Abstract
This paper studies a multi-agent scheduling problem on two identical parallel machines. There are g agents, and each agent’s objective is to minimize its makespan. We present an approximation algorithm such that the performance ratio of the makespan achieved by our algorithm relative to the minimum makespan is no more than \(i+\frac{1}{6}\) for the ith \((i=1,2,\ldots ,g)\) completed agent. Moreover, we show that the performance ratio is tight.
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References
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.
Agnetis, A., Billaut, J. C., Gawiejnowicz, S., Pacciarelli, D., & Soukhal, A. (2014). Multiagent scheduling—models and algorithms, Springer, Berlin. ISBN 978-3-642-41879-2.
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.
Graham, R. L. (1969). Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics, 17, 416–429.
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. (2010). Scheduling (4th ed.). Berlin: Springer.
Saule, E., & Trystram, D. (2009). Multi-users scheduling in parallel systems. In Proceedings of IEEE International Parallel and Distributed Processing Symposium 2009, Washington, DC, 1C9.
Acknowledgments
The authors would like to thank the editor and anonymous referees for their helpful comments and suggestions which significantly improve the results and presentation of this paper. This research is supported by National Natural Science of China (11371137, 11201282) and the Fund for the Doctoral Program of China (20120074110021).
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Zhao, K., Lu, X. & Gu, M. A new approximation algorithm for multi-agent scheduling to minimize makespan on two machines. J Sched 19, 21–31 (2016). https://doi.org/10.1007/s10951-015-0460-y
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DOI: https://doi.org/10.1007/s10951-015-0460-y