Distributionally robust CVaR optimization for refinery integrated production–maintenance scheduling under uncertainty

In the petroleum refining industry, efficient production planning and maintenance scheduling are crucial for economic performance and operational efficiency. Moreover, the production processes face significant uncertainties stemming from market fluctuations and equipment failures. However, traditional optimization methods often treat production and maintenance independently and neglect the risk management associated with uncertainties in the production process, leading to unreliable plans and suboptimal execution. To address these issues, this paper proposes an innovative data-driven distributionally robust conditional value-at-risk (DRCVaR) method to tackle the integrated production–maintenance optimization problem under crude oil price uncertainty. By constructing confidence sets with $L_2$ norm constraints based on historical data, our approach directly links the model’s conservatism to the amount of available data, effectively managing risk. In addition, we propose robust linear transformation to simplify the min–max nonlinear problem into a conic constraint problem, enhancing solution efficiency and ensuring better operational stability. Refinery case studies demonstrate that the proposed DRCVaR consistently achieves a practical and acceptable solution, significantly outperforming state-of-the-art approaches.