Abstract We examine machine scheduling problems that have been inspired by the production environment of semiconductor manufacturing. In semiconductor manufacturing a job processing machine is often enforced to go through a preventive maintenance operation with an objective of minimizing the wafer quality risk. In this research such periodic machine maintenance is considered for single machine and flow shop scheduling models. For the flow shop model we focus on an important special case with proportionate processing times. We first present that the maximum lateness and the total completion time in a single machine can be minimized by a monotone scheduling rule. For the maximum lateness it is shown that the scheduling rule of a single machine special case is also optimal for a proportionate flow shop. However, for the total completion time we observe that the scheduling algorithm of a single machine is not necessarily optimal for its extension to a proportionate flow shop. We prove that the total completion time in a proportionate flow shop is solvable by an O ( n 2 ) algorithm, and even the total weighted completion time is minimized with the same computational complexity. Lastly, we discuss how these results are further generalized when setup operations are additionally considered.

中文翻译：

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通过预防性机器维护安排成比例的流水车间

摘要 我们研究了受半导体制造生产环境启发的机器调度问题。在半导体制造中，作业处理机器经常被强制执行预防性维护操作，目的是将晶片质量风险降至最低。在这项研究中，针对单机和流水车间调度模型考虑了这种定期机器维护。对于流水车间模型，我们关注具有成比例处理时间的重要特殊情况。我们首先提出了单调调度规则可以最小化单个机器中的最大延迟和总完成时间。对于最大延迟，单机特例的调度规则对于比例流水车间也是最优的。然而，对于总完成时间，我们观察到单台机器的调度算法对于其扩展到成比例的流水车间不一定是最佳的。我们证明了比例流水车间的总完成时间可以通过 O ( n 2 ) 算法求解，并且在相同的计算复杂度下，甚至可以最小化总加权完成时间。最后，我们讨论了在额外考虑设置操作时如何进一步推广这些结果。