A Closed-loop Supply Chain Network Equilibrium Model with Multi-criteria and Stochastic Demand
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.
KeywordsEquilibrium 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).
- 1.Nagurney A, Dong J, Zhang D (2002) A supply chain network equilibrium model. Transportation Research Part E: Logistics and Transportation Review 38(5):281–303Google Scholar
- 2.Dong J, Zhang D, Nagurne A (2004) A supply chain network equilibrium model with random demands. European Journal of Operational Research 156(1):194–212Google Scholar
- 3.Xu B, Zhu DL (2007) A multi-commodity flow supply chain network equilibrium model with stochastic choice. Systems Engineering — Theory & Practice 27:82–90 (In Chinese)Google Scholar
- 4.Xu B, Zhu DL (2008) Supply chain network equilibrium mode with multiclass multicriteria stochastic choice. Journal of Systems Engineering 23:547–553 (In Chinese)Google Scholar
- 5.Xu B, Zhu DL (2008) A supply chain network equilibrium model with stochastic multicriteria decision. In: Proceedings of IEEE International Conference on Automation and Logistics 169–174Google Scholar
- 6.Savaskan RC, Bhattacharya S, VanWassenhove L (2004) A closed-loop supply chain models with product remanufacturing. Management Science 50(2):239–252Google Scholar
- 7.Yang GF (2009) The optimization of the closed-loop supply chain supernetwork recycled by the retailers. Systems Engineering 27:42–47 (In Chinese)Google Scholar
- 8.Yang GF,Wang YY (2011) The research of the closed-loop supply chain supernetwork based on the variational inequality. Math in Practice and Theory 41:15–26 (In Chinese)Google Scholar
- 9.Xu B, Zhang XP (2011) A closed-loop supply chain network equilibrium model based on variation inequality. In: Proceedings of the Fifth International Conference on Management Science and Engineering Management 3–7Google Scholar