Unary NP-hardness of minimizing the number of tardy jobs with deadlines

Jinjiang Yuan ()
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Jinjiang Yuan: Zhengzhou University

Journal of Scheduling, 2017, vol. 20, issue 2, No 7, 218 pages

Abstract: 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.

Keywords: Scheduling; Number of tardy jobs; Deadlines; NP-hard (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10951-016-0479-8

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