Pricing management for a closed-loop supply chain

A closed-loop supply chain includes the forward supply chain and the reverse supply chain. In a reverse supply chain, the used products are collected from the end-customers. Hence, the return rate of used products is affected by the end-customer's willingness, and the end-customer's willingness is affected by the collecting price. In a forward supply chain, the wholesale price and the retail price will be affected by the collecting price. In this paper, we focus on the managements of the collecting price, the wholesale price and the retail price for the closed-loop supply chain. On the assumption that the return rate of the used products is an increasing function of the collecting price, we obtain the optimal collecting price, the optimal wholesale price and the optimal retail price based on the following models: Model CMRC (The manufacturer for collecting), Model CRMRC (The retailer for collecting) and Model CTMRC (The third party for collecting). By comparing the optimal pricing and the profits of the models, we find that the manufacturer for collecting is the best choice, and the retailer for collecting is another choice if the manufacturer has decided to transfer all its cost saving to the retailer. At the end of the paper, a numerical example is given to illustrate the optimal results.