In this paper, we study a new type of flow shop and open shop models, which handle so-called “pliable” jobs: their total processing times are given, but individual processing times of operations which make up these jobs are flexible and need to be determined. Our analysis demonstrates that many versions of flow shop and open shop problems with pliable jobs appear to be computationally easier than their traditional counterparts, unless the jobs have job-dependent restrictions imposed on minimum and maximum operation lengths. In the latter case, most problems with pliability become NP-hard even in the case of two machines.

中文翻译：

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灵活作业的车间调度问题

在本文中，我们研究了一种新型的流水车间和开放式车间模型，它们处理所谓的“柔韧”作业：它们的总处理时间是给定的，但构成这些作业的各个操作的处理时间是灵活的，需要被确定。我们的分析表明，许多版本的流水车间和开放车间问题似乎比传统的同类问题在计算上更容易，除非这些工作对最小和最大操作长度施加了与工作相关的限制。在后一种情况下，即使在两台机器的情况下，大多数柔韧性问题也变成了 NP-hard 问题。