Bilevel optimization of mixed-integer nonlinear integrated planning and scheduling problems using the DOMINO framework.

Abstract

We study the solution of integrated planning and scheduling problems that are formulated as bilevel programming problems with mixed-integer nonlinear lower levels using data-driven optimization algorithms. Due to their inherent interdependence, multi-scale nature, and volatile market conditions, decision-making in such multi-level supply chain networks poses challenging task. Traditionally, these problems are addressed sequentially but, this approach often results in production schedules that are not feasible. Motivated by this, we formulate enterprise-wide decision-making problems with linear production planning and mixed-integer nonlinear scheduling level as a bilevel optimization problem. We solve the resulting integrated problem using the DOMINO framework which is a data-driven optimization strategy to handle general constrained bilevel optimization problems. We demonstrate our approach on case studies with varying complexities from crude oil scheduling using a continuous-time formulation to scheduling of continuous manufacturing processes using a traveling salesman problem formulation. The results show that DOMINO can address bilevel programming problems with high-dimensional mixed-integer nonlinear lower levels and can be applied to complex integrated enterprise-wide optimization problems, regardless of the lower-level formulation type.