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## Graph Simplex Algorithm for Solving Minimal Flow Problem of a Network

Ning Xuanxi (College of Industry and Business,NUAA Nanjing,210016)
Blockage is a kind of phenomenon, happened frequently in a transport network in which human beings are the moving subjects. The minimal flow of a network defined in this paper means the maximal flow through the network in the most seriously blocked situation. It is an important parameter in designing a transport network, especially an emergency evacuation network. In this paper the combinatorial optimization model of the minimal flow problem is presented on the concept of saturated flow of a network which is defined for the research work on the blocking flow theory, and a practical method called Graph Simplex Algorithm is developed to solve the minimal flow problem with an example in detail.
【Fund】： 国家自然科学基金
【CateGory Index】： O157.5
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 【References】
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 【Citations】
 Chinese Journal Full-text Database 2 Hits
 1 Ning Xuanxi;The Two -Way How -Augmenting Algorithm for Solving the Minimum Flow Problem of a Network[J];系统工程;1997-01 2 Ning Xuanxi;A Branch -and -Bound Method for the Minimal Flow Problem of a Directed Network[J];系统工程;1996-05
 【Co-citations】
 Chinese Journal Full-text Database 10 Hits
 1 HUANG Yuda;LI Xuewei;ZHAO Hongzhuan;WANG Yiran;Information and Engineering Department,Zhoukou Vocational and Technical College;College of Automation,Chongqing University;College of Computer Science and Technology,Zhoukou Normal University;;Shortest Time Flow Optimization Problem Considering Congestion[J];计算机与数字工程;2016-09 2 LIN Hao;LIN Lan;School of Science,Henan University of Technology;School of Electronics and Information Engineering,Tongji University;;The minimum cover flow problem in networks[J];运筹学学报;2014-04 3 LIN Hao;LIN Lan;School of Science,Henan University of Technology;School of Electronics and Information Engineering,Tongji University;;Polynomial Time Solvable Variants of the Minimum Saturated Flow Problem[J];工程数学学报;2014-03 4 XIA Lin-lin,YE Mao-ying,YANG Ling-yun,MOU Lian-ming(College of Mathematic and Information Science,Neijiang Normal University,Neijiang,Sichuan 641100,China);Ant Colony Algorithm for Solving Minimum-cost Flow Problems[J];内江师范学院学报;2010-06 5 LI Xin-hua1 ZHANG Zhao-ning2 HOU Rui1 1.Flight Service Center,Southwest Air Traffic Management Bureau of CAAC,Chengdu 610202,China 2.Air Traffic Management Department, Civil Aviation University of China,Tianjin 300300,China;Research of the Structural Stability of the Route Network System[J];交通运输工程与信息学报;2009-01 6 XIE Fan-rong1,JIA Ren-an2(1.Department of Mathematics,Nanchang University,Nanchang 330031,China;2.Institute of System Engineering,Nanchang University,Nanchang 330031,China);Problem of Maximum Flow & Minimum Cut Set of Network with Lower & Upper Arc Capacities[J];运筹与管理;2008-02 7 WANG Ji,ZHOU Shu-min(Science College,Wuhan University of Technology,Wuhan 430070,China);A Global Optimization Method for Minimum-CostSaturated Flow Problem[J];汕头大学学报(自然科学版);2007-04 8 Wu Weiwei1,Ning Xuanxi2(1.College of Civil Aviation,Nanjing University of Aeronautics & Astronautics,Nanjing,210016,China;2.College of Economics and Management,Nanjing University of Aeronautics & Astronautics,Nanjing,210016,China);Minimum Saturated Flow Problem in Directed Network and Its Algorithm[J];南京航空航天大学学报;2007-05 9 WU Wei-wei and NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,Jiangsu,China);A Monte-Carlo simulation approach for stochastic flow of emergency evacuation networks based on different forward directed augmented paths[J];山东大学学报(理学版);2006-06 10 WANG Ji(Wuhan Science Technology University,Wuhan,Hubei,430070);A Solution of the Fuzzy Network Minimal Flow Problem[J];广东广播电视大学学报;2006-04
 【Co-references】
 Chinese Journal Full-text Database 10 Hits
 1 WU Wei-wei,NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronauticsand Astronautics,Nanjing 210016,China);Research of improving the blockage of emergency network[J];系统工程学报;2006-03 2 WU Wei-wei,NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China);Simulation Research on Improving the Flow Capability of Emergency Networks[J];中国管理科学;2006-03 3 WU Wei-wei,NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing Jiangsu 210016,China);Solve of the Minimum Saturated Flow in the Transportation Network[J];数学的实践与认识;2006-09 4 DANG Yao\|guo\+1, LIU Si\|feng\+1, FANG Zhi\|geng\+2(1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics,Nanjing 210016, China; 2. Auto Management Institute, Bengbu 233000, China);Algorithm of Cutting-set Matrix on the Maximum Flows of Network[J];系统工程理论与实践;2003-09 5 Xu Guobiao 1 Yu Jiang 21 (Inst.of S&R,CAAC Flight College,Deyang,Sichuan618307) 2 (Dept.of Flight Tech.,CAAC Flight College,Deyang,Sichuan618307);An approach of Route_Segment-Based Collision Alert Technology[J];计算机工程与应用;2003-04 6 Ning Xuanxi Qian Lei Sun Yu College of Economics and Management,Nanjing University of Aeronautics & Astronautics Nanjing 210016,P.R.China;Research on Stochastic Flow in a Transportation Network by Simulational Method[J];数据采集与处理;2002-03 7 YIXUN LIN ,XIANGLU LI,JUNQIANG DENG (Department of Mathematics, Zhengzhou University, Zhengzhou 450052);The Minimum Saturated Flow Problem in Emergency Networks[J];运筹学学报;2001-02 8 Ning Xuanxi (College of Industry and Business,NUAA Nanjing,210016);Graph Simplex Algorithm for Solving Minimal Flow Problem of a Network[J];南京航空航天大学学报;1997-05 9 Ning Xuanxi;The Two -Way How -Augmenting Algorithm for Solving the Minimum Flow Problem of a Network[J];系统工程;1997-01 10 Ning Xuanxi (College of Industry and Business, NUAA Nanjing,210016);Graph Simplex Method for Solution of Maximum Flow Problem in a Network[J];南京航空航天大学学报;1996-05
 【Secondary References】
 Chinese Journal Full-text Database 7 Hits
 1 GUO Jianke;WANG Shaobo;WANG Dandan;LIU Tianbao;Center for Studies of Marine Economy and Sustainable Development, Liaoning Normal University;Institute of Finance and Economics, Shanghai University of Finance and Economics;;Spatial Structural Pattern and Vulnerability of China-Japan-Korea Shipping Network[J];Chinese Geographical Science;2017-05 2 YANG Zhao-hui,ZHOU Cheng-lin (Department of Basis,Henan Communications Polytechnic,Zhengzhou 450005,China);The New Model of Conveying Network——The Improvement on K-H Model[J];数学的实践与认识;2012-03 3 WU Wei-wei~1,NING Xuan-xi~2 (1.Civil Aviation College,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;2.College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China);Evaluation of the reconstructing scheme making streets one-way[J];系统工程理论与实践;2009-07 4 XIE Fan-rong1,JIA Ren-an2(1.Department of Mathematics,Nanchang University,Nanchang 330031,China;2.Institute of System Engineering,Nanchang University,Nanchang 330031,China);Problem of Maximum Flow & Minimum Cut Set of Network with Lower & Upper Arc Capacities[J];运筹与管理;2008-02 5 Wu Weiwei1,Ning Xuanxi2(1.College of Civil Aviation,Nanjing University of Aeronautics & Astronautics,Nanjing,210016,China;2.College of Economics and Management,Nanjing University of Aeronautics & Astronautics,Nanjing,210016,China);Minimum Saturated Flow Problem in Directed Network and Its Algorithm[J];南京航空航天大学学报;2007-05 6 WU Wei-wei and NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,Jiangsu,China);A Monte-Carlo simulation approach for stochastic flow of emergency evacuation networks based on different forward directed augmented paths[J];山东大学学报(理学版);2006-06 7 WU Wei-wei,NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China);Simulation Research on Improving the Flow Capability of Emergency Networks[J];中国管理科学;2006-03
 【Secondary Citations】
 Chinese Journal Full-text Database 2 Hits
 1 Ning Xuanxi (College of Industry and Business, NUAA Nanjing,210016);Graph Simplex Method for Solution of Maximum Flow Problem in a Network[J];南京航空航天大学学报;1996-05 2 Ning Xuanxi;A Branch -and -Bound Method for the Minimal Flow Problem of a Directed Network[J];系统工程;1996-05
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