The single-machine family scheduling problem of minimizing the number of late jobs has been known to be NP-hard, but whether it is NP-hard in the strong sense is cited as an open problem in several reviews. In this note, we prove that this problem is strongly NP-hard even if all set-up times and pro
Open shop scheduling to minimize the number of late jobs
โ Scribed by Christos Koulamas; George J. Kyparisis
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 63 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0894-069X
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โฆ Synopsis
We develop polynomial algorithms for several cases of the NP-hard open shop scheduling problem of minimizing the number of late jobs by utilizing some recent results for the open shop makespan problem. For the two machine common due date problem, we assume that either the machines or the jobs are ordered. For the m machine common due date problem, we assume that one machine is maximal and impose a restriction on its load.
๐ SIMILAR VOLUMES
We present the first polynomial-time algorithm for an open-shop problem with unit execution times, arbitrary release dates, and due dates. The objective is to minimize maximum lateness. 0 I995 John Wiley & Sons. Inc.
The paper considers the open shop scheduling problem to minimize the makespan, provided that one of the machines has to process the jobs according to a given sequence. We show that in the preemptive case the problem is polynomially solvable for an arbitrary number of machines. If preemption is not a
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"p H "p, r H " w H ; H ), t