Bi-level Mixed-Integer Data-Driven Optimization of Integrated Planning and Scheduling Problems.

Abstract

Supply chain management is an interconnected problem that requires the coordination of various decisions and elements across long-term (i.e., supply chain structure), medium-term (i.e., production planning), and short-term (i.e., production scheduling) operations. Traditionally, decision-making strategies for such problems follow a sequential approach where longer-term decisions are made first and implemented at lower levels, accordingly. However, there are shared variables across different decision layers of the supply chain that are dictating the feasibility and optimality of the overall supply chain performance. Multi-level programming offers a holistic approach that explicitly accounts for this inherent hierarchy and interconnectivity between supply chain elements, however, requires more rigorous solution strategies as they are strongly NP-hard. In this work, we use the DOMINO framework, a data-driven optimization algorithm initially developed to solve single-leader single-follower bi-level mixed-integer optimization problems, and further develop it to address integrated planning and scheduling formulations with multiple follower lower-level problems, which has not received extensive attention in the open literature. By sampling for the production targets over a pre-specified planning horizon, DOMINO deterministically solves the scheduling problem at each planning period per sample, while accounting for the total cost of planning, inventories, and demand satisfaction. This input-output data is then passed onto a data-driven optimizer to recover a guaranteed feasible, near-optimal solution to the integrated planning and scheduling problem. We show the applicability of the proposed approach for the solution of a two-product planning and scheduling case study.