A Closed-loop Supply Chain Network Equilibrium Model with Multi-criteria and Stochastic Demand

  • Bing Xu
  • Kun Jiang
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 242)


Consider a multi-commodity flow closed-loop supply chain network consisting of many manufacturers, retailers, recovery enterprises, demand and recovery markets, respectively manufacturing, selling, consuming same kinds of new products, and recycling and supplying the used products. Manufacturer makes decision to maximize its profit and the benefit of environmental protection. Logit model is used to characterize the consumer behavior on product choice with insufficient information. Firstly, based on Nash equilibrium theory, competitive behaviors of manufacturers, retailers and recovery enterprises are analyzed respectively together with the corresponding variational inequality equilibrium models. The stochastic equilibrium conditions of demand markets with stochastic demand are obtained. The equilibrium of recovery markets is realized if and only if the quantities and prices of supply and demand are balanced. Then a variational inequality model is obtained to characterize the equilibrium of multi-commodity closed-loop supply chain network with multi-criteria and stochastic demand. Finally, a numerical example shows the reasonability of the model and the sensitivity analysis of the factors of consumers’ environment value and government’s subsidy.


Equilibrium model of closed-loop supply chain network Variational inequality Logit model Stochastic demand Multi-criteria decision 


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This work is partially supported by National Natural Science Foundation of China (NSFC 70961006), China Postdoctoral Science Foundation (20100481186), China Postdoctoral Science Foundation Special sustentation (2012T50593).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Bing Xu
    • 1
  • Kun Jiang
    • 1
  1. 1.Department of Management Science and EngineeringNanchang UniversityNanchangPeople’s Republic of China

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