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.
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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.
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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
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DOI: https://doi.org/10.1007/s10951-017-0546-9