Stackelberg-game-based modeling and optimization for supply chain design and operations: A mixed integer bilevel programming framework

• An MIBP modeling and optimization framework under Stackelberg games is proposed.
• The model allows for discrete decisions in the follower's optimization problem.
• An improved reformulation and decomposition algorithm for MIBPs is developed.
• A non-cooperative integrated forestry and biofuel supply chain is studied.

While Stackelberg leader–follower games and bilevel programming have become increasingly prevalent in game-theoretic modeling and optimization of decentralized supply chains, existing models can only handle linear programming or quadratic programming followers’ problems. When discrete decisions are involved in the follower's problem, the resulting lower-level mixed-integer program prohibits direct transformation of the bilevel program into a single-level mathematical program using the KKT conditions. To address this challenge, we propose a mixed-integer bilevel programming (MIBP) modeling framework and solution algorithm for optimal supply chain design and operations, where the follower is allowed to have discrete decisions, e.g., facility location, technology selection, and opening/shutting-down of production lines. A reformulation-and-decomposition algorithm is developed for global optimization of the MIBP problems. A case study on an integrated forestry and biofuel supply chain is presented to demonstrate the application, along with comparisons to conventional centralized modeling and optimization methods.