This paper studies an integrated optimization problem of production scheduling and flexible preventive maintenance (PM) in a multi-state single machine system with deteriorating effects. A flexible PM strategy is proposed to proactively cope with machine failures while ensuring relatively regular PM intervals, which is composed of time-based PM (TBPM) and condition-based PM (CBPM). TBPM is conducted within every flexible time window and CBPM is implemented immediately after the most deteriorated yet still functional state. An illustrative case is presented using the enumeration approach to demonstrate the integration of production scheduling and machine maintenance. Then, Q-learning-based solution framework (QLSF) is further designed with proper state and action sets and reward functions to facilitate the determination of appropriate production scheduling rule under the constraint of the flexible maintenance. Numerical experiments show that the proposed QLSF outperforms the other four state-of-the-art scheduling rules in different scenarios. Moreover, the performance of the proposed flexible PM strategy is also examined and validated in comparison with three candidate maintenance strategies, i.e., run-to-failure corrective maintenance (CM), combination of TBPM and CM, and CBPM. The proposed flexible maintenance and solution approach can enrich the relevant academic knowledge base, and provide managerial insights and guidance in practical production systems.

本文研究了多状态单机系统中的生产调度和柔性预防性维护（PM）的集成优化问题，其效果不断恶化。提出了一种灵活的 PM 策略来主动应对机器故障，同时确保相对规律的 PM 间隔，它由基于时间的 PM（TBPM）和基于条件的 PM（CBPM）组成。TBPM 在每个灵活的时间窗口内进行，而 CBPM 在最恶化但仍然有效的状态之后立即实施。使用枚举方法展示了一个说明性案例，以演示生产调度和机器维护的集成。然后，基于 Q-learning 的解决方案框架 (QLSF) 进一步设计了适当的状态和动作集以及奖励函数，以促进在灵活维护的约束下确定适当的生产调度规则。数值实验表明，所提出的 QLSF 在不同场景下优于其他四种最先进的调度规则。此外，还检查和验证了所提出的灵活 PM 策略的性能，并与三种候选维护策略进行了比较，即运行到故障的纠正性维护 (CM)、TBPM 和 CM 的组合以及 CBPM。所提出的灵活维护和解决方法可以丰富相关的学术知识库，并为实际生产系统提供管理见解和指导。