Data-Driven Chance-Constrained Mixed Integer Nonlinear Bi-level Optimisation Via Copulas: Application To Integrated Planning And Scheduling Problems

Planning and scheduling are integral components of process supply chains. The presence of data correlation, particularly multivariate demand data dependency, can pose significant challenges to the decision-making process. This necessitates the consideration of dependency structures inherent in the underlying data to generate good-quality, feasible solutions to optimisation problems such as planning and scheduling. This work proposes a chance-constrained optimisation framework integrated with copulas, a non-parametric data estimation technique to forecast uncertain demand levels in accordance with specified risk thresholds in the context of a planning and scheduling problem. We focus on the integrated planning and scheduling problem following a bi-level optimisation formulation. The estimated demand forecasts are subsequently utilised within the Data-driven Optimisation of bi-level Mixed-Integer NOnlinear problems (DOMINO) framework to solve the integrated optimisation problem, and derive decisions with guaranteed demand satisfaction rates. Computational experiments demonstrate that our proposed copula-based chance-constrained optimisation framework can incorporate demand correlation and achieve higher joint demand satisfaction rate, lower total costs with higher efficiency.