快递营运网络优化设计与竞争网络均衡研究
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摘要
随着电子商务、网络购物等新型服务业对快递服务需求的不断增加,快递在社会经济发展中服务民生和生产的基础性作用不断增强。提高我国快递企业竞争力,降低社会快递物流成本,一方面需提高快递企业的营运能力,特别是营运网络优化能力,另一方面提高整条快递供应链的能力。快递营运网络优化设计与竞争网络均衡研究就是对快递主干运输网络、取送网络进行优化,并探究由运输企业、快递企业、消费市场构成的快递供应链竞争网络均衡问题。通过研究,将有助于降低快递企业的成本并优化快递供应链,促进整个行业运营成本的降低和竞争力的提升,进一步丰富和完善快递运营网络优化及供应链竞争网络理论与方法。
     论文首先研究了快递整体运作流程,通过全连通快递网络与轴辐式快递网络的成本、服务效率的比较和快递企业网点布局的实证,以多分配轴辐式网络结构为基础,对快递主干网络的实体网络、组织网络和路径网络进行优化。然后,以客户满意为出发点,研究了不同取送模式的适用范围、取送区域范围及基于客户特征研究的优化策略。最后,研究了基于快递运输组织方案的快递市场竞争网络均衡问题,建立了快递市场竞争网络均衡变分不等式模型。具体研究内容与创新工作如下:
     (1)研究了快递营运网络的特点和优化目标。通过界定快递的定义及其特征,分析了快递市场的竞争态势与发展趋势,结合不同所有制快递企业情况,研究了快递企业整体运作流程,详细分析了由主干网络、配送网络、取送网络构成的快递企业营运网络的特点和优化目标。
     (2)研究了快递主干网络的结构选择问题。比较分析了全连通快递网络与轴辐式快递网络的各环节的成本、效率、网络总成本和网络服务效率,分析了各种参数变化对快递服务成本和效率的影响,确定影响快递网络结构选择的决定性因素。然后,以某快递企业为实证,分析其网点布局的影响因素及其网络结构变化的影响因素,确定快递主干网络优化的结构。
     (3)通过分析快递运送路径的合并式特征,以多分配轴辐式网络结构为基础,以快递运送过程中的分拣费用、运输费用、中转费用之和最小为目标函数,建立了考虑快递运输时间预算约束的快递主干网络的枢纽选址与分配优化模型,并设计了基于条件最短路的模拟退火算法。
     (4)通过分析现有三种取送模式的客户成本和快递企业成本构成,及其影响因素,研究了不同取送模式的适用范围,并以门到门取送模式为例,建立了满足客户容忍时限约束的快递取送区域范围的确定模型。同时,分析了消费者对快递产品的购买决策特征,并以总线模块化为基础,结合可选择模块化设计方法对快递服务进行模块化设计。
     (5)在详细分析基于合并式快递运输组织方案的快递作业流程的基础上,研究了快递竞争市场中快递企业行为、消费者行为、运输企业行为及其均衡条件,应用变分不等式方法,建立了快递市场竞争网络均衡模型,并采用修正投影算法对算例进行求解分析,对多个参数进行分析,得出影响快递价格的因素,提出降低快递价格的途径以及快递企业提升市场竞争力的策略。
With the continuously increasing express services demand of the new type of service industries such as e-commerce and online shopping, express as the fundamental role to service livelihood and production in the social economic development strengthens continuously. Improving express enterprises competitiveness and decreasing social express logistics cost need to improve operation capability of express enterprises, especially optimizing the capability of operation network, and improve the capability of express supply chain. Express operation network optimization design and competitive network equilibrium research is to optimize the backbone transportation network and the fetching and dispatching network, to explore competitive network equilibrium problem of express supply chain composed of transportation enterprises and express enterprises and cosumerconsumer market. The research can be helpful to decrease the cost of express enterprises and optimize express supply chain, and be beneficial to the reduction of operation cost as well as the improvement of competitiveness of the whole industry, and furthermore, enrich and perfect the theories and methods of express operation network optimization and supply chain competitive network equilibrium.
     Firstly, the article studied express's whole operation process, by comparison of cost and efficiency of fully-connected express network and hub-and-spoke express network and empirical study on express enterprise, based on multiple allocation hub-and-spoke express network structure, the physical network, organization network and path network of express backbone network were optimized. Secondly, on the basic of customer satisfaction, the scope of application of the different fetching and dispatching modes and the model of determining the adaptation scopes of fetching and dispatching region and the optimization strategies based on the research of customer characteristics were studied. Lastly, through studying on competitive network equilibrium problem of express market, express market competitive network variational inequality model was built. The main content and innovation work are following:
     (1) The features and optimization objective of operation networks of express enterprises were studied. Through defining the express and describing its characteristics, competition situation and development trend of express market were analyzed. Combined with express enterprises of different ownership, the whole operation process of express enterprises was studied, and the features and optimization objective of operation networks of express enterprises made up of backbone network,distribution network and fetching and dispatching network were analyzed.
     (2) The selection of express backbone network structure was studied. Cost and efficiency of each link and the whole network of fully-connected express network and hub-and-spoke express network were analyzed. By comparison the influence of parameter variations to cost and efficiency of express service were analyzed, so decisive factor of the selection of express network structure was determined. Then taking an empirical study of an express enterprise, influencing factors of nodes layout and network structure changes were studied and the structure of express backbone network optimization was determined.
     (3) Through analyzing the union character of express delivering path and based on the network structure of multiple allocation hub-and-spoke network, hub location selection and allocation optimization model of multiple allocation hub-and-spoke express networks was built with the objective function of minimizing the total costs that included sorting costs and transportation costs and transfer costs, with transport time budget constraint. The simulated annealing algorithm based on the conditional shortest path was developed to solve the problem.
     (4) Through analyzing cost structure of customer cost and express enterprise cost of three fetching and dispatching modes and theirs influence factors, the adaptation scopes of different fetching and dispatching modes were studied, and the model to determine the adaptation scopes of fetching and dispatching region was built with door-to-door fetching and dispatching mode as an example. Meanwhile, decision-making characteristics of consumer to purchase the product of express were analyzed, and express service was designed on the basic of bus modularity combined with sectional modularity.
     (5) After analysis on express operation procedures based on the union express transportation organization plan, express enterprises behavior and consumer behavior and transport enterprises behavior as well as the equilibrium condition in express competitive market, express market competitive network equilibrium model was built by variational inequality method. A modified projection algorithm was designed to solve this model, and by analyzing the multiple parameters, influencing factors of express price were concluded and ways to lower express price and to improve the market competitiveness of express enterprise were proposed.
引文
[1]中投顾问.2010-2015年中国快递业投资分析及前景预测报告[R].2010
    [2]IBISWorld. ACMR China Industry Report(2010-2016年中国快递业研究报告)[R].2010
    [3]国家邮政局.2010快递市场监管报告[R].2011
    [4]国家邮政局.邮政业“十二五”规划[R].2011邮政业标准化“十二五”发展规划
    [5]国家邮政局.长江三角洲地区快递服务发展规划(2009—2013年)[R].2009.
    [6]国家邮政局.珠江三角洲地区快递服务发展规划(2010-2014)[R].2010
    [7]国家邮政局.京津冀地区快递服务发展规划(2010-2014)[R].2010
    [8]上海市邮政管理局.上海快递服务发展规划(2009—2013年)[R].2009
    [9]Oxford Economic Forecasting. The Impact of The Express Delivery Industry on The Global Economy[R]. March 2005:7-8.
    [10]商务部研究院课题组.中国快递市场发展研究报告[J].经济研究参考.2006年第34期(总第1994期).2-24.
    [11]王成金.中国物流企业的空间组织网络[J].地理学报,2008.63(2):135-146.
    [12]Megan Smirti, Arnaud Boubert.Modeling the Logistics of FedEx Internatio nal Express. http://www.metrans.org/nuf/2007/documents/Smirti_000.pdf.20 090928.2007
    [13]Alexandre Lafaye. Integrator's air network A review of the Domestic Express European Market[D]. Cranfield University School of Engineering. MSc Thesis.2007.
    [14]Hua Yang,Yuchao Ni et al. Insight to the express transport network[J]. Computer Physics Communications(2009), in press.
    [15]张洪斌,聂玉超.中国快递企业的网络系统分析[J].物流技术,2009,28(9):35-37.
    [16]匡旭娟.演化视角下的快递业网络形态研究[D].北京:北京交通大学,博士学位论文,2008.
    [17]黄建华.快递网络的复杂性及鲁棒性分析—以某快递企业为例[J].西南交通大学学报(社会科学版).2009,10(6):98-103.
    [18]周敏,黄福华.长株潭城市群快递服务网络的拓扑特性研究[J].物流工程与管理,2010,32(8):107-109.
    [19]张润生.基于GIS的快递网络系统研究[D].北京:北京交通大学,硕士论文.2009
    [20]莫辉辉,王娇娥等.交通运输网络的复杂性研究[J].地理科学进展.2008年第6期:112-120.
    [21]O'Kelly. A quadratic integer program for the location of interacting hub facilities[J]. European Journal of Operational Research.32(1987):393-404.
    [22]O'Kelly, D.Bryan. Hub location with flow economies of scale[J]. Transportation Research-B,1998, Vol.32, No.8, pp.605-616.
    [23]W. Horner, O'Kelly. Embedding economies of scale concepts for hub network design[J]. Journal of Transport Geography.9(2000):255-265.
    [24]Claudio B. Cunha, Marcos Roberto Silva. A genetic algorithm for the problem of configuring a hub-and-spoke network for a LTL trucking company in Brazil[J]. European Journal of Operational Research.179 (2007):747-758.
    [25]Aykin. The hub location and routing problem[J]. European Journal of Operational Research.83 (1995):200-219.
    [26]Seung-Ju Jeong, Chi-Guhn Lee et al. The European freight railway system as a hub-and-spoke network[J]. Transportation Research Part A.41 (2007):523-536.
    [27]Jamie Ebery, Mohan Krishnamoorthy et al. The capacitated multiple allocation hub location problem:Formulations and algorithms[J]. European Journal of Operational Research.120 (2000):614-631.
    [28]Samir Elhedhli, Frank Xiaolong Hu. Hub-and-spoke network design with congestion[J]. Computers & Operations Research.32 (2005):1615-1632.
    [29]V. Rodriguez,M.J. Alvarez et al. Hub location under capacity constraints[J].Transportation Research Part E.43 (2007):495-505.
    [30]Campbell, J. Lowe et al. The p-hub center allocation problem[J]. European Journal of Operational Research.176 (2007):819-835.
    [31]R.S. de Camargo, G. Miranda Jr. et al.Multiple allocation hub-and-spoke network design under hub congestion[J]. Computers & Operations Research.36 (2009):3097-3106.
    [32]Darko Skorin-Kapov et al. Tight linear programming relaxations of uncapacitated p-hub median problems[J]. European Journal of Operational Research.94 (1996):582-593.
    [33]Michael J. Kuby,Robert Gordon Gray.The hub network design problem with stopovers and feeders:the case of Federal Express[J].Transportation Research Part A. Vol.21A, No.1. pp.1-12,1993.
    [34]O'Kelly, D.Bryan et al. Hub network design with single and multiple allocation: A computational study[J]. Locafion Science,V ol.4, No.3, pp.125-138,1996.
    [35]John G. Klincewicz. Hub location in backbone/tributary network design:a review[J]. Location Science.6 (1998):307-335.
    [36]Andreas T. Ernst, Mohan Krishnamoorthy.Efficient Algorithms for the Uncapacitated Single Allocation p-hub median problem[J]. Location Science, Vol.4, No.3, pp.139-154.1996.
    [37]Andreas T. Ernst, Mohan Krishnamoorthy. Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem[J]. European Journal of Operational Research.104 (1998):100-112.
    [38]Ebery,Krishnamoorthy et al. The capacitated multiple allocation hub location problem Formulations and algorithms[J]. European Journal of Operational Research.120 (2000):614-631.
    [39]Alfredo Marin, Lazaro Canovas et al. New formulations for the uncapacitated multiple allocation hub location problem[J]. European Journal of Operational Research.172 (2006):274-292.
    [40]R.S. de Camargo, G. Miranda Jr. et al.Multiple allocation hub-and-spoke network design under hub congestion[J]. Computers & Operations Research.36 (2009):3097-3106.
    [41]Andreas T. Ernsta, Horst Hamacherb et al.Uncapacitated single and multiple allocation p-hub center problems[J]. Computers & Operations Research 36 (2009):2230-2241
    [42]李红启,刘鲁.Hub-and-Spoke型运输网络改善方法及其应用[J].运筹与管理.16(2007):63-68.
    [43]Tommy Thomadsen, Jesper Larsen.A hub location problem with fully interconnected backbone and access networks[J]. Computers & Operations Research.34 (2007):2520-2531.
    [44]Tommy Thomadsen, Thomas Stidsen.The generalized fixed-charge network design problem[J]. Computers & Operations Research.34 (2007):997-1007.
    [45]Jiyin Liu、Chung-Lun Li et al. Mixed truck delivery systems with both hub-and-spoke and direct shipment[J]. Transportation Research Part E.39 (2003):325-339.
    [46]Cheng-Chang Lin et al. The multistage stochastic integer load planning problem[J].Transportation Research Part E.43(2007):143-156.
    [47]Chaug-Ing Hsu,Yu-Ping Hsieh.Routing, ship size, and sailing frequency decision-making for a maritime hub-and-spoke container network[J]. Mathematical and Computer Modeling.45(2007):899-916.
    [48]Daeki Kim.Large Scale Transportation Service Network Design:Models, Algorithms and Applications[D]. Ph.D. thesis. Center for TransportationStudies, Massachusetts Institute of Technology, Cambridge, MA,1997.
    [49]Daeki Kim,Cynthia Barnhart. Multi-modal express package delivery:A service network design application[J]. Transportation Science. Vol.33, No.4,1999.
    [50]Tore Grunert, Hans-Jurgen Sebastian. Planning models for long-haul operations of postal and express shipment companies[J]. European Journal of Operational Research.122(2000):289-309.
    [51]Andrew P. Armacost.composite variable formulations for expess shipment service network design[D]. Ph.D. thesis, Massachusetts Institute of Technology, 2000.
    [52]Cynthia Barnhart et al. network design for express shipment delivery[J]. Computational Optimization and Applications,21,239-262,2002.
    [53]Gunther Zapfel, Michael Wasner. Planning and optimization of hub-and-spoke transportation networks of cooperative third-party logistics providers[J]. International Journal of production economics.78(2002):207-220.
    [54]Michael Wasner, Gunther Zapfel. An integrated multi-depot hub-location vehicle routing model for network planning of parcel service[J]. International Journal of Production Economics.90 (2004):403-419.
    [55]Subrat Mahapatra. Analysis of routing strategies in air transportation networks for express package delivery services[D]. University of Maryland College Park. MSc Thesis.2005.
    [56]Cheng-Chang Lin, Yu-Jen Lin et al. The economic effects of center-to-center directs on hub-and-spoke networks for air express common carriers[J]. Journal of Air Transport Management.9 (2003):255-265.
    [57]Cheng-Chang Lin, Sheu-Hua Chen. An integral constrained generalized hub-and-spoke network design problem[J]. Transportation Research Part E.44 (2008):986-1003.
    [58]陈秀华.一般化轴辐式网络问题设计与应用[D].中国台湾:国立中央大学. 博士学位论文.2003.
    [59]黄文姬.具规模经济之轴辐式网络设计[D].中国台湾:国立成功大学.硕士学位论文.2005.
    [60]王怡真.国际快递业一般化航空网路设计之研究[D].中国台湾:国立成功大学.硕士学位论文.2003.
    [61]Cheng-Chang Lin et al. The multistage stochastic integer load planning problem[J].Transportation Research Part E.43(2007):143-156.
    [62]林蒿然.路线货物运输业需求不确定性载运规划问题之研究[D].中国台湾:国立中央大学.硕士学位论文.2005.
    [63]颜上荛.Cargo container loading plan model and solution method for international air express carriers[J]. Transportation Planning and Technology. 2006(29):445-470.
    [64]颜上荛.Optimal cargo container loading plans under stochastic demands for air express carriers[J]. Transportation Research Part E-logistics and Transportation Review.2008(44):555-575.
    [65]赖俊宏.国际快递业飞航排程暨班次表建立之研究[D].中国台湾:国立中央大学.硕士学位论文.2004.
    [66]翁佩珏.国际航空快递货物装柜规划模式及求解演算法之研究[D].中国台湾:国立中央大学.硕士学位论文.2004.
    [67]萧妃晏.随机需求下航空快递货物装柜规划模式之研究[D].中国台湾:国立成功大学.硕士学位论文.2005.
    [68]胡向东,张海盛.多目标邮政运输分层模型[J].系统工程与电子技术.2001(9):74-77.
    [69]叶耀华,王律等.我国邮政网络的优化设计方法[J].管理工程学报.2004(2):39-43.
    [70]范承浩.基于轴辐式理论的中铁快运物流网络规划研究[D].北京:北京交通大学.硕士学位论文.2007.
    [71]张建,吴耀华.公路快速货运复合轴辐式网络规划分析[J].山东大学学报(工学版).2008,38(5).
    [72]路欢欢,晏绍庆.长三角地区快递网络构建研究[J].物流科技.2010年第12期:43-48.
    [73]刘世萌.基于服务效率的快递企业派送区域优化问题研究[D].北京:北京交通大学,2010.
    [74]黄建华,党延忠.快递超网络模型及基于效率的优化方法[J].北京理工大 学学报(社会科学版).2011,(03):68-72.
    [75]黄建华,党延忠.快递超网络模型及基于成本的优化方法[J].系统管理学报.2010,19(6):689-695.
    [76]黄建华,党延忠..基于时间阈值的多标准快递超网络优化方法[J].系统工程理论与实践.2010,30(12):2129-2136.
    [77]尹传忠.铁路行包物流配送系统优化若干问题研究[D].成都:西南交通大学.博士学位论文.2006.
    [78]黄由衡,王娟.铁路快递物品目的地市内配送派单的优化算法[J].铁道学报.2008,30(2):17-23.
    [79]李炳会.快递企业多点配送线网模型优化相关理论与方法的研究[D].上海:同济大学,博士学位论文.2008.
    [80]Nagurney, June Dong, Ding Zhang. A supply chain network equilibrium model[J]. Transportation Research Part E.2002 (38):281-303.
    [81]June Dong, Ding Zhang, Nagurney. A supply chain network equilibrium model with random demands[J]. European Journal of Operational Research.2004 (156):194-212.
    [82]Nagurney, Toyasaki. Reverse supply chain management and electronic waste recycling:a multitiered network equilibrium framework for e-cycling[J]. Transportation Research Part E.2005 (41):1-28.
    [83]Guang-fen Yang, Zhi-ping Wang, Xiao-qiang Li. The optimization of the closed-loop supply chain network[J]. Transportation Research Part E.2009 (45):16-28.
    [84]Nagurney. Supply chain network design under profit maximization and oligopolistic competition[J]. Transportation Research Part E.2010 (46):281 294.
    [85]张铁柱,刘志勇等.多商品流供应链网络均衡模型的研究[J].系统工程理论与实践.2005(7):61-65.
    [86]徐兵,朱道立.随机产品选择下多商品流供应链网络均衡模型研究[J].系统工程理论与实践,2007,27(3):82-90.
    [87]滕春贤,姚锋敏,胡宪武.具有随机需求的多商品流供应链网络均衡模型的研究[J].系统工程理论与实践,2007,10:77-83.
    [88]徐兵,朱道立.多用户多准则随机选择下供应链网络均衡模型[J].系统工程学报.2008(5):547-553.
    [89]《中华人民共和国邮政法》.http://www.spb.gov.cn/folder2/folder13/2009/0 4/2009-04-2528456.html.
    [90]张兰.快递企业网点布局研究[D].中南大学,2008.
    [91]顺丰速递网站.http://www.sf-express.com.
    [92]联邦快递中国网站.http://cndxp.apac.fedex.com/dxp.html.
    [93]中华人民共和国国家邮政局.http://www.spb.gov.cn/.
    [94]中国邮政速递物流.http://www.ems.com.cn/.
    [95]中国物流与采购联合会.中国物流统计年鉴2006.2006
    [96]中国物流与采购联合会.中国物流统计年鉴2007.2007
    [97]中国物流与采购联合会.中国物流统计年鉴2008.2008
    [98]中国物流与采购联合会.中国物流统计年鉴2009.2009
    [99]中国物流与采购联合会.中国物流统计年鉴2010.2010
    [100]中国铁路.http://www.chineserailways.com/html/xbys/xbys.html.
    [101]RFID世界网.Fedex将推出Senseaware实时追踪系统.http://news.rfidwor ld.com.cn/2009 12/20091211035554565.html
    [102]姚锦宝,夏禾等.同时取送货车辆路径问题的改进的蚁群算法[J].物流技术.2010年Z1期:76-82.
    [103]张军,唐加福等.分散搜索算法求解带货物权重的车辆路径问题[J].系统工程学报.2010年01期:91-97.
    [104]张景玲,赵燕伟等.多车型动态需求车辆路径问题建模及优化[J].计算机集成制造系统.2010,Vol.16 No.3 P.543-550.
    [105]宾松,符卓.求解带软时间窗的车辆路径问题的改进遗传算法[J].系统工程.2003,Vol.21 No.6 P.12-15.
    [106]刘小兰,郝志峰等.有时间窗的车辆路径问题的近似算法研究[J].计算机集成制造系统.2004,Vo1.10 No.7 P.825-831.
    [107]张丽萍,柴跃廷.车辆路径问题的改进遗传算法[J].系统工程理论与实践.2002年08期:79-84.
    [108]李阳.轴辐式网络理论及应用研究[D].上海:复旦大学,博士论文.2000.
    [109]秦进.多商品物流网络设计相关优化模型及算法研究[D].长沙:中南大学博士论文.2000.
    [110]蒋长兵.同城快递服务新模式(塘鹅件)研究[J].中国储运.2008年12期:111-113.
    [111]刘臣.上海派送部派送时效改善汇报[R].http://www.docin.com/p-21166320 3.html
    [112]荣晓华,龚振.消费者行为学[M].东北财经大学出版社.2005年第2版
    [113]Baldwin and Clark. Managing an Age of Modularity[J]. Harvard Business Review,1997,75(5).
    [114]青木昌彦,安藤晴彦.模块时代一新产业结构的本质[M].上海:上海远东出版社,2003.
    [115]胡晓鹏.模块化整合标准化:产业模块化研究[J].中国工业经济,2005(6):69-76.
    [116]芮明杰,刘明宇.模块化网络产业链的知识分工与创新[J].当代财经,2006(4):83-86.
    [117]何大军,巫景飞,芮明杰.企业创新战略视角下产业模块化动力机制研究[J].管理学报,2010年第7卷第2期:177-181[J].
    [118]慕容而来.服务产品模块化机理分析[J].http://www.tianya.cn/publicforum/ Content/no100/1/16856.shtml.
    [119]魏江、赵江琦.基于模块化架构的金融服务创新模式研究[J].科学学研究.2009年11期:1720-1728.
    [120]关增产.面向大规模定制的服务模块化研究[J].价值工程.2009年第11期:99-103
    [121]李靖华.服务大规模定制实现机理分析:制造业与服务业融合视角.科技管理研究.2008年02期:143-145,169.
    [122]李秉翰.服务模块化的可行性[J].市场营销导刊.2009(1):26-30.
    [123]Yonghwa Park, Jung Kyu Choi, Anming Zhang. Evaluating competitiveness of air cargo express services[J]. Transportation Research Part E.2009 (45):321-334
    [124]谢如鹤,李志锋.中国民营快递企业竞争力指标体系探讨及实证分析[J].广州大学学报(社会科学版).2008年06期:41-44.
    [125]董莉.我国快递业发展问题的研究[D].大连海事学院.2003.
    [126]曾祥培.我国民营快递企业竞争力分析[D].北京:对外经济贸易大学国际贸易学.2007.
    [127]薛蓉娜,赵会娟.中国邮政快递业竞争力的比较研究[J].当代财经.2006(2):87-90.
    [128]肖远菊.促进我国民营快递业发展的税收政策选择[J].中国商贸.2011年23期:141-142.
    [129]王维婷,黄宝章.快递业发展影响因素的实证研究[J].中国物流与采购2011年13期:74-75.
    [130]秦启,马天山,吴群琪.航空快递业特性分析及其在中国发展的设想[J].长安大学学报(社会科学版).2005,9(3):26-30.
    [131]张宁.产品随机选择与运输的跨区域市场均衡[J].系统工程理沦与实践,1997,17(12):74-78.
    [132]SheffiY. Urban Transportation Networks:Equilibrium Analysis with Mathematical programming Methods [M]. NewJersey:Prentiee-Hall, INC, Englewood Cliffs,1985.324-331.
    [133]周晶.随机交通均衡配流模型及其等价的变分不等式问题[J].系统科学与数学,2003(1):120-127.
    [134]雷星晖,陈萍.基于交通网络均衡方法的供应链竞争模型研究[J].经济经纬,2009(3):116-118.
    [135]陆化普,殷亚峰.交通网络均衡分析的变分不等式方法[J].公路交通科技,1997(2):24-29.
    [136]徐兵,朱道立.多用户多准则固定需求随机交通均衡变分模型[J].公路交通科技,2007(4):129-133.
    [137]李巧茹,马寿峰等.动态混合行为交通网络平衡的遗传算法求解[J].长安大学学报(自然科学版).2007(6):87-90.
    [138]李声杰,陈光亚.多类物流,双指标的交通网络平衡问题与向量变分不等式[J].系统工程理论与实践.2008,Vol.28 No.1 P.141-145.
    [139]袁鹏程,韩印等.基于行程时间可靠性的随机交通网络均衡模型[J].上海理工大学学报.2008(4):352-356.
    [140]易昆南,李志纯等.非可加路径费用的交通网络平衡问题[J].中南大学学报(自然科学版).2004(5):865-868.
    [141]Qiang Meng, Yi Kai Huang, Ruey Long Cheu. A note on supply chain network equilibrium models[J]. Transportation Research Part E.2007 (43):60-71.
    [142]简金宝,赖炎连.变分不等式的几类求解方法[J].高校应用跟数学学报.1991,14卷A辑:197-212