Chapman & Hall/CRC Series in Operations Research – serie

Introduction to the Theory of Optimization in Euclidean Space is intended to provide students with a robust introduction to optimization in Euclidean space, demonstrating the theoretical aspects of the subject whilst also providing clear proofs and applications. Students are taken progressively through the development of the proofs, where they have the occasion to practice tools of differentiation (Chain rule, Taylor formula) for functions of several variables in abstract situations.Throughout this book, students will learn the necessity of referring to important results established in advanced Algebra and Analysis courses.Features Rigorous and practical, offering proofs and applications of theorems Suitable as a textbook for advanced undergraduate students on mathematics or economics courses, or as reference for graduate-level readers Introduces complex principles in a clear, illustrative fashion

Applied Mathematics with Open-source Software: Operational Research Problems with Python and R is aimed at a broad segment of readers who wish to learn how to use open-source software to solve problems in applied mathematics. The book has an innovative structure with 4 sections of two chapters covering a large range of applied mathematical techniques: probabilistic modelling, dynamical systems, emergent behaviour and optimisation. The pairs of chapters in each section demonstrate different families of solution approaches. Each chapter starts with a problem, gives an overview of the relevant theory, shows a solution approach in R and in Python, and finally gives wider context by including a number of published references. This structure will allow for maximum accessibility, with minimal prerequisites in mathematics or programming as well as giving the right opportunities for a reader wanting to delve deeper into a particular topic.Features An excellent resource for scholars of applied mathematics and operational research, and indeed any academics who want to learn how to use open-source software. Offers more general and accessible treatment of the subject than other texts, both in terms of programming language but also in terms of the subjects considered. The R and Python sections purposefully mirror each other so that a reader can read only the section that interests them. An accompanying open-source repository with source files and further examples is posted online at https://bit.ly/3kpoKSd.

Applied Mathematics with Open-source Software: Operational Research Problems with Python and R is aimed at a broad segment of readers who wish to learn how to use open-source software to solve problems in applied mathematics. The book has an innovative structure with 4 sections of two chapters covering a large range of applied mathematical techniques: probabilistic modelling, dynamical systems, emergent behaviour and optimisation. The pairs of chapters in each section demonstrate different families of solution approaches. Each chapter starts with a problem, gives an overview of the relevant theory, shows a solution approach in R and in Python, and finally gives wider context by including a number of published references. This structure will allow for maximum accessibility, with minimal prerequisites in mathematics or programming as well as giving the right opportunities for a reader wanting to delve deeper into a particular topic.Features An excellent resource for scholars of applied mathematics and operational research, and indeed any academics who want to learn how to use open-source software. Offers more general and accessible treatment of the subject than other texts, both in terms of programming language but also in terms of the subjects considered. The R and Python sections purposefully mirror each other so that a reader can read only the section that interests them. An accompanying open-source repository with source files and further examples is posted online at https://bit.ly/3kpoKSd.

This book covers using R for doing optimization, a key area of operations research, which has been applied to virtually every industry. The focus is on linear and mixed integer optimization. It uses an algebraic modeling approach for creating formulations that pairs naturally with an algebraic implementation in R.With the rapid rise of interest in data analytics, a data analytics platform is key. Working technology and business professionals need an awareness of the tools and language of data analysis. R reduces the barrier to entry for people to start using data analytics tools. Philosophically, the book emphasizes creating formulations before going intoimplementation. Algebraic representation allows for clear understanding and generalizationof large applications, and writing formulations is necessary to explain and convey the modeling decisions made.Appendix A introduces R. Mathematics is used at the level of subscripts and summations Refreshers are provided in Appendix B.This book: • Provides and explains code so examples are relatively clear and self-contained.• Emphasizes creating algebraic formulations before implementing.• Focuses on application rather than algorithmic details.• Embodies the philosophy of reproducible research.• Uses open-source tools to ensure access to powerful optimization tools.• Promotes open-source: all materials are available on the author’s github repository.• Demonstrates common debugging practices with a troubleshooting emphasis specific to optimization modeling using R.• Provides code readers can adapt to their own applications.This book can be used for graduate and undergraduate courses for students without a background in optimization and with varying mathematical backgrounds.

The aim of Understanding Analytic Hierarchy Process book is to provide the reader with a critical guide to AHP. In this book, the AHP method is considered primarily as a mathematical technique supporting the decision-making process.

Understand the Strategic Behavior in Queueing SystemsRational Queueing provides one of the first unified accounts of the dynamic aspects involved in the strategic behavior in queues. It explores the performance of queueing systems where multiple agents, such as customers, servers, and central managers, all act but often in a noncooperative manner.The book first addresses observable queues and models that assume state-dependent behavior. It then discusses other types of information in queueing systems and compares observable and unobservable variations and incentives for information disclosure. The next several chapters present relevant models for the maximization of individual utilities, social welfare, and profits. After covering queueing networks, from simple parallel servers to general network structures, the author describes models for planned vacations and forced vacations (such as breakdowns). Focusing on supply chain models, he then shows how agents of these models may have different goals yet they all profit when the system operates efficiently. The final chapter allows bounded rationality by lowering the assumption of fully rational agents.

Handbook of the Shapley Value contains 24 chapters and a foreword written by Alvin E. Roth, who was awarded the Nobel Memorial Prize in Economic Sciences jointly with Lloyd Shapley in 2012. The purpose of the book is to highlight a range of relevant insights into the Shapley value. Every chapter has been written to honor Lloyd Shapley, who introduced this fascinating value in 1953. The first chapter, by William Thomson, places the Shapley value in the broader context of the theory of cooperative games, and briefly introduces each of the individual contributions to the volume. This is followed by a further contribution from the editors of the volume, which serves to introduce the more significant features of the Shapley value. The rest of the chapters in the book deal with different theoretical or applied aspects inspired by this interesting value and have been contributed specifically for this volume by leading experts in the area of Game Theory.Chapters 3 through to 10 are more focused on theoretical aspects of the Shapley value, Chapters 11 to 15 are related to both theoretical and applied areas. Finally, from Chapter 16 to Chapter 24, more attention is paid to applications of the Shapley value to different problems encountered across a diverse range of fields. As expressed by William Thomson in the Introduction to the book, "The chapters contribute to the subject in several dimensions: Mathematical foundations; axiomatic foundations; computations; applications to special classes of games; power indices; applications to enriched classes of games; applications to concretely specified allocation problems: an ever-widening range, mapping allocation problems into games or implementation."Nowadays, the Shapley value continues to be as appealing as when it was first introduced in 1953, or perhaps even more so now that its potential is supported by the quantity and quality of the available results. This volume collects a large amount of work that definitively demonstrates that the Shapley value provides answers and solutions to a wide variety of problems.

The large and complex challenges the world is facing, the growing prevalence of huge data sets, and the new and developing ways for addressing them (artificial intelligence, data science, machine learning, etc.), means it is increasingly vital that academics and professionals from across disciplines have a basic understanding of the mathematical underpinnings of effective, optimized decision-making. Without it, decision makers risk being overtaken by those who better understand the models and methods, that can best inform strategic and tactical decisions.Introduction to Optimization-Based Decision-Making provides an elementary and self-contained introduction to the basic concepts involved in making decisions in an optimization-based environment. The mathematical level of the text is directed to the post-secondary reader, or university students in the initial years. The prerequisites are therefore minimal, and necessary mathematical tools are provided as needed. This lean approach is complemented with a problem-based orientation and a methodology of generalization/reduction. In this way, the book can be useful for students from STEM fields, economics and enterprise sciences, social sciences and humanities, as well as for the general reader interested in multi/trans-disciplinary approaches.Features Collects and discusses the ideas underpinning decision-making through optimization tools in a simple and straightforward manner Suitable for an undergraduate course in optimization-based decision-making, or as a supplementary resource for courses in operations research and management science Self-contained coverage of traditional and more modern optimization models, while not requiring a previous background in decision theory

Handbook of the Shapley Value contains 24 chapters and a foreword written by Alvin E. Roth, who was awarded the Nobel Memorial Prize in Economic Sciences jointly with Lloyd Shapley in 2012. The purpose of the book is to highlight a range of relevant insights into the Shapley value. Every chapter has been written to honor Lloyd Shapley, who introduced this fascinating value in 1953. The first chapter, by William Thomson, places the Shapley value in the broader context of the theory of cooperative games, and briefly introduces each of the individual contributions to the volume. This is followed by a further contribution from the editors of the volume, which serves to introduce the more significant features of the Shapley value. The rest of the chapters in the book deal with different theoretical or applied aspects inspired by this interesting value and have been contributed specifically for this volume by leading experts in the area of Game Theory.Chapters 3 through to 10 are more focused on theoretical aspects of the Shapley value, Chapters 11 to 15 are related to both theoretical and applied areas. Finally, from Chapter 16 to Chapter 24, more attention is paid to applications of the Shapley value to different problems encountered across a diverse range of fields. As expressed by William Thomson in the Introduction to the book, "The chapters contribute to the subject in several dimensions: Mathematical foundations; axiomatic foundations; computations; applications to special classes of games; power indices; applications to enriched classes of games; applications to concretely specified allocation problems: an ever-widening range, mapping allocation problems into games or implementation."Nowadays, the Shapley value continues to be as appealing as when it was first introduced in 1953, or perhaps even more so now that its potential is supported by the quantity and quality of the available results. This volume collects a large amount of work that definitively demonstrates that the Shapley value provides answers and solutions to a wide variety of problems.

With contributions from some of the top academics and scientists in the field, Advanced Studies in Multi-Criteria Decision Making presents an updated view of the landscape of Decision Sciences, current research topics, the interaction with other sciences and fields, as well as the prospects and challenges at an international level. Given that Decision Sciences are recognized today as indispensable for confronting the major societal challenges in science and technology, this book would be of interest to decision-makers, managers, and researchers from academia, and industrial/services companies that would like a fresh insight into MCDM.Features Integrates a wide range of scientific fields with a general reader approach, including applied researchers from the social, business, enterprise sciences Suitable for academics and professionals Presents a broad coverage of MCDM tools either in industry or in services companies and systems Provides a fresh overview on MCDM studies promoted by prestigious R&D institutions

Introduction to the Theory of Optimization in Euclidean Space is intended to provide students with a robust introduction to optimization in Euclidean space, demonstrating the theoretical aspects of the subject whilst also providing clear proofs and applications. Students are taken progressively through the development of the proofs, where they have the occasion to practice tools of differentiation (Chain rule, Taylor formula) for functions of several variables in abstract situations.Throughout this book, students will learn the necessity of referring to important results established in advanced Algebra and Analysis courses.Features Rigorous and practical, offering proofs and applications of theorems Suitable as a textbook for advanced undergraduate students on mathematics or economics courses, or as reference for graduate-level readers Introduces complex principles in a clear, illustrative fashion

Exploring Operations Research with R shows how the R programming language can be a valuable tool – and way of thinking – which can be successfully applied to the field of operations research (OR). This approach is centred on the idea of the future OR professional as someone who can combine knowledge of key OR techniques (e.g., simulation, linear programming, data science, and network science) with an understanding of R, including tools for data representation, manipulation, and analysis. The core aim of the book is to provide a self-contained introduction to R (both Base R and the tidyverse) and show how this knowledge can be applied to a range of OR challenges in the domains of public health, infectious disease, and energy generation, and thus provide a platform to develop actionable insights to support decision making.FeaturesCan serve as a primary textbook for a comprehensive course in R, with applications in ORSuitable for post-graduate students in OR and data science, with a focus on the computational perspective of OR The text will also be of interest to professional OR practitioners as part of their continuing professional developmentLinked to a Github repository including code, solutions, data sets, and other ancillary material

Exploring Operations Research with R shows how the R programming language can be a valuable tool – and way of thinking – which can be successfully applied to the field of operations research (OR). This approach is centred on the idea of the future OR professional as someone who can combine knowledge of key OR techniques (e.g., simulation, linear programming, data science, and network science) with an understanding of R, including tools for data representation, manipulation, and analysis. The core aim of the book is to provide a self-contained introduction to R (both Base R and the tidyverse) and show how this knowledge can be applied to a range of OR challenges in the domains of public health, infectious disease, and energy generation, and thus provide a platform to develop actionable insights to support decision making.FeaturesCan serve as a primary textbook for a comprehensive course in R, with applications in ORSuitable for post-graduate students in OR and data science, with a focus on the computational perspective of OR The text will also be of interest to professional OR practitioners as part of their continuing professional developmentLinked to a Github repository including code, solutions, data sets, and other ancillary material

This book covers using R for doing optimization, a key area of operations research, which has been applied to virtually every industry. The focus is on linear and mixed integer optimization. It uses an algebraic modeling approach for creating formulations that pairs naturally with an algebraic implementation in R.With the rapid rise of interest in data analytics, a data analytics platform is key. Working technology and business professionals need an awareness of the tools and language of data analysis. R reduces the barrier to entry for people to start using data analytics tools. Philosophically, the book emphasizes creating formulations before going intoimplementation. Algebraic representation allows for clear understanding and generalizationof large applications, and writing formulations is necessary to explain and convey the modeling decisions made.Appendix A introduces R. Mathematics is used at the level of subscripts and summations Refreshers are provided in Appendix B.This book: • Provides and explains code so examples are relatively clear and self-contained.• Emphasizes creating algebraic formulations before implementing.• Focuses on application rather than algorithmic details.• Embodies the philosophy of reproducible research.• Uses open-source tools to ensure access to powerful optimization tools.• Promotes open-source: all materials are available on the author’s github repository.• Demonstrates common debugging practices with a troubleshooting emphasis specific to optimization modeling using R.• Provides code readers can adapt to their own applications.This book can be used for graduate and undergraduate courses for students without a background in optimization and with varying mathematical backgrounds.

Tracing its roots back to World War II, operations research (OR) has become a vital tool in military and defense strategy. The second edition of the Handbook of Military and Defense Operations Research highlights this evolution, showcasing how OR integrates with cutting-edge areas like artificial intelligence, cybersecurity, and big data analytics.This volume is more than a historical account; it is a practical guide. The volume features expert voices and offers insights into OR applications in modern security challenges. Readers will discover a blend of theory and real-world case studies, making it an essential resource for both newcomers and seasoned defense analysis professionals.Dive into this handbook to explore the rich, dynamic field of military and defense operations research, a discipline at the heart of global security and strategic decision-making.New to the second edition:Reorganized into a three-part structureExtensive revisions throughoutNumerous new exercises, examples, and case studiesSeveral new chapters

The aim of this book is to provide the reader with a critical guide to AHP. In this book, the AHP method is considered primarily as a mathematical technique supporting the decision-making process. This method provides a convenient and versatile framework for modelling multi-criteria decision problems, evaluating alternatives and deriving final priorities. Rather than imposing a correct decision, AHP allows the user to create a ranking of alternatives, then choose the one which is the best (or among the best). At the core of AHP is a pairwise comparisons (PC) method. This is an old technique known in various forms since at least the Middle Ages.

The large and complex challenges the world is facing, the growing prevalence of huge data sets, and the new and developing ways for addressing them (artificial intelligence, data science, machine learning, etc.), means it is increasingly vital that academics and professionals from across disciplines have a basic understanding of the mathematical underpinnings of effective, optimized decision-making. Without it, decision makers risk being overtaken by those who better understand the models and methods, that can best inform strategic and tactical decisions.Introduction to Optimization-Based Decision-Making provides an elementary and self-contained introduction to the basic concepts involved in making decisions in an optimization-based environment. The mathematical level of the text is directed to the post-secondary reader, or university students in the initial years. The prerequisites are therefore minimal, and necessary mathematical tools are provided as needed. This lean approach is complemented with a problem-based orientation and a methodology of generalization/reduction. In this way, the book can be useful for students from STEM fields, economics and enterprise sciences, social sciences and humanities, as well as for the general reader interested in multi/trans-disciplinary approaches.Features Collects and discusses the ideas underpinning decision-making through optimization tools in a simple and straightforward manner Suitable for an undergraduate course in optimization-based decision-making, or as a supplementary resource for courses in operations research and management science Self-contained coverage of traditional and more modern optimization models, while not requiring a previous background in decision theory

With contributions from some of the top academics and scientists in the field, Advanced Studies in Multi-Criteria Decision Making presents an updated view of the landscape of Decision Sciences, current research topics, the interaction with other sciences and fields, as well as the prospects and challenges at an international level. Given that Decision Sciences are recognized today as indispensable for confronting the major societal challenges in science and technology, this book would be of interest to decision-makers, managers, and researchers from academia, and industrial/services companies that would like a fresh insight into MCDM.Features Integrates a wide range of scientific fields with a general reader approach, including applied researchers from the social, business, enterprise sciences Suitable for academics and professionals Presents a broad coverage of MCDM tools either in industry or in services companies and systems Provides a fresh overview on MCDM studies promoted by prestigious R&D institutions