Abstract: In this paper, the pricing and coordination problem of the patent-protected remanufacturing closed-loop supply chain under mixed demand of stochastic new products' demand and remanufactured products' price-dependent demand is studied using game theory. Through the analysis of two circumstances of centralized and decentralized decision-making, the optimal ordering quantity and wholesale price of new products, the optimal recycling price of waste products, the optimal patent licensing fees, the optimal retail price of remanufactured products and the optimal profit of the supply chain are obtained. Furthermore, the supply chain is coordinated by using revenue and expense sharing contract. Through the numerical example the impact of different remanufacturing cost saving on the optimal decision and the profits of the supply chain members, and the coordinating effect of the revenue and expense sharing contract are abtained. It can found that the manufacturer can influence the recycling price and recycling quantity of the used products recycled by the third re-manufacturer in the case of patent-protected remanufacturing, and then affect the revenue of manufacturer and the thirdre-manufacturer.

Key words: close-loop supply chain, mixed demand, patent protection, coordination