Game-theoretic modeling and optimization of multi-echelon supply chain design and operation under Stackelberg game and market equilibrium

We propose a bilevel mixed-integer nonlinear programming (MINLP) model for the optimal design and planning of non-cooperative supply chains from the manufacturer's perspective. 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. We also present two case studies, including a county-level biofuel supply chain in Illinois, to illustrate the application of the proposed modeling and solution methods.