The Differential Game of a Closed-Loop Supply Chain with Manufacturer Competition Considering Goodwill

The dynamic optimization of the closed-loop supply chain (CLSC) is a hot research topic. Members’ competitive behavior and product goodwill play an important role in the decision making of CLSC members. In this paper, a closed-loop supply chain (CLSC) with competitive manufacturers and single retailers is studied, in which the manufacturer produces and recycles the products, and the retailer is responsible for the sales of the products. On this basis, a dynamic linear differential equation of product goodwill is constructed, the optimal dynamic path of each decision variable is found, and the influence of price competition among manufacturers on the decision making of members in a dynamic closed-loop supply chain is studied. The conclusion is verified by an example. The results show that goodwill directly affects the wholesale price, the retail price, the recovery price, and the profit of supply chain members. The wholesale price and the retail price of products are not only positively affected by their own goodwill, but also by the goodwill of competing products. The manufacturer competition intensity will affect the product price and the supply chain member profit. To a certain extent, the more intense the manufacturer’s competition is, the higher the wholesale price and the retail price, and the greater the profit of the supply chain members.