Bilevel programming approach for manufacturing facility investment optimization with non-cooperative suppliers and customers

We propose a bilevel mixed-integer nonlinear programming (MINLP) model for the optimal decision-making in manufacturing facility investment considering non-cooperative suppliers and customers. Interactions among the supply chain participants are captured through a single-leader-multiple-follower Stackelberg game under the generalized Nash equilibrium assumption. Given a three-echelon superstructure, the lead manufacturer in the middle echelon first optimizes its design and operational decisions, including facility location, sizing, and technology selection, material input/output and price setting. The following suppliers and customers in the upstream and downstream then optimize their transactions with the manufacturer to maximize their individual profits. By replacing the lower level linear programs with their KKT conditions, we transform the bilevel MINLP into a single-level nonconvex MINLP, which is further globally optimized using an improved branch-and-refine algorithm. To illustrate the application, two case studies are presented.