While job scheduling problems have been studied extensively, scheduling problems with endogenous yield rates that may be affected by predictive maintenance is not thoroughly investigated. In this study, we consider the optimization of a joint predictive maintenance and job scheduling problem for the minimization of total shortage penalty. As maintenance may be conducted to raise machine yield rates, machine production rates and job processing times become endogenous, and the optimization problem is different from traditional scheduling problems. We formulate a mixed integer program for this problem and develop a heuristic algorithm based on Tabu search. We demonstrate the effectiveness of our algorithm through numerical experiments and a way of estimating the yield declining rate with industry defect and maintenance records. Note to Practitioners—This work is motivated by the real need of our industry collaborator, red electronics manufacturer. Every morning, the manufacturer chooses up to three out of eleven photolithography machines to conduct maintenance. Conducting maintenance helps raise machine yield rates to decrease the number of defects in expectation. However, the production schedule of some jobs must be postponed, and delay and shortage may arise. The decision is thus to schedule jobs as well as maintenance to find a balance between yield loss and shortage loss. We help the manufacturer by formulating an optimization model and develop an algorithm to solve the model. The algorithm may be applied to similar cases when one needs to schedule maintenance and production processes at the same time.

中文翻译：

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具有内生收益率的联合预测维护和作业调度问题的优化

尽管已经对作业调度问题进行了广泛研究，但尚未彻底研究可能受预测性维护影响的内生收益率的调度问题。在这项研究中，我们考虑优化联合预测性维护和作业调度问题，以最大限度地减少总短缺损失。由于可以进行维护以提高机器良率，因此机器生产率和作业处理时间成为内生的，优化问题不同于传统的调度问题。我们为这个问题制定了一个混合整数程序，并开发了一种基于禁忌搜索的启发式算法。我们通过数值实验证明了我们算法的有效性，并通过行业缺陷和维护记录来估计产量下降率。从业者须知——这项工作的动机是我们的行业合作者红色电子制造商的真正需求。每天早上，制造商会从 11 台光刻机中选择多达 3 台进行维护。进行维护有助于提高机器良率，以减少预期缺陷的数量。但是，一些工作的生产计划必须推迟，可能会出现延误和短缺。因此，决定是安排作业和维护，以在产量损失和短缺损失之间找到平衡。我们通过制定优化模型并开发求解模型的算法来帮助制造商。当需要同时安排维护和生产过程时，该算法可以应用于类似的情况。