Dynamic pricing model for new /used products in the processing of closed-loop supply chain operation

From the view of operation researches, the operation problem for a class of closed-loop supply chain system with one manufacturer and one supplier is considered. Demands of ultimate products and collecting quantity of used products are described by using prices and reference prices, a non-linear dynamic pricing model for new/used products in the processing of this system operation is established. The model is constructed as a dynamic programming problem and satisfying several conflict objectives, such as the operating coordination of system, making the maximum profit of all participants as much as possible. The model's validity to dynamic pricing for closed-loop supply chain system is verified by a numerical example. The results of the numerical example shows that, in the long run, through the regulations of price itself and price reference effect, the price of ultimate product and the collecting price of used product fix to a certain value without reference to the initial price of ultimate product and the collecting price of used product.