Abstract
Purpose
The purpose of this paper is to develop a closed-loop supply chain (CLSC) network equilibrium model which consists of manufactures, retailers and consumer markets engaged in a Cournot pricing game with heterogeneous multi-product.
Design/methodology/approach
The authors model the optimal behavior of the various decision makers and CLSC network equilibrium, and derive the equilibrium conditions based on variational inequality approach. The authors present a new Newton method to solve the proposed model.
Findings
The authors find that the algorithm converges to the solution rapidly for most cases. Besides, the authors discuss the effect of some parameters on the equilibrium solution of the model, and give some insights for policy makers, such as improving the technology level of the manufacturer, reducing the cost of waste disposal and increase the minimum ration of used product to total quantity.
Originality/value
The authors derive the network equilibrium conditions by the variational inequality formulation in order to obtain the computation of the equilibrium flows and prices. The authors present a new Newton method to solve the proposed model. The authors discuss the effect of some parameters on the equilibrium solution of the model, and give some managerial insights
Keywords
Acknowledgements
The authors are grateful to the Associate Editor and the anonymous referees for their helpful comments and suggestions. This research was supported by the National Basic Research Program of China (973 Program) under Grants 2012CB315805; the National Natural Science Foundation of China under Grants 71001035 and 71420107027; the Program for New Century Excellent Talents in University under Grants NCET-13-0181; and Training program for outstanding young teachers in Guangdong Province under Grant No. 20140202 and Educational Commission of Guangdong Province, China under Grant No. 2014KQNCX210.
Citation
Xu, H. and Cao, E. (2016), "Closed-loop supply chain network equilibrium model and its Newton method", Kybernetes, Vol. 45 No. 3, pp. 393-410. https://doi.org/10.1108/K-08-2013-0179
Publisher
:Emerald Group Publishing Limited
Copyright © 2016, Emerald Group Publishing Limited