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Optimization: 100 Examples is a book devoted to the analysis of scenarios for which the use of well-known optimization methods encounter certain difficulties. Analysing such examples allows a deeper understanding of the features of these optimization methods, including the limits of their applicability. In this way, the book seeks to stimulate further development and understanding of the theory of optimal control. The study of the presented examples makes it possible to more effectively diagnose problems that arise in the practical solution of optimal control problems, and to find ways to overcome the difficulties that have arisen. Features Vast collection of examples Simple. accessible presentation Suitable as a research reference for anyone with an interest in optimization and optimal control theory, including mathematicians and engineers Examples differ in properties, i.e. each effect for each class of problems is illustrated by a unique example. Simon Serovajsky is a professor of mathematics at Al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of optimization and optimal control theory, mathematical physics, mathematical modelling, philosophy and history of mathematics as well as a long list of high-quality publications in learned journals.

This book examines optimization problems that in practice involve random model parameters. It outlines the computation of robust optimal solutions, i.e., optimal solutions that are insensitive to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into corresponding deterministic problems.Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures, and differentiation formulas for probabilities and expectations.The fourth edition of this classic text has been carefully and thoroughly revised. It includes new chapters on the solution of stochastic linear programs by discretization of the underlying probability distribution, and on solving deterministic optimization problems by means of controlled random search methods and multiple random search procedures. It also presents a new application of stochastic optimization methods to machine learning problems with different loss functions. For the computation of optimal feedback controls under stochastic uncertainty, besides the open-loop feedback procedures, a new method based on Taylor expansions with respect to the gain parameters is presented. The book is intended for researchers and graduate students who are interested in stochastics, stochastic optimization, and control. It will also benefit professionals and practitioners whose work involves technical, economicand/or operations research problems under stochastic uncertainty.

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 is the first comprehensive guide to logic-based Benders decomposition (LBBD), a general and versatile method for breaking large, complex optimization problems into components that are small enough for practical solution. The author introduces logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method. It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems. On the theoretical side, this book provides a full account of inference duality concepts that underlie LBBD, as well as a description of how LBBD can be combined with stochastic and robust optimization, heuristic methods, and decision diagrams. It also clarifies the connection between LBBD and combinatorial Benders cuts for mixed integer programming. On the practical side, it explains how LBBD has been applied to a rapidly growingvariety of problem domains. After describing basic theory, this book provides a comprehensive review of the rapidly growing literature that describes these applications, in each case explaining how LBBD is adapted to the problem at hand. In doing so this work provides a sourcebook of ideas for applying LBBD to new problems as they arise.

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.

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.

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 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.

The formal optimization handbook is a comprehensive guide that covers a wide range of subjects. It includes a literature review, a mathematical formulation of optimization methods, flowcharts and pseudocodes, illustrations, problems and applications, results and critical discussions, and much more. The book covers a vast array of formal optimization fields, including mathematical and Bayesian optimization, neural networks and deep learning, genetic algorithms and their applications, hybrid optimization methods, combinatorial optimization, constraint handling in optimization methods, and swarm-based optimization. This handbook is an excellent reference for experts and non-specialists alike, as it provides stimulating material. The book also covers research trends, challenges, and prospective topics, making it a valuable resource for those looking to expand their knowledge in this field.

This book is a rigorous but practical presentation of the Bayesian techniques of uncertainty quantification, with applications in R. This volume includes mathematical arguments at the level necessary to make the presentation rigorous and the assumptions clearly established, while maintaining a focus on practical applications of Bayesian uncertainty quantification methods. Practical aspects of applied probability are also discussed, making the content accessible to students. The introduction of R allows the reader to solve more complex problems involving a more significant number of variables. Users will be able to use examples laid out in the text to solve medium-sized problems.The list of topics covered in this volume includes basic Bayesian probabilities, entropy, Bayesian estimation and decision, sequential Bayesian estimation, and numerical methods. Blending theoretical rigor and practical applications, this volume will be of interest to professionals, researchers, graduate and undergraduate students interested in the use of Bayesian uncertainty quantification techniques within the framework of operations research and mathematical programming, for applications in management and planning.

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 introduces readers to order analysis and various aspects of deep learning, and describes important connections to optimization, such as nonlinear optimization as well as vector and set optimization. Besides a review of the essentials, this book consists of two main parts. The first main part focuses on the introduction of order analysis as an application-driven theory, which allows to treat order structures with an analytical approach. Applications of order analysis to nonlinear optimization, as well as vector and set optimization with fixed and variable order structures, are discussed in detail. This means there are close ties to finance, operations research, and multicriteria decision making. Deep learning is the subject of the second main part of this book. In addition to the usual basics, the focus is on gradient methods, which are investigated in the context of complex models with a large number of parameters. And a new fast variant of a gradient method is presented in this part. Finally, the deep learning approach is extended to data sets given by set-valued data. Although this set-valued approach is more computationally intensive, it has the advantage of producing more robust predictions. This book is primarily intended for researchers in the fields of optimization, order theory, or artificial intelligence (AI), but it will also benefit graduate students with a general interest in these fields. The book assumes that readers have a basic understanding of functional analysis or at least basic analysis. By unifying and streamlining existing approaches, this work will also appeal to professionals seeking a comprehensive and straightforward perspective on AI or order theory approaches.

This contributed volume guides researchers and practitioners on resource collaborative management of supply chains and manufacturing enterprises within an industrial internet technological environment. The book comprises 10 chapters that cover two major topics in the subject of logistics 4.0, namely the utilization of both disruptive technologies and optimization techniques in smart logistic management. With global research on the book's topic expanding rapidly across various directions and disciplines, it provides a structured framework for international experts to showcase outstanding work and unique approaches. Researchers and students will find the comprehensive outline on collaborative optimization and management of smart manufacturing and production, warehousing, inventory, logistics, transportation, integrated supply chain, and supply network within the industrial internet platform a beneficial guide to understanding current and future practical problems that arise in manufacturing and supply chain management.

Combinatorial Optimization represents a major component of Operations Research, Mathematical Programming, and, in a broader sense, the development of digital intelligence (and society). It covers, in particular, such important areas as network design, location, routing, and scheduling, with major applications in transportation, logistics, health systems, production, communications, and energy.Starting from the exceptional contribution Professor Bernard Gendron made to combinatorial optimization and its applications in multiple areas, the book presents a state-of-the-art view on the field through a combination of surveys, expository articles, and focused methodological and applied research. The authors hail from various Operations Research areas and institutions around the world. Having collaborated closely with Professor Gendron, they drew on his foundational work to showcase a variety of models and algorithms that draw a living picture of the multifaceted word of applied combinatorial optimization.

This book offers a novel multi-portfolio approach and stochastic programming formulations for modeling and solving contemporary supply chain risk management problems. The focus of the book is on supply chain resilience under propagated disruptions, supply chain viability under severe crises, and supply chain cybersecurity under direct and indirect cyber risks. The content is illustrated with numerous computational examples, some of which are modeled on real-world supply chains subject to severe multi-regional or global crises, such as pandemics. In the computational examples, the proposed stochastic programming models are solved using an advanced algebraic modeling language AMPL and GUROBI solver. The book seamlessly continues the journey begun in the author's previously published book “Supply Chain Disruption Management: Using Stochastic Mixed Integer Programming.” It equips readers with the knowledge, tools, and managerial insights needed to effectively model and address modern supply chain risk management challenges. As such, the book is designed for practitioners and researchers who are interested in supply chain risk management. Master's and Ph.D. students in disciplines like supply chain management, operations research, industrial engineering, applied mathematics, and computer science will also find the book a valuable resource.

This is an updated version of what is still the only text to address basic questions about how to model uncertainty in mathematical programming, including how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This second edition has important extensions regarding how to represent random phenomena in the models (also called scenario generation) as well as a new chapter on multi-stage models. This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering disciplines where the instructor wants to explain where models come from and what the fundamental modeling issues are. The book is easy-to-read, highly illustrated with lots of examples and discussions. It will be suitable for graduate students and researchers working in operations research, mathematics, engineering and related departments where there is interest in learning how to model uncertainty. Alan King is a Research Staff Member at IBM's Thomas J. Watson Research Center in New York. Stein W. Wallace is a Professor of Operational Research and head of Center for Shipping and Logistics at NHH Norwegian School of Economics, Bergen, Norway.

Written by an experienced operations research practitioner with a strong applied mathematics background, this book offers practical insights into how to approach optimization problems, how to develop intelligent and efficient mathematical models and algorithms, and how to implement and deliver software products to customers. With a focus on revealing the similarities and differences between academia and industry in mathematical modeling, the book provides useful tips and advice based on the author's extensive experience as a principal developer working to solve real-world optimization problems for several major high-tech companies.The book offers valuable food for thought for researchers and practical guidance for graduate students preparing for their future projects in the industry. It is also an essential resource for practitioners working in the industrial, business, and service sectors.

This textbook introduces quantitative methods in operations management, based on operational research. Written for undergraduate and graduate students as well as practitioners, this book serves as a valuable compendium of essential tools for project planning, control, and strategic decision-making.Drawing from the expertise of both experienced scientists and seasoned practical managers, the descriptions of each tool are a harmonious blend of theoretical insights and real-world applicability. With a focus on accessibility, the authors have thoughtfully combined abstract concepts with easy-to-follow examples and detailed case studies.Readers will benefit from the abundance of well-explained recommendations and practical problem-solving approaches, where the book offers guidance on how to solve presented issues by using commercial software. Whether one seeks to refine project management, optimize operations, or make strategic choices, this book equips readers with theknowledge and proficiency required to excel in the dynamic field of operations management.

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 introduces the fundamentals of probability, statistical, and reliability concepts, the classical methods of uncertainty quantification and analytical reliability analysis, and the state-of-the-art approaches of design optimization under uncertainty (e.g., reliability-based design optimization and robust design optimization). The topics include basic concepts of probability and distributions, uncertainty quantification using probabilistic methods, classical reliability analysis methods, time-variant reliability analysis methods, fundamentals of deterministic design optimization, reliability-based design optimization, robust design optimization, other methods of design optimization under uncertainty, and engineering applications of design optimization under uncertainty.

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.

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.

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.

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 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 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 reviews the development of physics-based modeling and sensor-based data fusion for optimizing medical decision making in connection with spatiotemporal cardiovascular disease processes. To improve cardiac care services and patients'quality of life, it is very important to detect heart diseases early and optimize medical decision making. This book introduces recent research advances in machine learning, physics-based modeling, and simulation optimization to fully exploit medical data and promote the data-driven and simulation-guided diagnosis and treatment of heart disease. Specifically, it focuses on three major topics: computer modeling of cardiovascular systems, physiological signal processing for disease diagnostics and prognostics, and simulation optimization in medical decision making. It provides a comprehensive overview of recent advances in personalized cardiac modeling by integrating physics-based knowledge of the cardiovascular system with machine learning and multi-source medical data. It also discusses the state-of-the-art in electrocardiogram (ECG) signal processing for the identification of disease-altered cardiac dynamics. Lastly, it introduces readers to the early steps of optimal decision making based on the integration of sensor-based learning and simulation optimization in the context of cardiac surgeries. This book will be of interest to researchers and scholars in the fields of biomedical engineering, systems engineering and operations research, as well as professionals working in the medical sciences.

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.

The subject of (static) optimization, also called mathematical programming, is one of the most important and widespread branches of modern mathematics, serving as a cornerstone of such scientific subjects as economic analysis, operations research, management sciences, engineering, chemistry, physics, statistics, computer science, biology, and social sciences. This book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The authors expose said tools, along with results concerning the most common mathematical programming problems formulated in a finite-dimensional setting, forming the basis for further study of the basic questions on the various algorithmic methods and the most important particular applications of mathematical programming problems. This book assumes no previous experience in optimization theory, and the treatment of the various topics is largely self-contained. Prerequisites are the basic tools of differential calculus for functions of several variables, the basic notions of topology and of linear algebra, and the basic mathematical notions and theoretical background used in analyzing optimization problems. The book is aimed at both undergraduate and postgraduate students interested in mathematical programming problems but also those professionals who use optimization methods and wish to learn the more theoretical aspects of these questions.

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 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 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.

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 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.

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.

This book presents the state-of-the-art, current challenges, and future perspectives for the field of many-criteria optimization and decision analysis. The field recognizes that real-life problems often involve trying to balance a multiplicity of considerations simultaneously – such as performance, cost, risk, sustainability, and quality. The field develops theory, methods and tools that can support decision makers in finding appropriate solutions when faced with many (typically more than three) such criteria at the same time. The book consists of two parts: key research topics, and emerging topics. Part I begins with a general introduction to many-criteria optimization, perspectives from research leaders in real-world problems, and a contemporary survey of the attributes of problems of this kind. This part continues with chapters on fundamental aspects of many-criteria optimization, namely on order relations, quality measures, benchmarking, visualization, and theoretical considerations. Part II offers more specialized chapters on correlated objectives, heterogeneous objectives, Bayesian optimization, and game theory. Written by leading experts across the field of many-criteria optimization, this book will be an essential resource for researchers in the fields of evolutionary computing, operations research, multiobjective optimization, and decision science.

This book has two main objectives: • to provide a concise introduction to nonlinear optimization methods, which can be used as a textbook at a graduate or upper undergraduate level; • to collect and organize selected important topics on optimization algorithms, not easily found in textbooks, which can provide material for advanced courses or can serve as a reference text for self-study and research. The basic material on unconstrained and constrained optimization is organized into two blocks of chapters: • basic theory and optimality conditions • unconstrained and constrained algorithms. These topics are treated in short chapters that contain the most important results in theory and algorithms, in a way that, in the authors'experience, is suitable for introductory courses. A third block of chapters addresses methods that are of increasing interest for solving difficult optimization problems. Difficulty can be typically due to the high nonlinearity of the objective function, ill-conditioning of the Hessian matrix, lack of information on first-order derivatives, the need to solve large-scale problems. In the book various key subjects are addressed, including: exact penalty functions and exact augmented Lagrangian functions, non monotone methods, decomposition algorithms, derivative free methods for nonlinear equations and optimization problems. The appendices at the end of the book offer a review of the essential mathematical background, including an introduction to convex analysis that can make part of an introductory course.

This monograph discusses the theoretical and practical development of multicriteria decision making (MCDM). The main purpose of MCDM is the construction of systematized strategies for the'optimisation'of feasible options, as well as the justification of why some alternatives can be declared'optimal'. However, at time, we must make decisions in an uncertain environment and such inconvenience gives rise to a much more elaborate scenario. This book highlights models where this lack of certainty can be flexibly fitted in and goes on to explore valuable strategies for making decisions under a multiplicity of criteria. Methods discussed include bipolar fuzzy TOPSIS method, bipolar fuzzy ELECTRE-I method, bipolar fuzzy ELECTRE-II method, bipolar fuzzy VIKOR method, bipolar fuzzy PROMETHEE method, and two-tuple linguistic bipolar fuzzy Heronian mean operators. This book is a valuable resource for researchers, computer scientists, and social scientists alike.

Effective decision-making while trading off the constraints and conflicting multiple objectives under rapid technological developments, massive generation of data, and extreme volatility is of paramount importance to organizations to win over the time-based competition today. While agility is a crucial issue, the firms have been increasingly relying on evidence-based decision-making through intelligent decision support systems driven by computational intelligence and automation to achieve a competitive advantage. The decisions are no longer confined to a specific functional area. Instead, business organizations today find actionable insight for formulating future courses of action by integrating multiple objectives and perspectives. Therefore, multi-objective decision-making plays a critical role in businesses and industries. In this regard, the importance of Operations Research (OR) models and their applications enables the firms to derive optimum solutions subject to various constraints and/or objectives while considering multiple functional areas of the organizations together. Hence, researchers and practitioners have extensively applied OR models to solve various organizational issues related to manufacturing, service, supply chain and logistics management, human resource management, finance, and market analysis, among others. Further, OR models driven by AI have been enabled to provide intelligent decision-support frameworks for achieving sustainable development goals.The present issue provides a unique platform to showcase the contributions of the leading international experts on production systems and business from academia, industry, and government to discuss the issues in intelligent manufacturing, operations management, financial management, supply chain management, and Industry 4.0 in the Artificial Intelligence era. Some of the general (but not specific) scopes of this proceeding entail OR models such as Optimization and Control, Combinatorial Optimization, Queuing Theory, Resource Allocation Models, Linear and Nonlinear Programming Models, Multi-objective and multi-attribute Decision Models, Statistical Quality Control along with AI, Bayesian Data Analysis, Machine Learning and Econometrics and their applications vis-à-vis AI & Data-driven Production Management, Marketing and Retail Management, Financial Management, Human Resource Management, Operations Management, Smart Manufacturing & Industry 4.0, Supply Chain and Logistics Management, Digital Supply Network, Healthcare Administration, Inventory Management, consumer behavior, security analysis, and portfolio management and sustainability. The present issue shall be of interest to the faculty members, students, and scholars of various engineering and social science institutions and universities, along with the practitioners and policymakers of different industries and organizations.

The sequential quadratic hamiltonian (SQH) method is a novel numerical optimization procedure for solving optimal control problems governed by differential models. It is based on the characterisation of optimal controls in the framework of the Pontryagin maximum principle (PMP).The SQH method is a powerful computational methodology that is capable of development in many directions. The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems discusses its analysis and use in solving nonsmooth ODE control problems, relaxed ODE control problems, stochastic control problems, mixed-integer control problems, PDE control problems, inverse PDE problems, differential Nash game problems, and problems related to residual neural networks.This book may serve as a textbook for undergraduate and graduate students, and as an introduction for researchers in sciences and engineering who intend to further develop the SQH method or wish to use it as a numerical tool for solving challenging optimal control problems and for investigating the Pontryagin maximum principle on new optimisation problems.Features Provides insight into mathematical and computational issues concerning optimal control problems, while discussing many differential models of interest in different disciplines. Suitable for undergraduate and graduate students and as an introduction for researchers in sciences and engineering. Accompanied by codes which allow the reader to apply the SQH method to solve many different optimal control and optimisation problems.

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 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 book explains classic routing and transportation problems and solutions, before offering insights based on successful real-world solutions. The chapters in Part I introduce and explain the traveling salesperson problem (TSP), vehicle routing problems (VRPs), and multi-objective problems, with an emphasis on heuristic approaches and software engineering aspects. In turn, Part II demonstrates how to exploit geospatial data, routing algorithms, and visualization. In Part III, the above techniques and insights are combined in real-world success stories from domains such as food delivery in rural areas, postal delivery, workforce routing, and urban logistics.The book offers a valuable supporting text for advanced undergraduate and graduate courses and projects in Computer Science, Engineering, Operations Research, and Mathematics. It is accompanied by a repository of source code, allowing readers to try outthe algorithms and techniques discussed.

Using numerical examples to illustrate their concepts and results, this book examines recently developed fuzzy multi-criteria methods, such as Intuitionistic Fuzzy TOPSIS, Intuitionistic Fuzzy TOPSIS & DEA-AHP, Intuitionistic VIKOR, Pythagorean WASPAS, Pythagorean ENTROPI, Hesitant CBD, Hesitant MABAC, Triangular EDAS, Triangular PROMETHEE, q-Rung Orthopair COPRAS, and Fuzzy Type – 2 ELECTRE. Each chapter covers practical applications in addition to fresh developments and results. Given its structure and scope, the book can be used as a textbook in graduate courses on operations research and industrial engineering. It also offers a valuable resource for scientists working in a range of disciplines that require multi-criteria decision making.

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.

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

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.

Recent data shows that 87% of Artificial Intelligence/Big Data projects don't make it into production (VB Staff, 2019), meaning that most projects are never deployed. This book addresses five common pitfalls that prevent projects from reaching deployment and provides tools and methods to avoid those pitfalls. Along the way, stories from actual experience in building and deploying data science projects are shared to illustrate the methods and tools. While the book is primarily for data science practitioners, information for managers of data science practitioners is included in the Tips for Managers sections.

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.