A Stackelberg game for closed-loop supply chains under uncertainty with genetic algorithm and gray wolf optimization

This study uses a two-level programming model to present a Stackelberg game. The two-level programming problems consist of two levels of decision-making, each level having its objective function. This model's first player (leader) includes the supplier and manufacturer, while the second player (follower) includes the distributor, customer, and revival centers. The proposed model is proposed to determine the optimal amount of products and components in each network segment, minimizing the system's total costs and optimizing transportation in the system. This research (1) considers the environmental factors in the supply chain of wooden products, (2) uses game theory and the Stackelberg game for two players, (3) provides the competition mechanism for two players where the two players do not share their objective functions due to information security. The proposed model is compared with Genetic Algorithm (GA) and Gray Wolf Optimization (GWO) meta- heuristic algorithms. We show the calculation error of the GWO algorithm is less than that of GA. Therefore, it can better predict the behavior of the model in the long term. The results show lower production costs in case of no shortage.