期刊
JOURNAL OF SCHEDULING
卷 22, 期 6, 页码 663-676出版社
SPRINGER
DOI: 10.1007/s10951-019-00617-7
关键词
Scheduling; Flow-shop; Just-in-time; Parameterized complexity; Fixed-parameter tractability
资金
- United States-Israel Binational Science Foundation (BSF) [2016049]
- People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA [631163.11]
- Israel Science Foundation [551145/14]
We study the parameterized complexity of a set of flow-shop scheduling problems in which the objective is to maximize the weighted number of just-in-time jobs. Our analysis focuses on the case where the number of due dates is considerably smaller than the number of jobs and thus can be considered as a parameter. We prove that the two-machine problem is W[1]-hard with respect to this parameter, even if all processing times on the second machine are of unit length, while the problem is in XP when parameterized by the number of machines combined with the number of different due dates. We then move on to study the tractability of the problem when combining the number of different due dates with either the number of different weights or the number of different processing times on the first machine. We prove that in both cases the problem is fixed-parameter tractable for the two-machine case and is W[1]-hard for three or more machines.
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