Abstract
This paper considers a multi-agent scheduling problem, in which each agent has a set of non-preemptive jobs, and jobs of all agents are to be processed on m identical parallel machines. The objective is to find a schedule to minimize the makespan of each agent. For an agent, the definition of \(\alpha \) point is introduced, based on which an approximation algorithm is proposed for the problem. In the obtained schedule, the agent with the ith smallest \(\alpha \) point value is the ith completed agent, and the agent’s completion time is at most \(i+ \left( \frac{1}{3}-\frac{1}{3m}\right) \) times its minimum makespan. Finally, we show the performance analysis is tight.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Agnetis, A., Billaut, J. C., Gawiejnowicz, S., Pacciarelli, D., & Soukhal, A. (2014). Multiagent scheduling-models and algorithms. Berlin: Springer. ISBN 978-3-642-41879-2.
Agnetis, A., Mirchandani, P. B., Pacciarelli, D., & Pacifici, A. (2004). Scheduling problem with two competing agents. Operations Research, 52, 229–242.
Agnetis, A., Pacciarelli, D., & Pacifici, A. (2007). Multi-agent single machine scheduling. Annals of Operations Research, 150, 3–15.
Agnetis, A., Pascale, G., & Pacciarelli, D. (2009). A Lagrangian approach to single-machine scheduling problems with two competing agents. Journal of Scheduling, 12, 401–415.
Cheng, T. C. E., Ng, C. T., & Yuan, J. J. (2006). Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theoretical Computer Science, 362, 273–281.
Cheng, T. C. E., Ng, C. T., & Yuan, J. J. (2008). Multi-agent scheduling on a single machine with max-form criteria. European Journal of Operational Research, 188, 603–609.
Fan, B. Q., Cheng, T. C. E., Li, S. S., & Feng, Q. (2013). Bounded parallel-batching scheduling with two competing agents. Journal of Scheduling, 16, 261–271.
Lee, K., Choi, B.-C., Leung, J. Y.-T., & Pinedo, M. L. (2009). Approximation algorithms for multi-agent scheduling to minimize total weighted completion time. Information Processing Letters, 109, 913–917.
Leung, J. Y.-T., Pinedo, M., & Wan, G. (2010). Competitive two-agent scheduling and its applications. Operations Research, 58, 458–469.
Li, S., & Yuan, J. J. (2012). Unbounded parallel-batching scheduling with two competitive agents. Journal of Scheduling, 15, 629–640.
Pinedo, M. L. (2011). Scheduling-theory, algorithm, and systems (4th ed.). New York: Springer.
Saule, E., & Trystram, D. (2009). Multi-users scheduling in parallel systems. In Proceedings of IEEE international parallel and distributed processing symposium 2009, Roma, Italy (pp. 1–9).
Zhao, K., Lu, X., & Gu, M. (2016). A new approximation algorithm for multi-agent scheduling to minimize makespan on two machines. Journal of Scheduling, 19, 21–31.
Acknowledgements
We are grateful to the referees for providing comments for our paper. The authors thank Dr. Kejun Zhao for reviewing the paper before its formally submission. This work is supported by National Natural Science Foundation of China (Grant Nos. 11201282, 61304209, and 11371137), Innovation Program of Shanghai Municipal Education Commission (Grant No. 14YZ127), Humanities and Social Sciences planning fund of Ministry of Education (Grant No. 17YJAZH024), Pre-research project for young teachers from SUFE, and National project follow-up research project from SUFE.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gu, M., Gu, J. & Lu, X. An algorithm for multi-agent scheduling to minimize the makespan on m parallel machines. J Sched 21, 483–492 (2018). https://doi.org/10.1007/s10951-017-0546-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-017-0546-9