Multistage distributionally robust optimization for integrated production and maintenance scheduling

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.