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This book is intended as a guide to and manual on modeling complex problems in Multi Criteria Decision Making (MCDM). It encourages practitioners to consider the practicalities of real-world scenarios when modeling, while at the same time providing tips and examples of how to incorporate these realities into the initial decision matrix. The goal is to help readers build a decision matrix that replicates reality as closely as possible. Once this matrix has been constructed, the Decision Maker (DM) can select from more than a hundred MCDM methods the one that best fits the requirements and conditions of the matrix. The book features cases taken from real-world scenarios, which deal with various fields, aspects, and characteristics, and are solved using the SIMUS (Sequential Interactive Modeling for Urban Systems) method. This book is a valuable tool for practitioners, researchers and students dealing with MCDM problems.
It is quite an onerous task to edit the proceedings of a two week long institute with learned contributors from many parts of the world. All the same, the editorial team has found the process of refereeing and reviewing the contributions worthwhile and completing the volume has proven to be a satisfying task. In setting up the institute we had considered models and methods taken from a number of different disciplines. As a result the whole institute - preparing for it, attending it and editing the proceedings - proved to be an intense learning experience for us. Here I speak on behalf of the committee and the editorial team. By the time the institute took place, the papers were delivered and the delegates exchanged their views, the structure of the topics covered and their relative positioning appeared in a different light. In editing the volume I felt compelled to introduce a new structure in grouping the papers. The contents of this volume are organised in eight main sections set out below: 1 . Abstracts. 2. Review Paper. 3. Models with Multiple Criteria and Single or Multiple Decision Makers. 4. Use of Optimisation Models as Decision Support Tools. 5. Role of Information Systems in Decision Making: Database and Model Management Issues. 6. Methods of Artificial Intelligence in Decision Making: Intelligent Knowledge Based Systems. 7. Representation of Uncertainty in Mathematical Models and Knowledge Based Systems. 8. Mathematical Basis for Constructing Models and Model Validation.
This book provides basic tools for learning how to model in mathematical programming, from models without much complexity to complex system models. It presents a unique methodology for the building of an integral mathematical model, as well as new techniques that help build under own criteria. It allows readers to structure models from the elements and variables to the constraints, a basic modelling guide for any system with a new scheme of variables, a classification of constraints and also a set of rules to model specifications stated as logical propositions, helping to better understand models already existing in the literature. It also presents the modelling of all possible objectives that may arise in optimization problems regarding the variables values. The book is structured to guide the reader in an orderly manner, learning of the components that the methodology establishes in an optimization problem. The system includes the elements, which are all the actors that participate in the system, decision activities that occur in the system, calculations based on the decision activities, specifications such as regulations, impositions or actions of defined value and objective criterion, which guides the resolution of the system.
Mathematical Modeling for Business Analytics is written for decision makers at all levels. This book presents the latest tools and techniques available to help in the decision process. The interpretation and explanation of the results are crucial to understanding the strengths and limitations of modeling. This book emphasizes and focuses on the aspects of constructing a useful model formulation, as well as building the skills required for decision analysis. The book also focuses on sensitivity analysis. The author encourages readers to formally think about solving problems by using a thorough process. Many scenarios and illustrative examples are provided to help solve problems. Each chapter is also comprehensively arranged so that readers gain an in-depth understanding of the subject which includes introductions, background information and analysis. Both undergraduate and graduate students taking methods courses in methods and discrete mathematical modeling courses will greatly benefit from using this book. Boasts many illustrative examples to help solve problems Provides many solutions for each chapter Emphasizes model formulation and helps create model building skills for decision analysis Provides the tools to support analysis and interpretation
Mathematical modeling is both a skill and an art and must be practiced in order to maintain and enhance the ability to use those skills. Though the topics covered in this book are the typical topics of most mathematical modeling courses, this book is best used for individuals or groups who have already taken an introductory mathematical modeling course. This book will be of interest to instructors and students offering courses focused on discrete modeling or modeling for decision making.
Mathematical Modeling, Third Edition is a general introduction to an increasingly crucial topic for today's mathematicians. Unlike textbooks focused on one kind of mathematical model, this book covers the broad spectrum of modeling problems, from optimization to dynamical systems to stochastic processes. Mathematical modeling is the link between mathematics and the rest of the world. Meerschaert shows how to refine a question, phrasing it in precise mathematical terms. Then he encourages students to reverse the process, translating the mathematical solution back into a comprehensible, useful answer to the original question. This textbook mirrors the process professionals must follow in solving complex problems. Each chapter in this book is followed by a set of challenging exercises. These exercises require significant effort on the part of the student, as well as a certain amount of creativity. Meerschaert did not invent the problems in this book--they are real problems, not designed to illustrate the use of any particular mathematical technique. Meerschaert's emphasis on principles and general techniques offers students the mathematical background they need to model problems in a wide range of disciplines. Increased support for instructors, including MATLAB material New sections on time series analysis and diffusion models Additional problems with international focus such as whale and dolphin populations, plus updated optimization problems
This book aims at improving the mathematical modelling skills of users by enhancing the ability to understand, connect, apply and use the mathematical concepts to the problem at hand. This book provides the readers with an in-depth knowledge of the various categories/classes of research problems that professionals, researchers and students might encounter following which the applications of appropriate mathematical models is explained with the help of case studies. The book is targeted at academicians, researchers, students and professionals who belong to all engineering disciplines.
This book covers an interdisciplinary approach for understanding mathematical modeling by offering a collection of models, solved problems related to the models, the methodologies employed, and the results using projects and case studies with insight into the operation of substantial real-time systems. The book covers a broad scope in the areas of statistical science, probability, stochastic processes, fluid dynamics, supply chain, optimization, and applications. It discusses advanced topics and the latest research findings, uses an interdisciplinary approach for real-time systems, offers a platform for integrated research, and identifies the gaps in the field for further research. The book is for researchers, students, and teachers that share a goal of learning advanced topics and the latest research in mathematical modeling.
Statistical Decision Problems presents a quick and concise introduction into the theory of risk, deviation and error measures that play a key role in statistical decision problems. It introduces state-of-the-art practical decision making through twenty-one case studies from real-life applications. The case studies cover a broad area of topics and the authors include links with source code and data, a very helpful tool for the reader. In its core, the text demonstrates how to use different factors to formulate statistical decision problems arising in various risk management applications, such as optimal hedging, portfolio optimization, cash flow matching, classification, and more. The presentation is organized into three parts: selected concepts of statistical decision theory, statistical decision problems, and case studies with portfolio safeguard. The text is primarily aimed at practitioners in the areas of risk management, decision making, and statistics. However, the inclusion of a fair bit of mathematical rigor renders this monograph an excellent introduction to the theory of general error, deviation, and risk measures for graduate students. It can be used as supplementary reading for graduate courses including statistical analysis, data mining, stochastic programming, financial engineering, to name a few. The high level of detail may serve useful to applied mathematicians, engineers, and statisticians interested in modeling and managing risk in various applications.
This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion of new research problems and questions.