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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 |

### Keywords:

NP-hardness; preemptive scheduling; two-stage flow shop; identical parallel machines; makespan
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\textit{J. A. Hoogeveen} et al., Eur. J. Oper. Res. 89, No. 1, 172--175 (1996; Zbl 0908.90164)

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### References:

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