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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 786803, 11 pages
Research Article

Optimal Decisions in a Single-Period Supply Chain with Price-Sensitive Random Demand under a Buy-Back Contract

1Graduate School of Information Management and Security, Korea University, Seoul 136-713, Republic of Korea
2School of Industrial Management Engineering, Korea University, Seoul 136-713, Republic of Korea

Received 14 January 2014; Revised 15 June 2014; Accepted 19 June 2014; Published 16 July 2014

Academic Editor: Jung-Fa Tsai

Copyright © 2014 Feng Wang and In-Chan Choi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper studies a single-period supply chain with a buy-back contract under a Stackelberg game model, in which the supplier (leader) decides on the wholesale price, and the retailer (follower) responds to determine the retail price and the order quantity. We analytically investigate the decentralized retailer’s optimal decision. Our results demonstrate that the retailer has a unique optimal simultaneous decision on the retail price and the order quantity, under a mild restriction on the demand distribution. Moreover, as it can be shown that the decentralized supply chain facing price-sensitive random demand cannot be coordinated with buy-back contract, we propose a scheme for the system to achieve Pareto-improvement. Theoretical analysis suggests that there exists a unique Pareto-equilibrium for the supply chain. In particular, when the Pareto-equilibrium is reached, the supply chain is coordinated. Numerical experiments confirm our results.