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This book offers a self-contained introduction to the world of robust combinatorial optimization. It explores decision-making using the min-max and min-max regret criteria, while also delving into the two-stage and recoverable robust optimization paradigms. It begins by introducing readers to general results for interval, discrete, and budgeted uncertainty sets, and subsequently provides a comprehensive examination of specific combinatorial problems, including the selection, shortest path, spanning tree, assignment, knapsack, and traveling salesperson problems. The book equips both students and newcomers to the field with a grasp of the fundamental questions and ongoing advancements in robust optimization. Based on the authors'years of teaching and refining numerous courses, it not only offers essential tools but also highlights the open questions that define this subject area.

This textbook provides researchers, post-graduate students, and practitioners with a systematic framework for coping with uncertainty when making facility location decisions. In addition to in-depth coverage of models and solution techniques, application areas are discussed. The book guides readers through the field, showing how to successfully analyze new problems and handle new applications. Initially, the focus is on base models and concepts. Then, gradually, more comprehensive models and more involved solution algorithms are discussed. Throughout the book, two perspectives are intertwined: the paradigm for capturing uncertainty, and the facility location problem at hand. The former includes stochastic programming, robust optimization, chance-constrained programming, and distributional robust optimization; the latter includes classical facility location problems and those arising in many real-world applications such as hub location, location routing, andlocation inventory.

This book provides university students and practitioners with a collection of importance measures to design systems with high reliability, maintain them with high availability, and restore them in case of failures. Optimal reliability design, properly system maintenance and resilience management are vital for retaining a high level of system availability. Reliability importance measures, which are used to identify the weakest components from different perspectives, can be used to achieve this goal. The book has seven parts. Chapter 1 introduces the basic concepts. Chapter 2 focuses on importance measures for the system design phase and introduces how the system reliability can be improved with importance measures. Chapters 3 and 4 provide importance measures-related methods for scheduling maintenance policies under different scenarios. Chapter 5 provides importance measures for networks. Chapter 6 proposes importance measures for resilience management. The last chapter, or Chapter 7, illustrates the importance measures with case studies adopted from four types of systems: mechanical systems, energy systems, transport networks, and supply chain networks.

This book explores optimization under uncertainty and related applications in agriculture, sustainable supply chains and the agrifood industry. Rapid changes in the primary sector are leading to more and more industrialized structures, which require optimization methods in order to cope with today's challenges. Addressing uncertainty in the agrifood industry may lead to more robust supply chain designs or to diversified risk. Sustainability requires interaction with the environmental or social sciences. This book bridges the gap between optimization theory, uncertainty, sustainability and primary-sector applications (mainly in the agriculture and food industry, but also fisheries, forestry and natural resources in general). Although it has been a major challenge for the operations research community, this urgently needed interdisciplinary collaboration is not adequately covered in most current curricula in applied mathematics, economics or (agronomic/industrial/forest) engineering. This book highlights research that can help fill this gap. The individual chapters cover applications of stochastic integer linear programming and multicriteria decision methods in agriculture. The topics addressed include uncertainty in areas such as the sugar cane industry, pig farming, and cold storage for perishable products. Large-scale sustainable food production is a growing concern; this book offers solutions to help meet global demand in agriculture by using and improving the methods of optimization theory and operations research.

This book demonstrates how decision-making models can be applied to solve specific real-life problems, with a particular emphasis on wind energy. In a step-by-step manner, it guides the reader through decision-making, the formulation of optimization models, and the methods for solving them. After providing an overview of various models for the design of wind farms, it presents an optimization model for deciding which economy (country) to invest in and models for selecting suppliers. A dedicated chapter focuses on different models for monitoring and predictive maintenance for wind turbines (farms) due to the construction of turbine blades and vibration. It shows how combinatorial optimization models can help to make optimal decisions for one-dimensional cutting stock of blanks, their processing, and determining the optimal composition for production. Moreover, it discusses how the energy consumption balance index formed by conventional and renewable sources can be determined and presents a means of identifying the relative share of wind energy consumption among the other renewable sources. Operations research professionals, students, and decision-makers alike will find this book to be a valuable resource for tackling real-world challenges and driving sustainable advances in wind energy solutions.

This book provides models and methods for the optimal management of electrical vehicles through an interdisciplinary approach that brings together knowledge from the sectors of transportation, manufacturing and smart grids. Optimization of Electric-Vehicle Charging explores several optimization models for the scheduling of electric vehicles in a smart grid. Both discrete-time and discrete-event approaches are considered to minimize tardiness, charging and production costs, on the basis of information like release time, due date, deadline, energy request, and availability of energy generated from renewable sources. Transportation demand is assessed, as well as user-equilibrium-based approaches, for the location of charging stations and for the assignment of users to multiple charging stations. Employing illustrations, tables and examples to elucidate the ideas presented, this book will be of value to researchers and practitioners in the fields of electrical engineering and transportation, as well as to graduate and PhD students.

The unique book advances understanding of modelling complex systems using hybrid approaches that combine discrete-event, agent-based, and system dynamic simulations with research approaches and artefacts from other scientific disciplines. As systems become increasingly large and complex, it is a challenge to capture the intricacies of the underlying system and offer novel forms of analysis using only models that employ a single simulation technique. The book underscores the importance of both hybrid simulation (employing techniques primarily developed in the field of modelling and simulation) and hybrid modelling (incorporating simulation with methods from wider disciplines such as applied computing, data science, engineering, and soft/qualitative operations research). Furthermore, the text aims to inspire further research and practice, fostering the growth of cross-disciplinary hybrid models. Topics and features: Provides a comprehensive overview of hybrid modelling and simulation, including methodological extensions and novel applications Features case studies and examples demonstrating the synergy realized by applying hybrid methods Calls for innovation and growth of the discipline by incorporating diverse scientific perspectives Encourages adoption of interdisciplinary methods to engender improved insights from simulation studies Promotes interdisciplinary collaboration, pushing modelling and simulation into new research and application areas This comprehensive volume will appeal to researchers, academics, students, and practitioners who seek to advance their modelling and simulation work. The book also will serve as a reference, informing research communities of the potential of hybrid models that combine simulation with disciplinary research artefacts, methods, and approaches.

This book introduces solutions for sports scheduling problems in a variety of settings. In particular the book covers timetabling, the traveling tournament problem, carryover minimization, breaks minimization, tournament design, tournament planning, and referee assignment. A rich selection of applications to sports such as football, baseball, basketball, cricket or hockey are employed to illustrate the methods and techniques. In a step-by-step tutorial format the book describes the use of graph theory concepts, local search operators and integer programming in the context of sports scheduling. The methods presented in this book are essential to sports scheduling in all its dimensions, from tournaments that are followed by millions of people across the world, with broadcast rights that amount to hundreds of millions of dollars in some competitions, to amateur leagues that require coordination and logistical efforts due to the large number of tournaments and competitors.

This book gathers a selection of peer-reviewed papers presented at the International Conference on Operations Research (OR 2022), which was held at Karlsruhe Institute of Technology, Germany, on September 6-9, 2022. KIT's Institute for Operations Research (IOR) hosted the conference together with the Institute for Industrial Production (IIP), the Institute for Automation and Applied Informatics (IAI), and the Institute for Material Handling and Logistics (IFL). The respective papers discuss classical mathematical optimization, statistics and simulation techniques. These are complemented by computer science methods, and by tools for processing data, designing and implementing information systems. The book also examines recent advances in information technology, which allow big data volumes to be processed and enable real-time predictive and prescriptive business analytics to drive decisions and actions. Lastly, it includes problems modeled and treated while taking into account uncertainty, risk management, behavioral issues, etc.

This book introduces the advances in synchromodal logistics and provides a framework to classify various optimisation problems in this field. It explores the application of this framework to solve a broad range of problems, such as problems with and without a central decision-maker, problems with and without full information, deterministic problems, problems coping with uncertainty, optimisation of a full network design problem. It covers theoretical constructs, such as discrete optimisation, robust optimisation, optimisation under uncertainty, multi-objective optimisation and agent based equilibrium models. Moreover, practical elaborated use cases are presented to deepen understanding. The book gives both researchers and practitioners a good overview of the field of synchromodal optimisation problems and offers the reader practical methods for modelling and problem-solving.

This book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets. At the same time, the underlying geometrical meaning of all the involved concepts and operations is highlighted and duly emphasized. A notable feature of the book is its unifying methodology, as well as the novelty of providing an alternative or complementary viewto the traditional one in which the discipline is presented to students and researchers. This textbook can be used for courses on optimization, convex and variational analysis, addressed to graduate and post-graduate students of mathematics, and also students of economics and engineering. It is also oriented to provide specific background for courses on optimal control, data science, operations research, economics (game theory), etc. The book represents a challenging and motivating development for those experts in functional analysis, convex geometry, and any kind of researchers who may be interested in applications of their work.

This volume consists of 14 contributed chapters written by leading experts, offering in-depth discussions of the mathematical modeling and algorithmic aspects for tackling a range of space engineering applications. This book will be of interest to researchers and practitioners working in the field of space engineering. Since it offers an in-depth exposition of the mathematical modelling, algorithmic and numerical solution aspects of the topics covered, the book will also be useful to aerospace engineering graduates and post-graduate students who wish to expand their knowledge by studying real-world applications and challenges that they will encounter in their profession. Readers will obtain a broad overview of some of the most challenging space engineering operational scenarios of today and tomorrow: this will be useful for managers in the aerospace field, as well as in other industrial sectors. The contributed chapters are mainly focused on space engineering practice. Researchers andpractitioners in mathematical systems modelling, operations research, optimization, and optimal control will also benefit from the case studies presented in this book. The model development and optimization approaches discussed can be extended towards other application areas that are not directly related to space engineering. Therefore, the book can be a useful reference to assist in the development of new modelling and optimization applications.

This book defines and studies a combinatorial object called the pedigree and develops the theory for optimising a linear function over the convex hull of pedigrees (the Pedigree polytope). A strongly polynomial algorithm implementing the framework given in the book for checking membership in the pedigree polytope is a major contribution.This book challenges the popularly held belief in computer science that a problem included in the NP-complete class may not have a polynomial algorithm to solve. By showing STSP has a polynomial algorithm, this book settles the P vs NP question.This book has illustrative examples, figures, and easily accessible proofs for showing this unexpected result. This book introduces novel constructions and ideas previously not used in the literature. Another interesting feature of this book is it uses basic max-flow and linear multicommodity flow algorithms and concepts in theseproofs establishing efficient membership checking for the pedigree polytope. Chapters 3-7 can be adopted to give a course on Efficient Combinatorial Optimization. This book is the culmination of the author's research that started in 1982 through a presentation on a new formulation of STSP at the XIth International Symposium on Mathematical Programming at Bonn.

After developing fuzzy set theory, many contributors focused their research on the extension of fuzzy sets and their computational methodologies, strengthening modern science and technology. In some real-life phenomena, the conventional methods and traditional fuzzy sets cannot be explained, whereas the extension of fuzzy sets and effective new computing methods can explain it adequately. This edited book presents a new view of fuzzy set-measurement methods entitled'Fuzzy Optimization, Decision Making and Operations Research: Theory and Applications', which deals with different perspectives and areas of research. All chapters are divided into three parts: fuzzy optimization, fuzzy decision-making, and fuzzy operation research. The goal of this book is to provide a relevant methodological framework covering the core fields of fuzzy decision-making method, fuzzy optimization method, fuzzy graphics method, fuzzy operations research, fuzzy optimization using graph theory, fuzzy support systems and its real and industrial applications. For many people, fuzzy words'industrial engineering and scientific meanings are still an advanced system for improving modern science and technology. Although fuzzy logic can be applied to many different areas, people do not know how different fuzzy approaches can be applied to various products currently on the market. It is written for professionals who wish to share their expertise, improve their findings, and provide relevant information in the fields of fuzzy methods and their application in decision-making, optimization theory, graph theory and operations research. This book is aimed at experts and practitioners in the fields of fuzzy optimization, fuzzy decision-making, and fuzzy operation research.

This book deals with an often-neglected feature of location problems, namely uncertainty, by combining two related fields: location theory and optimization. Written by leading researchers and practitioners in these fields, each chapter examines one aspect of the location process in different contexts, such as supply chains; location decisions under congestion; disaster management; design of resilient facilities; uncertainty in the health sector; and facility location in the retail sector under uncertainty. The book also addresses methodological aspects, such as chance-constrained approaches, heuristic algorithms, scenario approaches, and simulation. As such, it provides decision-makers with essential methods, tools and approaches to help them deal with these uncertainties. It is mainly intended for graduate students in the fields of operations research and logistics, as well as professionals in logistics and supply chain management.

The book contains selected contributions from the 48th Annual Meeting of the EURO Working Group on Operational Research Applied to Health Services (ORAHS 2022) held in Bergamo, Italy, July 2022. ORAHS 2022 provided a network for researchers involved in the application of systematic and quantitative analyses to support planning and management in the health services sector, with the ultimate goal of pursuing good health and well-being. It was the ORAHS in the red zone, focused on the organization and reaction of health systems in the face of emergency situations such as the COVID pandemic. The questions addressed were, for example, how can hospitals and public authorities react to extreme scenarios by reorganizing their resources? How and to what extent do local health systems integrate hospitals to deal with a pandemic? How can Decision Support Systems for diagnosis and treatment help when battling a new virus for the first time? Contributions included a variety of methodological viewpoints (optimization, simulation, data analysis, predictive models, decision science, mathematical programming, machine learning,...) and health services applications (hospital management, therapy calibration, analysis of statistical and epidemiological data, minimization of logistics costs,...). This work strongly contributes to the Sustainable Development Goals (SDG) Programme.

The book addresses optimization in the petroleum industry from a practical, large-scale-application-oriented point of view. The models and techniques presented help to optimize the limited resources in the industry in order to maximize economic benefits, ensure operational safety, and reduce environmental impact. The book discusses several important real-life applications of optimization in the petroleum industry, ranging from the scheduling of personnel time to the blending of gasoline. It covers a wide spectrum of relevant activities, including drilling, producing, maintenance, and distribution. The text begins with an introductory overview of the petroleum industry and then of optimization models and techniques. The main body of the book details a variety of applications of optimization models and techniques within the petroleum industry.Applied Optimization in the Petroleum Industry helps readers to find effective optimization-based solutions to their own practical problems in a large and important industrial sector, still the main source of the world's energy and the source of raw materials for a wide variety of industrial and consumer products.

This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Ampère measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area. Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory and integration, as well as basic knowledge of functional analysis.

This book provides the current status of research on the application of OR methods to solve emerging and relevant operations management problems. Each chapter is a selected contribution of the IO2021 - XXI Congress of APDIO, the Portuguese Association of Operational Research, held in Figueira da Foz from 7 to 8 November 2021. Under the theme of analytics for a better world, the book presents interesting results and applications of OR cutting-edge methods and techniques to various real-world problems. Of particular importance are works applying nonlinear, multi-objective optimization, hybrid heuristics, multicriteria decision analysis, data envelopment analysis, simulation, clustering techniques and decision support systems, in different areas such as supply chain management, production planning and scheduling, logistics, energy, telecommunications, finance and health. All chapters were carefully reviewed by the members of the scientific program committee.

This monograph represents a historic breakthrough in the field of linear programming (LP)since George Dantzig first discovered the simplex method in 1947. Being both thoughtful and informative, it focuses on reflecting and promoting the state of the art by highlighting new achievements in LP. This new edition is organized in two volumes. The first volume addresses foundations of LP, including the geometry of feasible region, the simplex method and its implementation, duality and the dual simplex method, the primal-dual simplex method, sensitivity analysis and parametric LP, the generalized simplex method, the decomposition method, the interior-point method and integer LP method. The second volume mainly introduces contributions of the author himself, such as efficient primal/dual pivot rules, primal/dual Phase-I methods, reduced/D-reduced simplex methods, the generalized reduced simplex method, primal/dual deficient-basis methods, primal/dual face methods, a new decomposition principle, etc.Many important improvements were made in this edition. The first volume includes new results, such as the mixed two-phase simplex algorithm, dual elimination, fresh pricing scheme for reduced cost, bilevel LP models and intercepting of optimal solution set. In particular, the chapter Integer LP Method was rewritten with great gains of the objective cutting for new ILP solvers {\it controlled-cutting/branch} methods, as well as with an attractive implementation of the controlled-branch method. In the second volume, the `simplex feasible-point algorithm'was rewritten, and removed from the chapter Pivotal Interior-Point Method to form an independent chapter with the new title `Simplex Interior-Point Method', as it represents a class of efficient interior-point algorithms transformed from traditional simplex algorithms. The title of the original chapter was then changed to `Facial Interior-Point Method', as the remaining algorithms represent another class of efficient interior-point algorithms transformed from normal interior-point algorithms. Without exploiting sparsity, the original primal/dual face methods were implemented using Cholesky factorization. In order to deal with sparse computation, two new chapters discussing LU factorization were added to the second volume. The most exciting improvement came from the rediscovery of the reduced simplex method. In the first edition, the derivation of its prototype was presented in a chapter with the same title, and then converted into the so-called `improved'version in another chapter. Fortunately, the author recently found a quite concise new derivation, so he can now introduce the distinctive fresh simplex method in a single chapter. It is exciting that the reduced simplex method can be expected to be the best LP solver ever.With a focus on computation, the current edition contains many novel ideas, theories and methods, supported by solid numerical results. Being clear and succinct, its content reveals in a fresh manner, from simple to profound. In particular, a larger number of examples were worked out to demonstrate algorithms. This book is a rare work in LP and an indispensable tool for undergraduate and graduate students, teachers, practitioners, and researchers in LP and related fields.

This proceedings book contains selected papers from the Fourth International Workshop on Best-Worst Method (BWM2023), held in Delft, the Netherlands, from 8 to 9 June 2023. It presents recent advancements in theory and applications of the Best-Worst Method (BWM). It provides valuable insights on why and how to use BWM in a diverse set of applications including health, energy, supply chain management, and engineering. The book highlights the use of BWM in different settings including single decision-making vs group decision-making, full information vs incomplete and uncertain situations. Academics and practitioners who are involved in multi-criteria decision-making and decision analysis benefit from the papers published in this book.

This proceedings volume gathers selected, blinded peer-reviewed contributions presented at the XXIX International Joint Conference on Industrial Engineering and Operations Management (IJCIEOM), held in Lisbon, Portugal, from June 28th to 30th, 2023. This volume focuses especially on the applications of Industrial Engineering and Operations Management for research and practice. It includes relevant information for academics since most of the chapters focus on real-world case studies and systematic reviews. It also provides valuable insights for professionals in the industrial sector by presenting solutions to complex industrial challenges. The 2023 iteration of the IJCIEOM conference had the theme'Developing resilience in Industrial Engineering and Operations Management'and aimed to analyze the resilience of supply chains in the post-COVID-19 era. The works published in this volume focus on how Digital Transformation (DX) and Artificial Intelligence (AI) have made themanufacturing and service industry more resistant to VUCA elements (i.e., volatile, uncertain, complex, and ambiguous). Regarding DX and AI, the research specifically focused on supply chain management, project management, and Industry 4.0. Other studies explore how industrial engineering incorporated innovative and technological concepts into service and product operations. Overall, this volume provides a valuable resource for researchers and practitioners alike as it presents numerous relevant contributions in identifying new challenges and opportunities for industrial engineering and operations management. This conference was sponsored by renowned international industry engineering associations, particularly the American Society for Engineering Management (ASEM), the Institute of Industrial & Systems Engineers (IISE), and the Asociación para el Desarrollo de la Ingeniería de Organización (ADINGOR).

This book gathers selected high-quality papers presented at the 31st European Conference on Operational Research, which was held in Athens, Greece on June 11-14, 2021.It highlights the latest advances in the application of operations research (OR) to technology-driven areas in business, finance, and economics, covering both theoretical and methodological developments, as well as real-world case studies. It also explores the connections between OR and other analytical disciplines, such as soft computing and computer science, which can promote the development of new decision support technologies.

This edited volume is an in-depth collation of the usage of different quantitative decision making techniques in practical areas such as lean & green supply chain, reverse logistics, perishable logistics, closed loop supply chain, sustainable project management, retail management, block chain applications, optimal supplier selection problem, demand/supply modelling, forecasting under uncertainties, scheduling & sequencing, resource constraint logistics, dynamic network supply chain, risk evaluation, and so on. Additionally, the book also solves these issues in theoretical and practical context using innovative mathematical tools. Consisting of selected papers from the 23rd Annual International Conference of the Society of Operations Management, this book's highlight is not only the coverage of interesting topics, but also how these topics are dealt with, such that post-graduate students as well as researchers and industry personnel working in areas like engineering, economics, social sciences, management, mathematics, etc., can derive the maximum benefit by reading or referring to this book. Apart from the emphasis on new mathematical, operations research, operations management, and statistical techniques, the authors also ensure that all the concepts are made clear by highlighting their practical significance in different areas of applications of operations management. By using novel presentation methods, the book offers a good practical flavor of all the different topics relevant to operations management in the coming decades.

In this book, the theory, methods and applications of separable optimization are considered. Some general results are presented, techniques of approximating the separable problem by linear programming problem, and dynamic programming are also studied. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and convergent iterative algorithms of polynomial complexity are proposed. As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. The problems of numerical approximation of tabulated functions and numerical solution of overdetermined systems of linear algebraic equations and some systems of nonlinear equations are solved by separable convex unconstrained minimization problems. Some properties of the Knapsack polytope are also studied. This second edition includes a substantial amount of new and revised content. Three new chapters, 15-17, are included. Chapters 15-16 are devoted to the further analysis of the Knapsack problem. Chapter 17 is focused on the analysis of a nonlinear transportation problem. Three new Appendices (E-G) are also added to this edition and present technical details that help round out the coverage. Optimization problems and methods for solving the problems considered are interesting not only from the viewpoint of optimization theory, optimization methods and their applications, but also from the viewpoint of other fields of science, especially the artificial intelligence and machine learning fields within computer science. This book is intended for the researcher, practitioner, or engineer who is interested in the detailed treatment of separable programming and wants to take advantage of the latest theoretical and algorithmic results. It may also be used as a textbook for a special topics course or as a supplementary textbook for graduate courses on nonlinear and convex optimization.

This book is addressed to researchers in operations research, data science and artificial intelligence. It collects selected contributions from the first hybrid “Optimization and Decision Science - ODS2021” international conference on the theme Optimization and Artificial Intelligence and Data Sciences, which was held in Rome 14-17 September 2021 and organized by AIRO, the Italian Operations Research Society and the Department of Statistical Sciences of Sapienza University of Rome. The book offers new and original contributions on different methodological optimization topics, from Support Vector Machines to Game Theory Network Models, from Mathematical Programming to Heuristic Algorithms, and Optimization Methods for a number of emerging problems from Truck and Drone delivery to Risk Assessment, from Power Networks Design to Portfolio Optimization. The articles in the book can give a significant edge to the general themes of sustainability and pollution reduction, distributive logistics, healthcare management in pandemic scenarios and clinical trials, distributed computing, scheduling, and many others. For these reasons, the book is aimed not only at researchers in the Operations Research community but also for practitioners facing decision-making problems in these areas and to students and researchers from other disciplines, including Artificial Intelligence, Computer Sciences, Finance, Mathematics, and Engineering.

Written by a leading expert in turnpike phenomenon, this book is devoted to the study of symmetric optimization, variational and optimal control problems in infinite dimensional spaces and turnpike properties of their approximate solutions. The book presents a systematic and comprehensive study of general classes of problems in optimization, calculus of variations, and optimal control with symmetric structures from the viewpoint of the turnpike phenomenon. The author establishes generic existence and well-posedness results for optimization problems and individual (not generic) turnpike results for variational and optimal control problems. Rich in impressive theoretical results, the author presents applications to crystallography and discrete dispersive dynamical systems which have prototypes in economic growth theory.This book will be useful for researchers interested in optimal control, calculus of variations turnpike theory and their applications, suchas mathematicians, mathematical economists, and researchers in crystallography, to name just a few.

This book presents the construction and resolution of 50 practical optimization problems and covers an exceptionally wide range, including games-associated problems (Unblock Me, Sudokus), logistical problems, and problems concerning plant distribution, production, operations scheduling, management and resource allocation. The problems are divided into 5 difficulty levels. Problems in the first few levels are focused on learning the model construction methodology, while those in the last level include complex optimization environments. For each problem solution, the specific steps are illustrated, promoting reader comprehension. In addition, all the models are implemented in an optimization library, LINGO, their solutions have been analyzed and their correct construction has been verified. The book also includes a simple guide to implementing models in LINGO in a straightforward manner and in any input data format (text files, spreadsheets or databases). As anideal companion to the author's previously published work Modelling in Mathematical Programming, the book is intended as a basic tool for students of operations research, and for researchers in any advanced area involving mathematical programming.

This textbook provides a comprehensive step-by-step guide for new public transport modelers. It includes an introduction to mathematical modeling, continuous and discrete optimization, numerical optimization, computational complexity analysis, metaheuristics, and multi-objective optimization. These tools help engineers and modelers to use better existing public transport models and also develop new models that can address future challenges. By reading this book, the reader will gain the ability to translate a future problem description into a mathematical model and solve it using an appropriate solution method.The textbook provides the knowledge needed to develop highly accurate mathematical models that can serve as decision support tools at the strategic, tactical, and operational planning levels of public transport services. Its detailed description of exact optimization methods, metaheuristics, bi-level, and multi-objective optimization approaches together with the detailed description of implementing these approaches in classic public transport problems with the use of open source tools is unique and will be highly useful to students and transport professionals.

This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates MESP in information theory, as the algorithmic problem of calculating a sub-vector of pre-specificed size from a multivariate Gaussian random vector, so as to maximize Shannon's differential entropy. The text collects and expands on state-of-the-art algorithms for MESP, and addresses its application in the field of environmental monitoring. While MESP is a central optimization problem in the theory of statistical designs (particularly in the area of spatial monitoring), this book largely focuses on the unique challenges of its algorithmic side. From the perspective of mathematical-optimization methodology, MESP is rather unique (a 0/1 nonlinear program having a nonseparable objective function), and the algorithmic techniques employed are highly non-standard. In particular, successful techniques come from several disparate areas within the field of mathematical optimization; for example: convex optimization and duality, semidefinite programming, Lagrangian relaxation, dynamic programming, approximation algorithms, 0/1 optimization (e.g., branch-and-bound), extended formulation, and many aspects of matrix theory. The book is mainly aimed at graduate students and researchers in mathematical optimization and data analytics.

The quadratic binary optimization problem (QUBO) is a versatile combinatorial optimization model with a variety of applications and rich theoretical properties. Application areas of the model include finance, cluster analysis, traffic management, machine scheduling, VLSI physical design, physics, quantum computing, engineering, and medicine. In addition, various mathematical optimization models can be reformulated as a QUBO, including the resource constrained assignment problem, set partitioning problem, maximum cut problem, quadratic assignment problem, the bipartite unconstrained binary optimization problem, among others.This book presents a systematic development of theory, algorithms, and applications of QUBO. It offers a comprehensive treatment of QUBO from various viewpoints, including a historical introduction along with an in-depth discussion of applications modelling, complexity and polynomially solvable special cases, exact and heuristic algorithms, analysis of approximation algorithms, metaheuristics, polyhedral structure, probabilistic analysis, persistencies, and related topics. Available software for solving QUBO is also introduced, including public domain, commercial, as well as quantum computing based codes.

Discover the practical impacts of current methods of optimization with this approachable, one-stop resource Linear and Convex Optimization: A Mathematical Approach delivers a concise and unified treatment of optimization with a focus on developing insights in problem structure, modeling, and algorithms. Convex optimization problems are covered in detail because of their many applications and the fast algorithms that have been developed to solve them. Experienced researcher and undergraduate teacher Mike Veatch presents the main algorithms used in linear, integer, and convex optimization in a mathematical style with an emphasis on what makes a class of problems practically solvable and developing insight into algorithms geometrically. Principles of algorithm design and the speed of algorithms are discussed in detail, requiring no background in algorithms. The book offers a breadth of recent applications to demonstrate the many areas in which optimization is successfully and frequently used, while the process of formulating optimization problems is addressed throughout. Linear and Convex Optimization contains a wide variety of features, including: Coverage of current methods in optimization in a style and level that remains appealing and accessible for mathematically trained undergraduates Enhanced insights into a few algorithms, instead of presenting many algorithms in cursory fashion An emphasis on the formulation of large, data-driven optimization problems Inclusion of linear, integer, and convex optimization, covering many practically solvable problems using algorithms that share many of the same concepts Presentation of a broad range of applications to fields like online marketing, disaster response, humanitarian development, public sector planning, health delivery, manufacturing, and supply chain management Ideal for upper level undergraduate mathematics majors with an interest in practical applications of mathematics, this book will also appeal to business, economics, computer science, and operations research majors with at least two years of mathematics training.Software to accompany the text can be found here: https://www.gordon.edu/michaelveatch/optimization

This book is devoted to the study of a class of optimal control problems arising in mathematical economics, related to the Robinson–Solow–Srinivasan (RSS) model. It will be useful for researches interested in the turnpike theory, infinite horizon optimal control and their applications, and mathematical economists. The RSS is a well-known model of economic dynamics that was introduced in the 1960s and as many other models of economic dynamics, the RSS model is determined by an objective function (a utility function) and a set-valued mapping (a technology map). The set-valued map generates a dynamical system whose trajectories are under consideration and the objective function determines an optimality criterion. The goal is to find optimal trajectories of the dynamical system, using the optimality criterion. Chapter 1 discusses turnpike properties for some classes of discrete time optimal control problems. Chapter 2 present the description of the RSS model and discuss its basic properties. Infinite horizon optimal control problems, related to the RSS model are studied in Chapter 3. Turnpike properties for the RSS model are analyzed in Chapter 4. Chapter 5 studies infinite horizon optimal control problems related to the RSS model with a nonconcave utility function. Chapter 6 focuses on infinite horizon optimal control problems with nonautonomous optimality criterions. Chapter 7 contains turnpike results for a class of discrete-time optimal control problems. Chapter 8 discusses the RSS model and compares different optimality criterions. Chapter 9 is devoted to the study of the turnpike properties for the RSS model. In Chapter 10 the one-dimensional autonomous RSS model is considered and the continuous time RSS model is studied in Chapter 11.

This textbook provides an introduction to the use and understanding of optimization and modeling for upper-level undergraduate students in engineering and mathematics. The formulation of optimization problems is founded through concepts and techniques from operations research: Combinatorial Optimization, Linear Programming, and Integer and Nonlinear Programming (COLIN). Computer Science (CS) is also relevant and important given the applications of algorithms and Apps/algorithms (A) in solving optimization problems. Each chapter provides an overview of the main concepts of optimization according to COLINA, providing examples through App Inventor and AMPL software applications. All apps developed through the text are available for download. Additionally, the text includes links to the University of Wisconsin NEOS server, designed to handle more computing-intensive problems in complex optimization. Readers are encouraged to have some background in calculus, linear algebra, and relatedmathematics.

The book is intended for graduate students and researchers in mathematics, computer science, and operational research. The book presents a new derivative-free optimization method/algorithm based on randomly generated trial points in specified domains and where the best ones are selected at each iteration by using a number of rules. This method is different from many other well established methods presented in the literature and proves to be competitive for solving many unconstrained optimization problems with different structures and complexities, with a relative large number of variables. Intensive numerical experiments with 140 unconstrained optimization problems, with up to 500 variables, have shown that this approach is efficient and robust. Structured into 4 chapters, Chapter 1 is introductory. Chapter 2 is dedicated to presenting a two level derivative-free random search method for unconstrained optimization. It is assumed that the minimizing function is continuous, lower bounded and its minimum value is known. Chapter 3 proves the convergence of the algorithm. In Chapter 4, the numerical performances of the algorithm are shown for solving 140 unconstrained optimization problems, out of which 16 are real applications. This shows that the optimization process has two phases: the reduction phase and the stalling one. Finally, the performances of the algorithm for solving a number of 30 large-scale unconstrained optimization problems up to 500 variables are presented. These numerical results show that this approach based on the two level random search method for unconstrained optimization is able to solve a large diversity of problems with different structures and complexities. There are a number of open problems which refer to the following aspects: the selection of the number of trial or the number of the local trial points, the selection of the bounds of the domains where the trial points and the local trial points are randomly generated and a criterion for initiating the line search.

This book is devoted to a detailed study of the subgradient projection method and its variants for convex optimization problems over the solution sets of common fixed point problems and convex feasibility problems. These optimization problems are investigated to determine good solutions obtained by different versions of the subgradient projection algorithm in the presence of sufficiently small computational errors. The use of selected algorithms is highlighted including the Cimmino type subgradient, the iterative subgradient, and the dynamic string-averaging subgradient. All results presented are new. Optimization problems where the underlying constraints are the solution sets of other problems, frequently occur in applied mathematics. The reader should not miss the section in Chapter 1 which considers some examples arising in the real world applications. The problems discussed have an important impact in optimization theory as well. The book will be useful for researches interested in the optimization theory and its applications.

This textbook offers graduate students a concise introduction to the classic notions of convex optimization. Written in a highly accessible style and including numerous examples and illustrations, it presents everything readers need to know about convexity and convex optimization. The book introduces a systematic three-step method for doing everything, which can be summarized as'conify, work, deconify'. It starts with the concept of convex sets, their primal description, constructions, topological properties and dual description, and then moves on to convex functions and the fundamental principles of convex optimization and their use in the complete analysis of convex optimization problems by means of a systematic four-step method. Lastly, it includes chapters on alternative formulations of optimality conditions and on illustrations of their use.'The author deals with the delicate subjects in a precise yet light-minded spirit... For experts in the field, this book not only offers a unifying view, but also opens a door to new discoveries in convexity and optimization...perfectly suited for classroom teaching.'Shuzhong Zhang, Professor of Industrial and Systems Engineering, University of Minnesota

This book discusses inventory models for determining optimal ordering policies using various optimization techniques, genetic algorithms, and data mining concepts. It also provides sensitivity analyses for the models'robustness. It presents a collection of mathematical models that deal with real industry scenarios. All mathematical model solutions are provided with the help of various optimization techniques to determine optimal ordering policy. The book offers a range of perspectives on the implementation of optimization techniques, inflation, trade credit financing, fuzzy systems, human error, learning in production, inspection, green supply chains, closed supply chains, reworks, game theory approaches, genetic algorithms, and data mining, as well as research on big data applications for inventory management and control. Starting from deterministic inventory models, the book moves towards advanced inventory models. The content is divided into eight major sections: inventory control and management – inventory models with trade credit financing for imperfect quality items; environmental impact on ordering policies; impact of learning on the supply chain models; EOQ models considering warehousing; optimal ordering policies with data mining and PSO techniques; supply chain models in fuzzy environments; optimal production models for multi-items and multi-retailers; and a marketing model to understand buying behaviour. Given its scope, the book offers a valuable resource for practitioners, instructors, students and researchers alike. It also offers essential insights to help retailers/managers improve business functions and make more accurate and realistic decisions.

This book gathers a selection of peer-reviewed papers presented at the International Conference on Operations Research (OR 2019), which was held at Technische Universität Dresden, Germany, on September 4-6, 2019, and was jointly organized by the German Operations Research Society (GOR) the Austrian Operations Research Society (ÖGOR), and the Swiss Operational Research Society (SOR/ASRO). More than 600 scientists, practitioners and students from mathematics, computer science, business/economics and related fields attended the conference and presented more than 400 papers in plenary presentations, parallel topic streams, as well as special award sessions.The respective papers discuss classical mathematical optimization, statistics and simulation techniques. These are complemented by computer science methods, and by tools for processing data, designing and implementing information systems. The book also examines recent advances in information technology, which allow big data volumes to be processed and enable real-time predictive and prescriptive business analytics to drive decisions and actions. Lastly, it includes problems modeled and treated while taking into account uncertainty, risk management, behavioral issues, etc.

This book presents the proceedings of the Fourth International Conference on Health Care Systems Engineering (HCSE 2019), which took place in Montreal, Canada, from May 30 to June 1, 2019. The event took place in the mother and child university hospital CHU Sainte-Justine in Montréal, and each session was co-chaired by a discussant coming from the clinical practice.The conference offered scientists and practitioners an opportunity to discuss operations management issues in health care delivery systems, and to share new ideas, methods and technologies for improving the operation of health care organizations.Focusing on applications of systems engineering, optimization and statistics to improve health care delivery and health systems, the book covers topics relating to a broad spectrum of concrete problems that pose challenges for researchers and practitioners alike, including hospital drug logistics, operating theatre management, blood donation, home care services,modeling, simulation, process mining and data mining in patient care and health care organizations.

This textbook provides students with fundamentals and advanced concepts in optimization and operations research. It gives an overview of the historical perspective of operations research and explains its principal characteristics, tools, and applications. The wide range of topics covered includes convex and concave functions, simplex methods, post optimality analysis of linear programming problems, constrained and unconstrained optimization, game theory, queueing theory, and related topics. The text also elaborates on project management, including the importance of critical path analysis, PERT and CPM techniques. This textbook is ideal for any discipline with one or more courses in optimization and operations research; it may also provide a solid reference for researchers and practitioners in operations research.

This book provides a comprehensive introduction to nonlinear programming, featuring a broad range of applications and solution methods in the field of continuous optimization. It begins with a summary of classical results on unconstrained optimization, followed by a wealth of applications from a diverse mix of fields, e.g. location analysis, traffic planning, and water quality management, to name but a few. In turn, the book presents a formal description of optimality conditions, followed by an in-depth discussion of the main solution techniques. Each method is formally described, and then fully solved using a numerical example.

This book develops the concepts of various unique optimization techniques in the crisp and fuzzy environment. It provides an extensive overview of geometric programming methods within a unifying framework, and presents an in-depth discussion of the modified geometric programming problem, fuzzy geometric programming, as well as new insights into goal geometric programming. With numerous examples and exercises together with detailed solutions for several problems, the book also addresses fuzzy multi-objective geometric programming techniques. Geometric programming, which falls into the general class of signomial problems, has applications across disciplines, from engineering to economics, and is extremely useful in applications of a variety of optimization problems. Organized into thirteen chapters, this book is a valuable resource for graduate and advanced undergraduate students and researchers in applied mathematics and engineering.

Inventory Management in Multi-Echelon Networks presents methods to plan inventory in distribution networks. By holistically looking at the supply chain, it shows how safety stocks across all echelons can be optimized if inventory of all levels is taken into consideration. The gap between the existence of advanced inventory planning methods and their low penetration in the industry was the motivation for this book. Christopher Grob develops essential algorithms that companies can use for network inventory planning and highlights achievable implementation benefits. The work of the author was inspired by the needs of an after sales supply chain of a large automotive company. This company supplies customers all over the world with spare parts and operates a distribution network with more than 100 warehouses. This supply chain faces two particular challenges: demand is highly uncertain and customers expect a high service level.About the Author Christopher Grob works in after sales supply chain management at a major German automotive company. He is responsible for the functional development of inventory planning systems for the spare parts business. He is an expert in the field of inventory management.

This book features a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in B ethlehem, Pennsylvania, USA between August 16-18, 2017. The conference brought together a diverse group of researchers and practitioners working on both theoretical and practical aspects of continuous and discrete optimization. Topics covered include algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and address the application of deterministic andstochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The selected contributions in this book illustrate the broad diversity of ideas discussed at the meeting.

The main purpose of the book is to give a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and their applications. Both the dynamic programming method and the stochastic maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton–Jacobi–Bellman equation and/or (quasi-)variational inequalities are formulated. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations. The 3rd edition is an expanded and updated version of the 2nd edition, containing recent developments within stochastic control and its applications. Specifically, there is a new chapter devoted to a comprehensive presentation of financial markets modelled by jump diffusions, and one on backward stochastic differential equations and convex risk measures. Moreover, the authors have expanded the optimal stopping and the stochastic control chapters to include optimal control of mean-field systems and stochastic differential games.

This book provides essential insights into a range of newly developed numerical optimization techniques with a view to solving real-world problems. Many of these problems can be modeled as nonlinear optimization problems, but due to their complex nature, it is not always possible to solve them using conventional optimization theory. Accordingly, the book discusses the design and applications of non-conventional numerical optimization techniques, including the design of benchmark functions and the implementation of these techniques to solve real-world optimization problems. The book's twenty chapters examine various interesting research topics in this area, including: Pi fraction-based optimization of the Pantoja–Bretones–Martin (PBM) antenna benchmarks; benchmark function generators for single-objective robust optimization algorithms; convergence of gravitational search algorithms on linear and quadratic functions; and an algorithm for the multi-variant evolutionary synthesis of nonlinear models with real-valued chromosomes. Delivering on its promise to explore real-world scenarios, the book also addresses the seismic analysis of a multi-story building with optimized damper properties; the application of constrained spider monkey optimization to solve portfolio optimization problems; the effect of upper body motion on a bipedal robot's stability; an ant colony algorithm for routing alternate-fuel vehicles in multi-depot vehicle routing problems; enhanced fractal dimension-based feature extraction for thermal face recognition; and an artificial bee colony-based hyper-heuristic for the single machine order acceptance and scheduling problem. The book will benefit not only researchers, but also organizations active in such varied fields as Aerospace, Automotive, Biotechnology, Consumer Packaged Goods, Electronics, Finance, Business & Banking, Oil, Gas & Geosciences, and Pharma, to name a few.

This book presents advanced case studies that address a range of important issues arising in space engineering. An overview of challenging operational scenarios is presented, with an in-depth exposition of related mathematical modeling, algorithmic and numerical solution aspects. The model development and optimization approaches discussed in the book can be extended also towards other application areas. The topics discussed illustrate current research trends and challenges in space engineering as summarized by the following list: • Next Generation Gravity Missions • Continuous-Thrust Trajectories by Evolutionary Neurocontrol • Nonparametric Importance Sampling for Launcher Stage Fallout • Dynamic System Control Dispatch • OptimalLaunch Date of Interplanetary Missions • Optimal Topological Design • Evidence-Based Robust Optimization • Interplanetary Trajectory Design by Machine Learning • Real-Time Optimal Control • Optimal Finite Thrust Orbital Transfers • Planning and Scheduling of Multiple Satellite Missions • Trajectory Performance Analysis • Ascent Trajectory and Guidance Optimization • Small Satellite Attitude Determination and Control • Optimized Packings in Space Engineering • Time-Optimal Transfers of All-Electric GEO Satellites Researchers working on space engineering applications will find this work a valuable, practical source of information. Academics, graduate and post-graduate students working in aerospace, engineering, applied mathematics, operations research, and optimal control will find useful information regarding model development and solution techniques, in conjunction with real-world applications.

This book promotes the use of mathematical optimization and operations research methods in rail transportation. The editors assembled thirteen contributions from leading scholars to present a unified voice, standardize terminology, and assess the state-of-the-art.There are three main clusters of articles, corresponding to the classical stages of the planning process: strategic, tactical, and operational. These three clusters are further subdivided into five parts which correspond to the main phases of the railway network planning process: network assessment, capacity planning, timetabling, resource planning, and operational planning. Individual chapters cover:SimulationCapacity AssessmentNetwork DesignTrain RoutingRobust TimetablingEvent SchedulingTrack AllocationBlockingShuntingRolling StockCrew SchedulingDispatching Delay Propagation

This book takes a unique approach to linear optimization by focusing on the underlying principles and business applications of a topic more often taught from a mathematical and computational perspective. By shifting the perspective away from heavy math, students learn how optimization can be used to drive decision making in real world business settings.The book does not shy away from the theory underlying linear optimization but rather focuses on ensuring students understand the logic without getting caught up in proving theorems. Plenty of examples, applications and case studies are included to help bridge the gap between the theory and the way it plays out in practice. The author has also included several Excel spreadsheets, showing worked-out models of linear optimization that have been used to drive decisions ranging from configuring a police force to purchasing crude oil and media planning.How can the routes and pricing structures of airlines be optimized? How much should be invested in the prevention and punishment of crimes? These are everyday problems that can be solved using linear optimization, and this book shows students just how to do that. It will prove a useful, math-free resource for all students of management science and operations research.