Fragile Networks : Identifying Vulnerabilities and Synergies in an Uncertain World

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  • Format: Hardcover
  • Copyright: 2009-07-07
  • Publisher: Wiley

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The study of networks spans many disciplines due to their wide application and importance. Providing a unified and rigorous treatment of network systems, Fragile Networks presents new and novel methodological approaches that both capture and measure network vulnerabilities and performance. Identifying how performance, vulnerabilities, and synergy can be quantified, the book deftly demonstrates how the new network measure has significant advantages over several existing measures. The authors explore an array of topics that are of vital interest to practicing applied mathematicians, statisticians, computer scientists, operations researchers, industrial engineers, civil engineers, and economists.

Author Biography

Anna Nagurney, PhD, is John F. Smith Memorial Professor in the Department of Finance and Operations Management at the University of Massachusetts Amherst, where she is also the Founding Director of the Virtual Center for Supernetworks and the Supernetworks Laboratory for Computation and Visualization. Dr. Nagurney has over twenty years of academic and industry experience in the areas of transportation networks and congestion management, supply chain management, financial networks, network economics, and dynamic networks. Qiang Qiang, PhD, currently focuses his research on the mathematical modeling of complex decision-making on network systems with a concentration on transportation and logistics.

Table of Contents

List of Figuresp. xv
List of Tablesp. xxi
Network Fundamentals, Efficiency Measurement, And Vulnerability Analysis
Introduction and Overviewp. 3
Fundamental Methodologies, Network Models, and Algorithmsp. 13
Review of Variational Inequality Theory and its Relationships to Optimizationp. 14
Decentralized Decision-Making and User-Optimizationp. 18
The Network Equilibrium (U-O) Model with Fixed Demandsp. 20
Network Equilibrium (U-O) Models with Elastic Demandsp. 24
Centralized Decision-Making and System-Optimizationp. 30
The System-Optimization (S-O) Modelsp. 30
System-Optimality Conditionsp. 31
Algorithmsp. 33
Equilibration Algorithmsp. 33
The Projection Methodp. 37
The Modified Projection Methodp. 38
The Euler Methodp. 38
Sources and Notesp. 44
Network Performance Measurement and Robustness Analysisp. 47
Some Preliminaries and Network Centrality Measuresp. 50
A Unified Network Performance Measure Based on Decentralized Decision-Makingp. 53
A Desirable Property of the Network Performance Measurep. 54
The Importance of Network Componentsp. 56
Numerical Examplesp. 56
An Application of the New Network Measure to the Braess Network with Varying Demandsp. 60
A Network Robustness Measure Under Decentralized Decision-Making Behaviorp. 65
Some Theoretical Results for the Network Robustness Measure under BPR Functions and Fixed Demandsp. 67
A Braess-Inspired Networkp. 70
Relative Total Cost Indices for Assessing Network Robustnessp. 72
Theoretical Results for Networks with BPR Functionsp. 74
A Network Examplep. 77
Summary and Conclusionsp. 80
Sources and Notesp. 81
Applications and Extensions
Application of the Measures to Transportation Networksp. 85
A Larger Fixed Demand Networkp. 89
The Sioux Falls Networkp. 91
Importance of Links in the Sioux Falls Networksp. 91
Robustness of the Sioux Falls Networkp. 92
The Relative Total Cost Indices for the Sioux Falls Networkp. 93
The Anaheim Networkp. 95
Robustness of the Anaheim Networkp. 96
The Relative Total Cost Indices for the Anaheim Networkp. 96
The Environmental Robustness and Link Importance of Transportation Networksp. 99
Environmental Emissionsp. 99
Environmental Impact Assessment Indices for Transportation Networksp. 100
Environmental Link Importance Identification and Rankingp. 101
Numerical Examplesp. 102
Summary and Conclusionsp. 110
Sources and Notesp. 111
Supply Chain Networks with Disruption Risksp. 113
Introductionp. 113
The Supply Chain Model with Disruption Risks and Random Demandsp. 118
The Behavior of the Manufacturersp. 118
The Behavior of the Retailersp. 121
The Market Equilibrium Conditionsp. 122
The Equilibrium Conditions of the Supply Chainp. 123
A Weighted Supply Chain Performance Measurep. 125
A Supply Chain Network Performance Measurep. 125
Supply Chain Robustness Measurementp. 126
The Algorithmp. 127
Examplep. 130
Example 5.1p. 130
Example 5.2p. 132
Summary and Conclusionsp. 133
Sources and Notesp. 134
Critical Nodes and Links in Financial Networksp. 137
Introductionp. 137
The Financial Network Modelp. 141
The Behavior of the Source Agentsp. 142
The Behavior of the Financial Intermediariesp. 144
The Consumers at the Demand Markets and the Equilibrium Conditionsp. 145
The Equilibrium Conditions for the Financial Network with Electronic Transactionsp. 146
The Financial Network Performance Measure and the Importance of Componentsp. 149
The Financial Network Performance Measurep. 149
Network Efficiency vs. Network Performancep. 150
The Importance of a Financial Network Componentp. 152
The Algorithmp. 152
Numerical Examplesp. 154
Summary and Conclusionsp. 161
Sources and Notesp. 162
Dynamic Networks, the Internet, and Electric Powerp. 165
Introductionp. 165
Evolutionary Variational Inequalities and the Internetp. 168
The Efficiency Measure for Dynamic Networks Modeled as Evolutionary Variational Inequalitiesp. 173
An Application to the Time-Dependent Braess Networkp. 178
Electric Power Networksp. 183
Discussionp. 185
Summary and Conclusionsp. 186
Sources and Notesp. 187
Mergers and Acquisitions, Network Integration, And Synergies
A System-Optimization Perspective for Supply Chain Network Integrationp. 191
Introductionp. 191
The Pre-and Post-Horizontal Mergers Supply Chain Network Modelsp. 194
The Pre-Merger Supply Chain Network Model(s)p. 194
The Horizontal Merger Supply Chain Network Modelsp. 198
Measuring the Strategic Advantage Associated with Horizontal Mergersp. 203
Numerical Examplesp. 204
Summary and Conclusionsp. 208
Sources and Notesp. 209
Environmental and Cost Synergy in Network Integrationp. 213
Introductionp. 213
The Pre- and Post-Merger Supply Chain Network Modelsp. 216
The Pre-Merger Supply Chain Network Model with Environmental Concernsp. 216
The Post-Merger Supply Chain Network Model with Environmental Concernsp. 219
Quantifying Synergy Associated with Environmental Concernsp. 222
Numerical Examplesp. 222
Additional Examplesp. 225
Summary and Concluding Remarksp. 226
Sources and Notesp. 228
Multiproduct Supply Chain Network Integrationp. 231
Introductionp. 231
The Pre- and Post-Integration Multiproduct Supply Chain Network Modelsp. 232
The Pre-Integration Multiproduct Supply Chain Network Modelp. 233
The Post-Integration Multiproduct Supply Chain Network Modelp. 235
Quantifying Synergy Associated with Multiproduct Supply Chain Network Integrationp. 237
Transformation of a Multiproduct Supply Chain Network into a Single Product Onep. 238
Numerical Examplesp. 240
Additional Examplesp. 245
Application to Humanitarian Logisticsp. 247
Summary and Conclusionsp. 250
Sources and Notesp. 251
Network Oligopolies and the Merger Paradoxp. 253
Introductionp. 253
The Network Oligopoly Modelp. 256
Mergers through Coalition Formationp. 262
The Algorithmp. 265
Numerical Examplesp. 266
Problem Set 1p. 266
Problem Set 2p. 272
Problem Set 3p. 273
Summary and Conclusionsp. 275
Sources and Notesp. 275
Appendixp. 276
Bibliographyp. 283
Glossaryp. 307
Indexp. 309
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