Pricing and strategy selection in a closed-loop supply chain under demand and return rate uncertainty

Closed-loop supply chain (CLSC) decision-making involves many uncertainties, which makes the decision-making process more complex and diversified. This study considered a two-stage CLSC consisting of an original manufacturer and a third-party recycler. Without any government policy support, considering the effects of market demand, product return rate, and consumer perceived value, a CLSC decision model based on market demand with a [0,1] distribution was established. The model analyzes three situations—a manufacturer monopoly, the Cournot duopoly game, and the Stackelberg competition game—and solves them. The optimal values of decision variables such as optimal pricing, market demand, and all parties’ profits in the CLSC are obtained, and a strict mathematical proof is given. Through the model-solving process, the effects of product return rate and consumer perceived value on decision variables are analyzed; then, the profit allocation between the original manufacturer and the third-party recycler under different cooperation modes is analyzed. In addition, the four combinations of competition and cooperation are analyzed based on game theory. The Nash equilibrium solution and Pareto optimal solution of the four modes are analyzed by drawing a bimatrix Nash equilibrium table. The results indicate that the cooperation–cooperation mode is difficult to produce automatically, and government policy guidance and support are often needed to achieve Pareto optimality. Finally, a numerical example is given to validate the proposed model. In this way, the proposed model provides reliable theoretical support for the decision-making of both sides in a CLSC.