Optimization of coordination configuration between product service system and supply chain based on Stackelberg game

Joint decisions regarding the product service system and supply chain coordination configuration have been made in practice. However, embodying the configuration decisions of the product service system in the supply chain decision-making process has not been clearly described. Existing relevant decision models are originated from an 'all-in-one' approach that assumes that both parties' decisions can be integrated into one optimization problem by aggregating two different types of objectives into a single objective function. Such an assumption neglects the complex trade-offs underlying two different decision-making problems and fails to reveal the inherent coupling of the product service system and supply chain configurations. This study constructs a bi-objective Stackelberg game model for the coordinated optimization of a product service system and supply chain configuration. Product service system decisions are modeled as an upper-level optimization problem (called a leader). Supply chain decisions are modeled as a lower-level optimization problem (called a follower). To solve the bi-objective model, an adaptive NSGA-II algorithm based on the dominance strength (ANSGA-II-DS) was developed and implemented. Finally, the effectiveness and practicability of the ANSGA-II-DS algorithm were verified by calculating the standard test function ZDT1-3, using numerical examples, and comparing it with the NSGA-II algorithm.