Distributionally robust optimization for planning and scheduling under uncertainty

Distributionally robust optimization (DRO) is an emerging and effective method to address the inexactness of probability distributions of uncertain parameters in decision-making under uncertainty. We propose an effective DRO framework for planning and scheduling under demand uncertainties. A novel data-driven approach is proposed to construct ambiguity sets based on principal component analysis and first-order deviation functions, which help excavating accurate and useful information from uncertainty data. Moreover, it leads to mixed-integer linear reformulations of planning and scheduling problems. To account for the multi-stage sequential decision-making structure in process operations, we further develop multi-stage DRO models and adopt affine decision rules to address the computational issue. Applications in industrial-scale process network planning and batch process scheduling demonstrate that, the proposed DRO approach can effectively leverage uncertainty data information, better hedge against distributional ambiguity, and yield more profits.