Abstract: In the double channel supply chain, there are manufacturers' direct sales channels in online stores and retailers' channels in physical stores. The consumer will return the goods that are not satisfied with the purchase. Because the products purchased by the online store lack the on-site experience, the return rate is high, but the return of the online channel is more complex than the return of the offline channel, which will affect the consumer shopping experience. Therefore, a closed-loop supply chain structure is constructed based on a single manufacturer's online store and a single retailer's physical offline store, and three return channels including cross-channel return are designed. Considering the impact of cross-channel return rate and consumer preference in the closed-loop supply chain, differential pricing is made. Two kinds of centralized decision-making (differential pricing strategy and unified pricing strategy) and three kinds of decentralized decision-making (manufacturer-dominated Stackelberg game, retailer-dominated Stackelberg game and Nash equilibrium game) are adopted to analyze the pricing decision and profit distribution of closed-loop system, and the conclusions are verified by numerical examples. The result shows that cross-channel return rate and consumer channel preference have direct impact on pricing strategies and profit allocation of closed loop supply chain. Under centralized decision-making, the price competition in two different channels is relatively weak, so the channel preference of consumers has little influence on the pricing decision of the two channels. In decentralized decision-making, the optimal price of two competitive channels is greatly influenced by the preference of customers for the channel. This paper can enrich and perfect the relevant theories of double channel supply chain and cross-channel returns, and provide series of useful guidance for the decisions of manufacturers and retailers.

Key words: cross-channel returns, double channel, centralized decision, decentralized decision making, game theory