Dynamic Networks And Evolutionary Variational Inequalities

'Since the extraordinary impact of networks is self-evident today both in the field of telecommunications and transportation as well as in the field of economic and financial equilibria, the scientific work carried out by Patrizia Daniele appears as an outstanding resource. The author employs with uncommon competence mathematical topics that are at the forefront of the science, while at the same time enabling the reader to understand the matter treated without any difficulty. Moreover the reader is fascinated by the clarity, depth and soundness with which the evolutionary equilibria problems are studied and by the original efficient computational procedures which allow for the solving of many significant examples and concrete problems. Without any doubt the book represents a shining light and a necessary tool for scholars of pure and applied mathematics, for economists and engineers as well as for practitioners, general managers and managing directors.' - Antonino Maugeri, Università di Catania, Italy This book offers a comprehensive analysis of dynamic networks and evolutionary variational inequalities, a topic of growing prominence in the study of networks. The extraordinary importance of networks in finance, mathematics, computer science and other areas is well known but the relatively new concept of 'dynamic' networks is less well understood. They become dynamic when the constitutive elements of the phenomena associated with the fixed geometry of networks are considered to be evolving over time. Patrizia Daniele offers many numerical examples to illustrate the issues discussed and provides a broad appendix to enrich this challenging but deeply informative book.

This volume collects peer-reviewed short papers presented at the Optimization and Decision Science conference (ODS 2022) held in Florence (Italy) from August 30th to September 2nd, 2022, organized by the Global Optimization Laboratory within the University of Florence and AIRO (the Italian Association for Operations Research). The book includes contributions in the fields of operations research, optimization, problem solving, decision making and their applications in the most diverse domains. Moreover, a special focus is set on the challenging theme Operations Research: inclusion and equity. The work offers 30 contributions, covering a wide spectrum of methodologies and applications. Specifically, they feature the following topics: (i) Variational Inequalities, Equilibria and Games, (ii) Optimization and Machine Learning, (iii) Global Optimization, (iv) Optimization under Uncertainty, (v) Combinatorial Optimization, (vi) Transportation and Mobility, (vii) Health Care Management, and (viii) Applications. This book is primarily addressed to researchers and PhD students of the operations research community. However, due to its interdisciplinary content, it will be of high interest for other closely related research communities.

The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.

This book presents advanced research in a relatively new field of scholarly inquiry that is usually referred to as dynamic network user equilibrium, now almost universally abbreviated as DUE. It provides the first synthesis of results obtained over the last decade from applying the differential variational inequality (DVI) formalism to study the DUE problem. In particular, it explores the intimately related problem of dynamic network loading, which determines the arc flows and effective travel delays (or generalized travel costs) arising from the expression of departure rates at the origins of commuter trips between the workplace and home. In particular, the authors show that dynamic network loading with spillback of queues into upstream arcs may be formulated as a differential algebraic equation system. They demonstrate how the dynamic network loading problem and the dynamic traffic user equilibrium problem may be solved simultaneously rather than sequentially, as well as how the first-in-first-out queue discipline may be maintained for each when Lighthill-Whitham-Richardson traffic flow theory is used. A number of recent and new extensions of the DVI-based theory of DUE and corresponding examples are presented and discussed. Relevant mathematical background material is provided to make the book as accessible as possible.

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/ .

This book addresses the question of the double exposure of marine ecosystems, i.e. to both global climate changes and economic globalization. This book contains a short, but self sufficient mathematical introduction, the formalization in the context of Network economics of global commodity chains, with both trophic and economic processes, and a series of cases studies, going from the re‐addressing of fundamental ecological questions such as Gause’s exclusion principles to practical studies such as the representation of the global supply chain for tuna.

The COVID-19 pandemic has vividly and dramatically demonstrated the importance of supply chains to the functioning of societies and our economies. The discussion in this timely book explores prominent issues concerning supply chain networks and labor. The readership is aimed to include students, researchers, practitioners, and policy-makers, interested in the wide range of topics presented in these pages. Labor has a particular focus as the driver behind supply chains, whether associated with food products, life-saving medicines and supplies, or high tech products that make innovation possible, just to name a few. The impacts of policy interventions, in the form of wage bounds, and their ramifications, in terms of volume of attracted labor, product prices, product volumes, as well as profits, are explored. Profit-maximizing firms are considered (with relevant associated issues such as waste management in the case of the food sector, for example), but also non-profits, as in blood services, as well as humanitarian organizations engaged in disaster relief. The book is filled with many network figures, graphs, and tables with data, both input and output and includes an appendix that provides the foundations of the underlying mathematical methodologies used. The book offers strong evidence for the need to provide a holistic, system-wide perspective for the modeling, analysis, and solution of supply chain problems with the inclusion of the critical labor resources. A formalism using the prism of supply chain networks, which yields a graphic representation of supply chains, consisting of multiple stakeholders, is constructed. Models that capture the behaviors and interactions of single decision-makers as well as multiple decision-makers engaged in supply chain activities of production, transportation, storage, and distribution, are considered. The models capture many realistic constraints faced by firms today, as they seek to produce and deliver products, while dealing with competition, various constraints on labor, a variety of disruptions, labor shortages, challenges associated with proper wage-determination, plus the computation of optimal investments in labor productivity subject to budget constraints. The book provides prescriptive suggestions in terms of how to ameliorate negative impacts of labor disruptions and demonstrate benefits of appropriate wage determination.

This book is the first to bring an economics perspective in a rigorous manner to complex decision-making in the management of supply chains. It provides the foundations for the modeling of the interrelationships among decision-makers in supply chains, ranging from manufacturers, distributors, and retailers, to the consumers, assuming individualized behavior. The models handle both competition and cooperation and provide the resulting product flows and prices in the chains. A unique network economics perspective is brought to the issue, setting the book apart from the numerous management and operations research volumes available. After an introduction of the theoretical foundations, the book then extends and applies the theory to energy supply chains in the form of electric power generation and distribution networks. The relationships between electric power supply chains and transportation networks are vividly captured through theoretical results and the solution of practical examples. The book then explores environmental supply chain and financial networks with intermediation, which are interpreted as supply chains and also solved as such. Throughout, the underlying theme is that of transportation networks and how the relationships between supply chain networks and the more established theory of transportation network equilibria can be applied and exploited for logistic-type applications. Economists and transportation researchers will find the book's theory and applications of great interest. Operations researchers and management scientists as well as practitioners in business logistics will be interested in the book's methodological and practical tools.