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Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard. (English) Zbl 0908.90164

Summary: In 1954, Johnson gave an efficient algorithm for minimizing makespan in a two-machine flow shop; there is no advantage to preemption in this case. McNaughton’s wrap-around rule of 1959 finds a shortest preemptive schedule on identical parallel machines in linear time. A similarly efficient algorithm is unlikely to exist for the simplest common generalization of these problems. We show that preemptive scheduling in a two-stage flow shop with at least two identical parallel machines in one of the stages so as to minimize makespan is NP-hard in the strong sense.

MSC:

90B35 Deterministic scheduling theory in operations research
90C60 Abstract computational complexity for mathematical programming problems
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