137.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wu, Y., Lu, X. Improved algorithms for single vehicle scheduling on tree/cycle networks. J Comb Optim 42, 565–580 (2021). https://doi.org/10.1007/s10878-019-00420-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-019-00420-2