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Fragile Networks: Identifying Vulnerabilities and Synergies in an Uncertain World

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A unified treatment of the vulnerabilities that exist in real-world network systems—with tools to identify synergies for mergers and acquisitions

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 network components 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.

Listen to Dr. Nagurney's podcast Supernetworks: Building Better Real and Virtual Highways at http://www.scienceofbetter.org/podcast/ .

Author(s): Anna Nagurney, Qiang Qiang
Publisher: Wiley
Year: 2009

Language: English
Pages: 313

FRAGILE NETWORKS: Identifying Vulnerabilities and Synergies in an Uncertain World......Page 5
CONTENTS......Page 11
List of Figures......Page 17
List of Tables......Page 23
PART I NETWORK FUNDAMENTALS, EFFICIENCY MEASUREMENT, AND VULNERABILITY ANALYSIS......Page 27
1 Introduction and Overview......Page 29
2 Fundamental Methodologies, Network Models, and Algorithms......Page 39
2.1 Review of Variational Inequality Theory and its Relationships to Optimization......Page 40
2.2 Decentralized Decision-Making and User-Optimization......Page 44
2.2.1 The Network Equilibrium (U-O) Model with Fixed Demands......Page 46
2.2.2 Network Equilibrium (U-O) Models with Elastic Demands......Page 50
2.3.1 The System-Optimization (S-O) Models......Page 56
2.3.2 System-Optimality Conditions......Page 57
2.4.1 Equilibration Algorithms......Page 59
2.4.2 The Projection Method......Page 63
2.4.4 The Euler Method......Page 64
2.5 Sources and Notes......Page 70
3 Network Performance Measurement and Robustness Analysis......Page 73
3.1 Some Preliminaries and Network Centrality Measures......Page 76
3.2 A Unified Network Performance Measure Based on Decentralized Decision-Making......Page 79
3.2.1 A Desirable Property of the Network Performance Measure......Page 80
3.2.3 Numerical Examples......Page 82
3.2.4 An Application of the New Network Measure to the Braess Network with Varying Demands......Page 86
3.3 A Network Robustness Measure Under Decentralized Decision-Making Behavior......Page 91
3.3.1 Some Theoretical Results for the Network Robustness Measure under BPR Functions and Fixed Demands......Page 93
3.3.2 A Braess-Inspired Network......Page 96
3.4 Relative Total Cost Indices for Assessing Network Robustness......Page 98
3.4.1 Theoretical Results for Networks with BPR Functions......Page 100
3.4.2 A Network Example......Page 103
3.5 Summary and Conclusions......Page 106
3.6 Sources and Notes......Page 107
PART II APPLICATIONS AND EXTENSIONS......Page 109
4 Application of the Measures to Transportation Networks......Page 111
4.1 A Larger Fixed Demand Network......Page 115
4.2.1 Importance of Links in the Sioux Falls Network......Page 117
4.2.2 Robustness of the Sioux Falls Network......Page 118
4.2.3 The Relative Total Cost Indices for the Sioux Falls Network......Page 119
4.3 The Anaheim Network......Page 121
4.3.2 The Relative Total Cost Indices for the Anaheim Network......Page 122
4.4.1 Environmental Emissions......Page 125
4.4.2 Environmental Impact Assessment Indices for Transportation Networks......Page 126
4.4.3 Environmental Link Importance Identification and Ranking......Page 127
4.4.4 Numerical Examples......Page 128
4.5 Summary and Conclusions......Page 136
4.6 Sources and Notes......Page 137
5.1 Introduction......Page 139
5.2.1 The Behavior of the Manufacturers......Page 144
5.2.2 The Behavior of the Retailers......Page 147
5.2.3 The Market Equilibrium Conditions......Page 148
5.2.4 The Equilibrium Conditions of the Supply Chain......Page 149
5.3.1 A Supply Chain Network Performance Measure......Page 151
5.3.2 Supply Chain Robustness Measurement......Page 152
5.4 The Algorithm......Page 153
5.5.1 Example 5.1......Page 156
5.5.2 Example 5.2......Page 158
5.6 Summary and Conclusions......Page 159
5.7 Sources and Notes......Page 160
6.1 Introduction......Page 163
6.2 The Financial Network Model......Page 167
6.2.1 The Behavior of the Source Agents......Page 168
6.2.2 The Behavior of the Financial Intermediaries......Page 170
6.2.3 The Consumers at the Demand Markets and the Equilibrium Conditions......Page 171
6.2.4 The Equilibrium Conditions for the Financial Network with Electronic Transactions......Page 172
6.3.1 The Financial Network Performance Measure......Page 175
6.3.2 Network Efficiency vs. Network Performance......Page 176
6.4 The Algorithm......Page 178
6.5 Numerical Examples......Page 180
6.6 Summary and Conclusions......Page 187
6.7 Sources and Notes......Page 188
7.1 Introduction......Page 191
7.2 Evolutionary Variational Inequalities and the Internet......Page 194
7.3 The Efficiency Measure for Dynamic Networks Modeled as Evolutionary Variational Inequalities......Page 199
7.4 An Application to the Time-Dependent Braess Network......Page 204
7.5 Electric Power Networks......Page 209
7.5.1 Discussion......Page 211
7.6 Summary and Conclusions......Page 212
7.7 Sources and Notes......Page 213
PART III MERGERS AND ACQUISITIONS, NETWORK INTEGRATION, AND SYNERGIES......Page 215
8.1 Introduction......Page 217
8.2.1 The Pre-Merger Supply Chain Network Model(s)......Page 220
8.2.2 The Horizontal Merger Supply Chain Network Models......Page 224
8.3 Measuring the Strategic Advantage Associated with Horizontal Mergers......Page 229
8.4 Numerical Examples......Page 230
8.5 Summary and Conclusions......Page 234
8.6 Sources and Notes......Page 235
9.1 Introduction......Page 239
9.2.1 The Pre-Merger Supply Chain Network Model with Environmental Concerns......Page 242
9.2.2 The Post-Merger Supply Chain Network Model with Environmental Concerns......Page 245
9.4 Numerical Examples......Page 248
9.4.1 Additional Examples......Page 251
9.5 Summary and Concluding Remarks......Page 252
9.6 Sources and Notes......Page 254
10.1 Introduction......Page 257
10.2 The Pre- and Post-Integration Multiproduct Supply Chain Network Models......Page 258
10.2.1 The Pre-Integration Multiproduct Supply Chain Network Model......Page 259
10.2.2 The Post-Integration Multiproduct Supply Chain Network Model......Page 261
10.3 Quantifying Synergy Associated with Multiproduct Supply Chain Network Integration......Page 263
10.4 Transformation of a Multiproduct Supply Chain Network into a Single Product One......Page 264
10.5 Numerical Examples......Page 266
10.5.1 Additional Examples......Page 271
10.6 Application to Humanitarian Logistics......Page 273
10.7 Summary and Conclusions......Page 276
10.8 Sources and Notes......Page 277
11.1 Introduction......Page 279
11.2 The Network Oligopoly Model......Page 282
11.3 Mergers through Coalition Formation......Page 288
11.4 The Algorithm......Page 291
11.5.1 Problem Set 1......Page 292
115.2 Problem Set 2......Page 298
115.3 Problem Set 3......Page 299
11.7 Sources and Notes......Page 301
Appendix......Page 302
Bibliography......Page 309
Glossary......Page 333
Index......Page 335