In this paper, we consider the two-machine flow shop scheduling with an operator non-availability period in the first stage to minimize makespan, where the operator non-availability period is an open time interval in which a job can neither start nor complete. We first prove that the problem is NP-hard, even if the length of the operator non-availability period is no more than the processing time of any job on the first machine. Then we show that Johnson’s rule is a 2-approximation algorithm and the bound is tight. Moreover, a better tight 3/2-approximation algorithm is provided.

中文翻译：

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两台机器的流水车间调度，具有操作员的不可用时间，以最大程度地缩短工期

在本文中，我们考虑第一阶段具有操作员不可用时间段的两机流水车间调度，以最大程度地缩短工期，其中操作员不可用时间段是工作既无法启动也无法完成的开放时间间隔。我们首先证明问题是NP困难的，即使操作员不可用时间的长度不超过第一台机器上任何作业的处理时间。然后，我们证明Johnson规则是2逼近算法，并且边界很紧。此外，提供了更好的紧3/2近似算法。