In chemical manufacturing processes, equipment degradation can have a significant impact on process performance or cause unit failures that result in considerable downtime. Hence, maintenance planning is an important consideration, and there have been increased efforts in scheduling production and maintenance operations jointly. In this context, one major challenge is the inherent uncertainty in predictive equipment health models. In particular, the probability distribution associated with the stochasticity in such models is often difficult to estimate and hence not known exactly. In this work, we apply a distributionally robust optimization (DRO) approach to address this problem. Specifically, the proposed formulation optimizes the worst-case expected outcome with respect to a Wasserstein ambiguity set, and we apply a decision rule approach that allows multistage mixed-integer recourse. Computational experiments, including a real-world industrial case study, are conducted, where the results demonstrate the significant benefits from binary recourse and DRO in terms of solution quality.

中文翻译：

---

用于集成生产和维护调度的多级分布式稳健优化

在化学制造过程中，设备退化会对过程性能产生重大影响或导致设备故障，从而导致相当长的停机时间。因此，维护计划是一个重要的考虑因素，并且已经加大了联合安排生产和维护操作的力度。在这种情况下，一个主要挑战是预测设备健康模型中固有的不确定性。特别是，与此类模型中的随机性相关的概率分布通常难以估计，因此无法准确了解。在这项工作中，我们应用分布式鲁棒优化（DRO）方法来解决这个问题。具体来说，所提出的公式优化了关于 Wasserstein 歧义集的最坏情况预期结果，我们应用了一种决策规则方法，允许多阶段混合整数追索。进行了包括实际工业案例研究在内的计算实验，结果证明了二元资源和 DRO 在解决方案质量方面的显着优势。