In pursuit of enhancing the comprehensive efficiency of production systems, our study focused on the joint optimization problem of scheduling and machine maintenance in scenarios where product rework occurs. The primary challenge lies in the interdependence between product \underline{q}uality, machine \underline{r}eliability, and \underline{p}roduction scheduling, compounded by the uncertainties from machine degradation and product quality, which is prevalent in sophisticated manufacturing systems. To address this issue, we investigated the dynamic relationship among these three aspects, named as QRP-co-effect. On this basis, we constructed an optimization model that integrates production scheduling, machine maintenance, and product rework decisions, encompassing the context of stochastic degradation and product quality uncertainties within a mixed-integer programming problem. To effectively solve this problem, we proposed a dual-module solving framework that integrates planning and evaluation for solution improvement via dynamic communication. By analyzing the structural properties of this joint optimization problem, we devised an efficient solving algorithm with an interactive mechanism that leverages \emph{in-situ} condition information regarding the production system's state and computational resources. The proposed methodology has been validated through comparative and ablation experiments. The experimental results demonstrated the significant enhancement of production system efficiency, along with a reduction in machine maintenance costs in scenarios involving rework.

翻译：为提高生产系统的综合效率，本研究聚焦于存在产品返工情形下的调度与机器维护联合优化问题。主要挑战在于产品质量、机器可靠性与生产调度之间的相互依存关系，加之机器性能退化与产品质量不确定性所带来的复杂性，这在精密制造系统中尤为普遍。为解决此问题，我们深入探究了这三个方面之间的动态关联，并将其命名为QRP协同效应。基于此，我们构建了一个集成生产调度、机器维护与产品返工决策的优化模型，将随机退化与产品质量不确定性纳入混合整数规划问题框架。为有效求解该问题，我们提出了一个双模块求解框架，通过动态通信机制整合规划与评估模块以实现解的质量改进。通过分析该联合优化问题的结构特性，我们设计了一种高效的交互式求解算法，该算法能够利用生产系统状态与计算资源的原位条件信息。所提方法已通过对比实验与消融实验得到验证。实验结果表明，在存在返工的场景中，该方法能显著提升生产系统效率，同时降低机器维护成本。