LISS 2014 pp 1543-1548 | Cite as

The Variational Inequality Model of Closed-Loop Supply Chain Network Equilibrium with Environmental Indicators

Conference paper


Through variational inequality theory, we propose a model of the closed-loop supply chain network equilibrium with environmental indicators, consisting of raw material suppliers, manufacturers collecting recycled products directly, retailers and demand markets. To promote sustainable development, the Ministry of Environmental Protection set different upper limits of emission in the form of legislation in order to prevent the manufacturers from exceeding the limits. Specifically, the penalties should be greater than the corresponding shadow prices serving as the environmental indicators in the model. We describe their optimal behavior for pursuing maximum profit, establish the optimality conditions of four-tier decision-makers and provide the variational inequality in accordance with the closed-loop supply chain network equilibrium conditions.


Closed-loop supply chain Network equilibrium Variational inequality theory Environmental indicators 



The article has been supported by the project: Cotton storage environment monitoring information of remote acquisition, storage and display system (National science and technology support plan) (2012BAH20B030-4).

Hebei Province Department of science and technology Fund (1345090D)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Economics & ManagementHebei University of Science and TechnologyShijiazhuangChina
  2. 2.School of BusinessRenmin University of ChinaBeijingChina

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