Data-Driven Chance-Constrained Mixed Integer Nonlinear Bi-level Optimisation Via Copulas: Application To Integrated...

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.