Polynomial time algorithms for minimizing the weighted number of late jobs on a single machine with equal processing times

Polynomial time algorithms for minimizing the weighted number of late jobs on a single machine with equal processing times

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Article ID: iaor2001723
Country: United Kingdom
Volume: 2
Issue: 6
Start Page Number: 245
End Page Number: 252
Publication Date: Nov 1999
Journal: Journal of Scheduling
Authors:
Keywords: production
Abstract:

We study the problem of minimizing the weighted number of late jobs to be scheduled on a single machine when processing times are equal. In this paper, we show that this problem, as well as its preemptive variant, are strongly polynomial. When preemption is not allowed (1|pj = p, rj | ∑ wjUj), the problem can be solved in O(n7). In the preemptive case, (1|pj = p, pmtn, rj |wjUj), the problem can be solved in O(n10). Both algorithms are based upon dynamic programming.

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