Abstract
We study the multi-agent scheduling on a single machine with a fixed number of competing agents, in which, the objective function of each agent is either the number of tardy jobs or the makespan, and the goal of the problem is to minimize the weighted sum of agents’ objective functions. In the literature, the computational complexity of this problem was posed as open. By using enumerating, dynamic programming, and schedule-configuration, we show in this paper that the problem is solvable in polynomial time.
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Acknowledgments
The author would like to thank the associate editor and two anonymous referees for their constructive comments and kind suggestions. This research was supported by NSFC (11671368) and NSF-Henan (15IRTSTHN006)
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Yuan, J. Multi-agent scheduling on a single machine with a fixed number of competing agents to minimize the weighted sum of number of tardy jobs and makespans. J Comb Optim 34, 433–440 (2017). https://doi.org/10.1007/s10878-016-0078-9
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DOI: https://doi.org/10.1007/s10878-016-0078-9