Abstract
For single machine scheduling to minimize the number of tardy jobs with deadlines, Lawler showed in 1983 that the problem is binary NP-hard. But the exact complexity (unary NP-hard or pseudo-polynomial-time solvability) is a long- standing open problem. We show in this paper that the problem is unary NP-hard. Our research also implies that the scheduling problem for finding an optimal schedule to minimize the number of tardy jobs that also satisfies the restriction of deadlines is unary NP-hard. As a consequence, some multi-agent scheduling problems related to minimizing the number of tardy jobs and maximum lateness are unary NP-hard.
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Acknowledgments
We would like to thank the associate editor and two anonymous referees for their constructive comments and kind suggestions. This research was supported by NSFC(11271338) and NSF-Henan(15IRTSTHN006).
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Yuan, J. Unary NP-hardness of minimizing the number of tardy jobs with deadlines. J Sched 20, 211–218 (2017). https://doi.org/10.1007/s10951-016-0479-8
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DOI: https://doi.org/10.1007/s10951-016-0479-8