Fragile Networks: Identifying Vulnerabilities and Synergies in an Uncertain World / Edition 1

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Fragile Networks: Identifying Vulnerabilities and Synergies in an Uncertain World presents a comprehensive study of network systems and the roles these systems play in our everyday lives. This book successfully conceptualizes, defines, and constructs mathematically rigorous, computer-based tools for the assessment of network performance and efficiency, along with robustness and vulnerability analysis. The result is a thorough exploration that promotes an understanding of the critical infrastructure of today's network systems, from congested urban transportation networks and supply chain networks under disruption to financial networks and the Internet.

The authors approach the analyses by abstracting not only topological structures of networks, but also the behavior of network users, the demand for resources, the resulting flows, and the associated costs. Following an introduction to the fundamental methodologies and tools required for network analysis and network vulnerability, the book is organized into three self-contained parts:

Part I-Network Fundamentals, Efficiency Measurement, and Vulnerability Analysis explores the theoretical and practical foundations for a new network efficiency measure in order to assess the importance of network components in various network systems. Methodologies for distinct decision-making behaviors are outlined, along with the tools for qualitative analysis, the algorithms for the computation of solutions, and a thorough discussion of the unified network efficient measure and network robustness with the unified measure.

Part II-Applications and Extensions examines the efficiency changes and the associated cost increments after networkcomponents are eliminated or partially damaged. A discussion of the recently established connections between transportation networks and different critical networks is provided, which demonstrates how the new network measures and robustness indices can be applied to different supply chain, financial, and dynamic networks, including the Internet and electronic power networks.

Part III-Mergers and Acquisitions, Network Integration, and Synergies reveals the connections between transportation networks and different network systems and quantifies the synergies associated with the network systems, from total cost reduction to environmental impact assessment. In the case of mergers and acquisitions, the focus is on supply chain networks. The authors outline a system-optimization perspective for supply chain networks and also formalize coalition formation using game theory with insights into the merger paradox.

With its numerous network examples and real-world applications, Fragile Networks: Identifying Vulnerabilities and Synergies in an Uncertain World is an excellent book for courses in network science, transportation science, operations management, and financial networks at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners in the areas of applied mathematics, computer science, operations research, management science, finance, and economics, as well as industrial, systems, and civil engineering.

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Product Details

  • ISBN-13: 9780470444962
  • Publisher: Wiley
  • Publication date: 7/7/2009
  • Edition number: 1
  • Pages: 313
  • Product dimensions: 6.30 (w) x 9.30 (h) x 0.80 (d)

Meet the Author

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.
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Table of Contents

List of Figures xv

List of Tables xxi

Part I Network Fundamentals, Efficiency Measurement, And Vulnerability Analysis

1 Introduction and Overview 3

2 Fundamental Methodologies, Network Models, and Algorithms 13

2.1 Review of Variational Inequality Theory and its Relationships to Optimization 14

2.2 Decentralized Decision-Making and User-Optimization 18

2.2.1 The Network Equilibrium (U-O) Model with Fixed Demands 20

2.2.2 Network Equilibrium (U-O) Models with Elastic Demands 24

2.3 Centralized Decision-Making and System-Optimization 30

2.3.1 The System-Optimization (S-O) Models 30

2.3.2 System-Optimality Conditions 31

2.4 Algorithms 33

2.4.1 Equilibration Algorithms 33

2.4.2 The Projection Method 37

2.4.3 The Modified Projection Method 38

2.4.4 The Euler Method 38

2.5 Sources and Notes 44

3 Network Performance Measurement and Robustness Analysis 47

3.1 Some Preliminaries and Network Centrality Measures 50

3.2 A Unified Network Performance Measure Based on Decentralized Decision-Making 53

3.2.1 A Desirable Property of the Network Performance Measure 54

3.2.2 The Importance of Network Components 56

3.2.3 Numerical Examples 56

3.2.4 An Application of the New Network Measure to the Braess Network with Varying Demands 60

3.3 A Network Robustness Measure Under Decentralized Decision-Making Behavior 65

3.3.1 Some Theoretical Results for the Network Robustness Measure under BPR Functions and Fixed Demands 67

3.3.2 A Braess-Inspired Network 70

3.4 Relative Total Cost Indices for Assessing Network Robustness 72

3.4.1 Theoretical Results for Networks with BPR Functions 74

3.4.2 A Network Example 77

3.5 Summary and Conclusions 80

3.6Sources and Notes 81

Part II Applications and Extensions

4 Application of the Measures to Transportation Networks 85

4.1 A Larger Fixed Demand Network 89

4.2 The Sioux Falls Network 91

4.2.1 Importance of Links in the Sioux Falls Networks 91

4.2.2 Robustness of the Sioux Falls Network 92

4.2.3 The Relative Total Cost Indices for the Sioux Falls Network 93

4.3 The Anaheim Network 95

4.3.1 Robustness of the Anaheim Network 96

4.3.2 The Relative Total Cost Indices for the Anaheim Network 96

4.4 The Environmental Robustness and Link Importance of Transportation Networks 99

4.4.1 Environmental Emissions 99

4.4.2 Environmental Impact Assessment Indices for Transportation Networks 100

4.4.3 Environmental Link Importance Identification and Ranking 101

4.4.4 Numerical Examples 102

4.5 Summary and Conclusions 110

4.6 Sources and Notes 111

5 Supply Chain Networks with Disruption Risks 113

5.1 Introduction 113

5.2 The Supply Chain Model with Disruption Risks and Random Demands 118

5.2.1 The Behavior of the Manufacturers 118

5.2.2 The Behavior of the Retailers 121

5.2.3 The Market Equilibrium Conditions 122

5.2.4 The Equilibrium Conditions of the Supply Chain 123

5.3 A Weighted Supply Chain Performance Measure 125

5.3.1 A Supply Chain Network Performance Measure 125

5.3.2 Supply Chain Robustness Measurement 126

5.4 The Algorithm 127

5.5 Example 130

5.5.1 Example 5.1 130

5.5.2 Example 5.2 132

5.6 Summary and Conclusions 133

5.7 Sources and Notes 134

6 Critical Nodes and Links in Financial Networks 137

6.1 Introduction 137

6.2 The Financial Network Model 141

6.2.1 The Behavior of the Source Agents 142

6.2.2 The Behavior of the Financial Intermediaries 144

6.2.3 The Consumers at the Demand Markets and the Equilibrium Conditions 145

6.2.4 The Equilibrium Conditions for the Financial Network with Electronic Transactions 146

6.3 The Financial Network Performance Measure and the Importance of Components 149

6.3.1 The Financial Network Performance Measure 149

6.3.2 Network Efficiency vs. Network Performance 150

6.3.3 The Importance of a Financial Network Component 152

6.4 The Algorithm 152

6.5 Numerical Examples 154

6.6 Summary and Conclusions 161

6.7 Sources and Notes 162

7 Dynamic Networks, the Internet, and Electric Power 165

7.1 Introduction 165

7.2 Evolutionary Variational Inequalities and the Internet 168

7.3 The Efficiency Measure for Dynamic Networks Modeled as Evolutionary Variational Inequalities 173

7.4 An Application to the Time-Dependent Braess Network 178

7.5 Electric Power Networks 183

7.5.1 Discussion 185

7.6 Summary and Conclusions 186

7.7 Sources and Notes 187

Part III Mergers and Acquisitions, Network Integration, And Synergies

8 A System-Optimization Perspective for Supply Chain Network Integration 191

8.1 Introduction 191

8.2 The Pre-and Post-Horizontal Mergers Supply Chain Network Models 194

8.2.1 The Pre-Merger Supply Chain Network Model(s) 194

8.2.2 The Horizontal Merger Supply Chain Network Models 198

8.3 Measuring the Strategic Advantage Associated with Horizontal Mergers 203

8.4 Numerical Examples 204

8.5 Summary and Conclusions 208

8.6 Sources and Notes 209

9 Environmental and Cost Synergy in Network Integration 213

9.1 Introduction 213

9.2 The Pre- and Post-Merger Supply Chain Network Models 216

9.2.1 The Pre-Merger Supply Chain Network Model with Environmental Concerns 216

9.2.2 The Post-Merger Supply Chain Network Model with Environmental Concerns 219

9.3 Quantifying Synergy Associated with Environmental Concerns 222

9.4 Numerical Examples 222

9.4.1 Additional Examples 225

9.5 Summary and Concluding Remarks 226

9.6 Sources and Notes 228

10 Multiproduct Supply Chain Network Integration 231

10.1 Introduction 231

10.2 The Pre- and Post-Integration Multiproduct Supply Chain Network Models 232

10.2.1 The Pre-Integration Multiproduct Supply Chain Network Model 233

10.2.2 The Post-Integration Multiproduct Supply Chain Network Model 235

10.3 Quantifying Synergy Associated with Multiproduct Supply Chain Network Integration 237

10.4 Transformation of a Multiproduct Supply Chain Network into a Single Product One 238

10.5 Numerical Examples 240

10.5.1 Additional Examples 245

10.6 Application to Humanitarian Logistics 247

10.7 Summary and Conclusions 250

10.8 Sources and Notes 251

11 Network Oligopolies and the Merger Paradox 253

11.1 Introduction 253

11.2 The Network Oligopoly Model 256

11.3 Mergers through Coalition Formation 262

11.4 The Algorithm 265

11.5 Numerical Examples 266

11.5.1 Problem Set 1 266

11.5.2 Problem Set 2 272

11.5.3 Problem Set 3 273

11.6 Summary and Conclusions 275

11.7 Sources and Notes 275

Appendix 276

Bibliography 283

Glossary 307

Index 309

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