Multistage distributionally robust optimization for integrated production and maintenance scheduling

Abstract

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.

Two-Stage Robust Optimization with Decision Dependent Uncertainty

“…A general type of DDU-based robust linear optimization model is considered in Nohadani and Sharma (2018), where the model is proven to be NP-complete. General DDU set construction and modeling methods are investigated in Lappas and Gounaris (2018) and Feng et al (2021). It is noted that single stage DDU-based RO can often be reformulated as monolithic models computable by professional mixed integer program (MIP) solvers.…”

“…It is interesting to note a couple of studies presented in Vayanos et al (2020a,b) that adopt DDU sets to capture uncertain information whose availability is decision-dependent, a clear demonstration of active learning. Similarly, DRO with DDUs has also been studied recently (Noyan et al, 2018;Luo and Mehrotra, 2020;Ryu and Jiang, 2019;Yu and Shen, 2020;Doan, 2022;Basciftci et al, 2021;Feng et al, 2021). One assumption often made is that a DDU set has a finite decision-independent support.…”

A Model Predictive Control for Lot Sizing and Scheduling Optimization in the Process Industry under Bidirectional Uncertainty of Production Ability and Market Demand

“…(6) Intermediate inventories are allowed between different processes in the production process, but the number of intermediate inventories is limited. (7) When the equipment on a particular process is switched from the production process of the current product to the production of the next product, the equipment needs to be cleaned and adjusted. (8) e demand for products and the production ability of equipment are uncertain.…”

“…It can be seen that the existing historical order demand is analyzed to deal with the uncertain future market is a vital link [5,6]. In addition, with the growth of the processing cycle, a series of uncertain situations such as wear, aging, and even equipment failure will occur in the actual application process [7,8]. e abovementioned conditions will lead to a decline in its production ability.…”

Distributionally robust optimization for the closed‐loop supply chain design under uncertainty

“…In other words, the DRO approach is stable with regards to the underlying probability distributions, and shows better performance in out‐of‐sample simulations than SP and RO 24,25 . From the perspective of ambiguity set construction, DRO approaches covered in literature can be classified as moment‐based 26,27 and Wasserstein‐distance based 24,25,28 . Ambiguity sets constructed via the Wasserstein metric exhibit favorable asymptotic and finite sample guarantees 29…”