A novel stackelberg game-theoretic optimization model for interaction between two closed-loop supply chains with a queueing approach

Supply chain coordination is often facilitated through contracts, but these contracts can present numerous issues, such as production and distribution coordination problems, a lack of a holistic supply chain view, and long-term incompatibility. Game theory is a well-known method for finding solutions to these coordination problems. This research aims to evaluate communication and cooperation efficiency among industrial partners in supply chains, with a focus on stochastic customer demand. The primary objective is to optimize the coordination of the proposed supply chain by incorporating various types of contracts. Accordingly, a thorough exploration of game theory is conducted to identify solutions for the coordination problems inherent in supply chains. In this context, a comprehensive game theory formulation is proposed to determine the optimal interaction between supply chain members, with a particular focus on the variables of communication and coordination that need optimization. In this regard, the Stackelberg equilibrium is applied to find the best possible solution. The proposed model combines queuing theory to evaluate aspects and game theory when customers can communicate between two supply chains to make decisions. Numerical results show that implementing the proposed method increased the profit for the entire system by 7%. Moreover, cooperation between different companies in the distribution system can yield a higher expected profit for all partners under different scenarios.