第9期 刘国山等：生态产业共生网络均衡模型 ·1229· (③)在生产成本及交易成本均为凸函数的假设 terfactual analysis of a mining community.J Clean Prod. 下，证明了变分不等式的解也为生态产业共生网络 2007,15(17):1696 均衡解并构造数值算例以验证模型. [7]Dafermos S.Traffic equilibrium and variational inequali- 以后的研究将利用此数学模型继续探讨生态 ties.Transp Sci,1980,14(1):42 产业园区的形成和发展；尝试以交通网络均衡角度 [8]Liu Z G,Nagurney A.Multiperiod competitive supply 进一步研究衍生的复杂网络的有效求解方法 chain networks with inventorying and a transportation network equilibrium reformulation.Optim Eng,2012, 13(3):471 参考文献 [9]Nagurney A,Toyasaki F.Reverse supply chain manage ment and electronic waste recycling:a multitiered network [1]Xu D W,Wang Z Y,Li Y W.Study on descend mutual- equilibrium framework for e-cycling.Transp Res Part E. circular material flow of industrial eco-chain based on in- 2005,41(1):1 dustrial metabolism.Environ Sci Technol,2005,28(2): [10 Nagurney A.On the relationship between supply chain 43 and transportation network equilibria:a supernetwork (徐大伟，王子彦，李亚伟.基于工业代谢的工业生态链梯 equivalence with computations.Transp Res Part E,2006. 级循环物质流研究.环境科学与技术，2005,28(2)：43) 42(4),293 [2]Li Y S,Yu S J,Wang J H.Analysis of stable factors of [11]Nagurney A,Cruz J,Toyasaki F.Statics and dynamics of ecological-industrial chain and management countermea- global supply chain networks with environmental decision- sures research.J Hebei Univ Technol,2008,37(5):48 making//Game Theory and Equilibria.Berlin:Springer, (李艳双，于树江，王军花.生态产业链稳定性因素分析及 管理对策研究.河北工业大学学报，2008,37（⑤）：48) 2008:803 [3 Chen CF.Research on the Stability of Ecological Industry [12]Cruz J M.Dynamics of supply chain networks with corpo- Chain Based on Evolutionary Game [Dissertation].Hefei: rate social responsibility through integrated environmen- Hefei University of Technology,2010 tal decision-making.Eur J Oper Res,2008,184(3):1005 (陈翠芳.基于进化博弈的生态工业链稳定性研究[学位论 [13]Daniel P.Variational inequalities for evolutionary finan- 文].合肥：合肥工业大学，2010) cial equilibrium /Innovations in Financial and Eco. [4]Li J H.Research on synergistic profit allocation of eco- nomic Networks.Cheltenham:Edward Elgar Publishing, industrial chain network structure.J Xidian Univ Soc 2003 Sci Ed2011,21(3):56 [14]Nagurney A,Dong J.Management of knowledge inten- (李继宏.生态产业链网结构的协同收益分配研究.西安电 sive systems as supernetworks:modeling,analysis,com- 子科技大学学报：社会科学版，2011,21(3)：56) putations,and applications.Math Comput Modell,2005, 5]Hardy C,Graedel TE.Industrial ecosystems as food webs. 42(3/4):397 J Ind Ecol,2002,6(1:29 [15]Yang G.Wang Z,Li X.The optimization of the closed-loop [6]Salmi O.Eco-efficiency and industrial symbiosis-a coun- supply chain network.Transp Res Part E,2009,45(1):16第 9 期 刘国山等：生态产业共生网络均衡模型 1229 ·· (3) 在生产成本及交易成本均为凸函数的假设 下，证明了变分不等式的解也为生态产业共生网络 均衡解并构造数值算例以验证模型. 以后的研究将利用此数学模型继续探讨生态 产业园区的形成和发展; 尝试以交通网络均衡角度 进一步研究衍生的复杂网络的有效求解方法. 参 考 文 献 [1] Xu D W, Wang Z Y, Li Y W. Study on descend mutual￾circular material flow of industrial eco-chain based on in￾dustrial metabolism. Environ Sci Technol, 2005, 28(2): 43 (徐大伟, 王子彦, 李亚伟. 基于工业代谢的工业生态链梯 级循环物质流研究. 环境科学与技术, 2005, 28(2): 43) [2] Li Y S, Yu S J, Wang J H. Analysis of stable factors of ecological-industrial chain and management countermea￾sures research. J Hebei Univ Technol, 2008, 37(5): 48 (李艳双, 于树江, 王军花. 生态产业链稳定性因素分析及 管理对策研究. 河北工业大学学报, 2008, 37(5): 48) [3] Chen C F. Research on the Stability of Ecological Industry Chain Based on Evolutionary Game [Dissertation]. Hefei: Hefei University of Technology, 2010 (陈翠芳. 基于进化博弈的生态工业链稳定性研究 [学位论 文]. 合肥: 合肥工业大学, 2010) [4] Li J H. Research on synergistic profit allocation of eco￾industrial chain network structure. J Xidian Univ Soc Sci Ed, 2011, 21(3): 56 (李继宏. 生态产业链网结构的协同收益分配研究. 西安电 子科技大学学报: 社会科学版, 2011, 21(3): 56) [5] Hardy C, Graedel T E. Industrial ecosystems as food webs. J Ind Ecol, 2002, 6(1): 29 [6] Salmi O. Eco-efficiency and industrial symbiosis-a coun￾terfactual analysis of a mining community. J Clean Prod, 2007, 15(17): 1696 [7] Dafermos S. Traffic equilibrium and variational inequali￾ties. Transp Sci, 1980, 14(1): 42 [8] Liu Z G, Nagurney A. Multiperiod competitive supply chain networks with inventorying and a transportation network equilibrium reformulation. Optim Eng, 2012, 13(3): 471 [9] Nagurney A, Toyasaki F. Reverse supply chain manage￾ment and electronic waste recycling: a multitiered network equilibrium framework for e-cycling. Transp Res Part E, 2005, 41(1): 1 [10] Nagurney A. On the relationship between supply chain and transportation network equilibria: a supernetwork equivalence with computations. Transp Res Part E, 2006, 42(4), 293 [11] Nagurney A, Cruz J, Toyasaki F. Statics and dynamics of global supply chain networks with environmental decision￾making // Game Theory and Equilibria. Berlin: Springer, 2008: 803 [12] Cruz J M. Dynamics of supply chain networks with corpo￾rate social responsibility through integrated environmen￾tal decision-making. Eur J Oper Res, 2008, 184(3): 1005 [13] Daniel P. Variational inequalities for evolutionary finan￾cial equilibrium // Innovations in Financial and Eco￾nomic Networks. Cheltenham: Edward Elgar Publishing, 2003 [14] Nagurney A, Dong J. Management of knowledge inten￾sive systems as supernetworks: modeling, analysis, com￾putations, and applications. Math Comput Modell, 2005, 42(3/4): 397 [15] Yang G, Wang Z, Li X. The optimization of the closed-loop supply chain network. Transp Res Part E, 2009, 45(1): 16