Correspondence: Gu Quiaolun, Antai College of Economics & Management, Shanghai Jiaotong University, Shanghai 200052, China. Tel: +86 21 52301085; Fax: +86 21 62932982; E-mail: tjguqiaolun@sohu.com

¹Gu Qiaolun is a postdoctor at Antai College of Economics & Management, Shanghai Jiaotong University. She received the BE degree in Mathematics and Applied Mathematics from Hebei Teacher's University in 1989, the ME degree in Mathemuties and Applied Mathematics from Hebei University of Technology in 1992, and the PhD degree in Control Theory and Control Engineering from Nankai University in 2005, China. Since November 2006, she has been a Professor at Computer Department, Tianjin University of Technology and Education, China. Her research interests are in the areas of operations management, logistics and supply chain management.

²Ji Jianhua is professor, Doctorate supervisor, Secretary of Chinese Communist Party and Director of Logistics Research Introduction of Shanghai Jiaotong University, Professor JI also serve as China logistics expert granted by CFLP, logistics planning expert of China 11th five-year technology plan, member of operation management committee of China management modern research institute, journal reviewer of some important academic journals such as 'Systems Engineering — Theory & Practice', 'Journal of Tianjin University', etc, and professional expert of Council of Supply Chain Management Professionals (CSCMP). Her research interests are in the areas of operations management, logistics and supply chain management, and mass customisation.

³Gao Tiegang born in 1966, received BE and ME degrees in Mathematics and Applied Mathematics from Hebei Teacher's University and Huazhong University of Science and Technology, Chjian, in 1988 and 1990, respectively, and the PhD degree in Control Theory and Control Engineering from Nankai University, China, in 2005. Since July 2004, he has been working in College of Software, Nankai University, China. He is currently a professor, whose main research interests are nonlinear system, chaos theory and information security. He has authored/coauthored more than 40 journal papers in these areas.

Received 20 July 2007; Revised 20 July 2007.

Abstract

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.