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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 784637, 16 pages
Research Article

The Closed-Loop Supply Chain Network Equilibrium with Products Lifetime and Carbon Emission Constraints in Multiperiod Planning Horizon

School of Management Science and Engineering, Qingdao University, Qingdao 266071, China

Received 31 March 2014; Accepted 19 May 2014; Published 16 June 2014

Academic Editor: Xiaolin Xu

Copyright © 2014 Guitao Zhang et al. 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 closed-loop supply chain network equilibrium problem in multiperiod planning horizons with consideration of product lifetime and carbon emission constraints. The closed-loop supply chain network consists of suppliers tier, manufacturer tier, retailers tier, and demand markets tier, in which the manufacturers collect used products from the demand markets directly. Product lifetime is introduced to denote the maximum times of manufacturing and remanufacturing, and the relation between adjacent periods is described by inventory transfer. By variational inequalities and complementary theory, the optimal behaviors of all the players are modeled, and, in turn, the governing closed-loop supply chain network equilibrium model is established. The model is solved by modified project contraction algorithm with fixed step. Optimal equilibrium results are computed and analyzed through numerical examples. The impacts of collection rate, remanufacturing conversion rate, product lifetime, and carbon emission cap on equilibrium states are analyzed. Finally, several managerial insights are given to provide decision support for entrepreneurs and government official along with some inspirations for future research.