Research on Eco-Industrial Chain Network Equilibrium Problem Based on Variational Inequality

Abstract

Abstract: The eco-industrial chain network equilibrium model is researched by using the theories of variational inequality in this paper. The eco-industrial chain imitates natural ecosystem by manners of materials circulation and patterns of competition and symbiosis between biological colonies to make different enterprises share resources and exchange by-products. Then, it can make by-products generated in the production process of upstream firms become the raw material for the production of downstream firms in order to achieve the maximization of economic and environmental benefits for the enterprises and the whole eco-industrial park. According to the network structure of multi-product(main product, by-product and waste)and multi-level in eco-industrial chain network, we describe the optimizing behavior of the various decision-makers, derive the equilibrium conditions of the system with the corresponding economic interpretation, and establish the eco-industrial chain network equilibrium model. Based on the existence of the solution of the related variational inequality under reasonable assumptions, a numerical example is given to illustrate the rationality as well as the effectiveness of the model.

Key words: eco-industrial chain, variational inequality, network equilibrium, industrial symbiosis

摘要： 以变分不等式为基础提出生态工业链网络均衡模型。生态工业链是通过仿照自然生态系统中的物质循环方式与生物群体之间的竞争与共生模式,使不同企业之间形成共享资源和互换副产品从而实现园区各企业经济与环境效益的最大化。针对生态工业链网络的多产品(主副产品和废弃物)多层次的网络结构,模仿自然生态系统中的生产者、消费者和分解者,分别对各层决策者的独立优化决策行为及其相互作用进行分析,利用变分不等式分析各层均衡条件进而构建生态工业链网络均衡模型,得到系统达到均衡的条件并给出相应的经济解释。在证明系统变分不等式的解存在的基础上,通过数值算例验证模型的合理性与有效性。

关键词: 生态工业链, 变分不等式, 网络均衡, 工业共生

CLC Number:

F062.2

XU Shi-qin, LIU Guo-shan, LI Chun-fa, HAN Ji-ye. Research on Eco-Industrial Chain Network Equilibrium Problem Based on Variational Inequality[J]. Operations Research and Management Science, 2013, 22(2): 8-19.

徐士琴, 刘国山, 李春发, 韩继业. 基于变分不等式的生态工业链网络均衡问题研究[J]. 运筹与管理, 2013, 22(2): 8-19.

References

[1] 边均兴.面向可持续发展的生态工业园建设理论与方法研究[D].天津大学博士学位论文,2005.
[2] 方丽丽,齐振宏,王璟.生态产业链促进生态工业园区发展的机理模型分析[J].商场现代化,2008(6):275-276.
[3] 方丽丽,齐振宏,朱玉强.生态工业园生态产业链研究述评[J].中国集体经济,2007(8),20-21.
[4] Roberts B H. The application of industrial ecology principles and planning guidelines for the development of eco-industrial parks: an Australian case study[J]. Journal of Cleaner Production, 2004, 12(8/10): 997-1010.
[5] Assefa G, Björklund A, Eriksson O, Frostell B. Orware: an aid to environmental technology Chain assessment[J]. Journal of Cleaner Production, 2005, 13(3): 265-274.
[6] Chertow M R, Lombardi D R. Quantifying economic and environmental benefits of co-located firms[J], Environmental Science and Technology, 2005, 39(17): 6535-6541.
[7] 王兆华,尹建华.生态工业园中工业共生网络运作模式研究[J].中国软科学,2005,(2):80-85.
[8] 袁飚,陈雪梅.基于耗散结构理论的生态产业链形成机理研究[J].内蒙古社会科学(汉版),2010,31(6):101-105.
[9] 王秀丽,李春发.生态工业链构建中的博弈分析[J].系统工程,2006,(1):9-12.
[10] 郭莉,苏敬勤.基于Logistic增长模型的工业共生稳定分析[J]. 预测,2005,24(1): 25-29.
[11] Bailey R. Designing robust industrial ecosystems: a systems approach[D] G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 1997.
[12] Dafermos S C, Nagurney A. Isomorphism between spatial price and traffic equilibrium models[J]. Lefschetz Center for Dynamical Systems, Brown University, Providence, Rhode Island, 1985. 37-40.
[13] Daniel P. Variational inequalities for evolutionary financial equilibrium[M]. In: Nagurney A., ed. Innovations in Financial and Economic Networks, Cheltenham, England: Edward Elgar Publshing, 2003.
[14] Nagurney A, Dong J, Zhang D. A supply chain network equilibrium model[J]. Transportation Research E, 2002, 38(5): 281-303.
[15] Nagurney A, Cruz J, Dong J. Supply chain networks, electronic commerce, and supply side and demand side risk[J]. European Journal of Operational Research, 2005, (164): 120-142.
[16] Nagurney A, Dong J, Zhang D. Supply chain network and electronic commerce: a theoretical perspective[J]. Netnomics, 2002, (4): 187-220.
[17] Nagurney A, Ke K, Gruz J. Dynamics of supply chains: a multilevel(logistical/informational/financial)network perspective[J]. Environment & Planning B, 2002, (29): 795-818.
[18] Nagurney A, Dong J. Management of knowledge intensive systems as supernetworks: modelling, analysis, computations, and applications[J]. Mathematival and Computer Modelling, 2005, (42): 397-417.
[19] Hammond D, Beullens P. Closed-loop supply chain network equilibrium under legislation[J]. European Journal of Operational Research, 2007, 183(2): 895-908.
[20] Nagurney A, Toyasaki T. Reserve supply chain management and electronic waste recycling: a multitiered network equilibrium framework for e-cycling[J]. Transportation Research, 2005, 41(1): 1-28.
[21] Nagurney A, Zhang D. Projected dynamical systems and variational inequalities with applications[M]. Dordrecht: Kluwer Academic Publishers, 1996.
[22] Yang G, Wang Z and Wang Y. The Win-win optimization for the supply chain supernetwork with electronic commerce based on the variational inequalities[C]. IEEE The 2006 Asia-Pacific Services Computing Conference, South China University of Technology, 2006, 174-181.