Optimization for Decision Making

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Publisher :
ISBN 13 : 9783039432202
Total Pages : 290 pages
Book Rating : 4.4/5 (322 download)

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Book Synopsis Optimization for Decision Making by : Víctor Yepes

Download or read book Optimization for Decision Making written by Víctor Yepes and published by . This book was released on 2020-10-08 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the current context of the electronic governance of society, both administrations and citizens are demanding greater participation of all the actors involved in the decision-making process relative to the governance of society. This book presents collective works published in the recent Special Issue (SI) entitled "Optimization for Decision Making". These works give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and application of optimization techniques to support decisions are particularly complex and a wide range of optimization techniques and methodologies are used to minimize risks, improve quality in making decisions, or, in general, to solve problems. In addition, a sensitivity or robustness analysis should be done to validate/analyze the influence of uncertainty regarding decision-making. This book brings together a collection of inter-/multi-disciplinary works applied to the optimization for decision making in a coherent manner.

Optimization for Decision Making II

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Publisher : MDPI
ISBN 13 : 3039436074
Total Pages : 300 pages
Book Rating : 4.0/5 (394 download)

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Book Synopsis Optimization for Decision Making II by : Víctor Yepes

Download or read book Optimization for Decision Making II written by Víctor Yepes and published by MDPI. This book was released on 2020-11-25 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the current context of the electronic governance of society, both administrations and citizens are demanding the greater participation of all the actors involved in the decision-making process relative to the governance of society. This book presents collective works published in the recent Special Issue (SI) entitled “Optimization for Decision Making II”. These works give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex and a wide range of optimization techniques and methodologies are used to minimize risks, improve quality in making decisions or, in general, to solve problems. In addition, a sensitivity or robustness analysis should be done to validate/analyze the influence of uncertainty regarding decision-making. This book brings together a collection of inter-/multi-disciplinary works applied to the optimization of decision making in a coherent manner.

Optimization for Decision Making

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Publisher : Springer Science & Business Media
ISBN 13 : 1441912916
Total Pages : 502 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Optimization for Decision Making by : Katta G. Murty

Download or read book Optimization for Decision Making written by Katta G. Murty and published by Springer Science & Business Media. This book was released on 2010-03-14 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear programming (LP), modeling, and optimization are very much the fundamentals of OR, and no academic program is complete without them. No matter how highly developed one’s LP skills are, however, if a fine appreciation for modeling isn’t developed to make the best use of those skills, then the truly ‘best solutions’ are often not realized, and efforts go wasted. Katta Murty studied LP with George Dantzig, the father of linear programming, and has written the graduate-level solution to that problem. While maintaining the rigorous LP instruction required, Murty's new book is unique in his focus on developing modeling skills to support valid decision making for complex real world problems. He describes the approach as 'intelligent modeling and decision making' to emphasize the importance of employing the best expression of actual problems and then applying the most computationally effective and efficient solution technique for that model.

Introduction to Optimization-Based Decision-Making

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Publisher : CRC Press
ISBN 13 : 1351778722
Total Pages : 263 pages
Book Rating : 4.3/5 (517 download)

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Book Synopsis Introduction to Optimization-Based Decision-Making by : Joao Luis de Miranda

Download or read book Introduction to Optimization-Based Decision-Making written by Joao Luis de Miranda and published by CRC Press. This book was released on 2021-12-24 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Optimization for Decision Making II.

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Publisher :
ISBN 13 : 9783039436088
Total Pages : 302 pages
Book Rating : 4.4/5 (36 download)

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Book Synopsis Optimization for Decision Making II. by : Víctor Yepes

Download or read book Optimization for Decision Making II. written by Víctor Yepes and published by . This book was released on 2020 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the current context of the electronic governance of society, both administrations and citizens are demanding the greater participation of all the actors involved in the decision-making process relative to the governance of society. This book presents collective works published in the recent Special Issue (SI) entitled “Optimization for Decision Making II”. These works give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex and a wide range of optimization techniques and methodologies are used to minimize risks, improve quality in making decisions or, in general, to solve problems. In addition, a sensitivity or robustness analysis should be done to validate/analyze the influence of uncertainty regarding decision-making. This book brings together a collection of inter-/multi-disciplinary works applied to the optimization of decision making in a coherent manner.

Advanced Optimization and Decision-Making Techniques in Textile Manufacturing

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Author :
Publisher : CRC Press
ISBN 13 : 0429996837
Total Pages : 302 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Advanced Optimization and Decision-Making Techniques in Textile Manufacturing by : Anindya Ghosh

Download or read book Advanced Optimization and Decision-Making Techniques in Textile Manufacturing written by Anindya Ghosh and published by CRC Press. This book was released on 2019-03-18 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization and decision making are integral parts of any manufacturing process and management system. The objective of this book is to demonstrate the confluence of theory and applications of various types of multi-criteria decision making and optimization techniques with reference to textile manufacturing and management. Divided into twelve chapters, it discusses various multi-criteria decision-making methods such as AHP, TOPSIS, ELECTRE, and optimization techniques like linear programming, fuzzy linear programming, quadratic programming, in textile domain. Multi-objective optimization problems have been dealt with two approaches, namely desirability function and evolutionary algorithm. Key Features Exclusive title covering textiles and soft computing fields including optimization and decision making Discusses concepts of traditional and non-traditional optimization methods with textile examples Explores pertinent single-objective and multi-objective optimizations Provides MATLAB coding in the Appendix to solve various types of multi-criteria decision making and optimization problems Includes examples and case studies related to textile engineering and management

Business Intelligence

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Publisher : John Wiley & Sons
ISBN 13 : 1119965470
Total Pages : 314 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis Business Intelligence by : Carlo Vercellis

Download or read book Business Intelligence written by Carlo Vercellis and published by John Wiley & Sons. This book was released on 2011-08-10 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Business intelligence is a broad category of applications and technologies for gathering, providing access to, and analyzing data for the purpose of helping enterprise users make better business decisions. The term implies having a comprehensive knowledge of all factors that affect a business, such as customers, competitors, business partners, economic environment, and internal operations, therefore enabling optimal decisions to be made. Business Intelligence provides readers with an introduction and practical guide to the mathematical models and analysis methodologies vital to business intelligence. This book: Combines detailed coverage with a practical guide to the mathematical models and analysis methodologies of business intelligence. Covers all the hot topics such as data warehousing, data mining and its applications, machine learning, classification, supply optimization models, decision support systems, and analytical methods for performance evaluation. Is made accessible to readers through the careful definition and introduction of each concept, followed by the extensive use of examples and numerous real-life case studies. Explains how to utilise mathematical models and analysis models to make effective and good quality business decisions. This book is aimed at postgraduate students following data analysis and data mining courses. Researchers looking for a systematic and broad coverage of topics in operations research and mathematical models for decision-making will find this an invaluable guide.

Decision Making and Optimization

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Publisher : Springer
ISBN 13 : 3319083236
Total Pages : 231 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Decision Making and Optimization by : Martin Gavalec

Download or read book Decision Making and Optimization written by Martin Gavalec and published by Springer. This book was released on 2014-10-08 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a benefit for graduate and postgraduate students in the areas of operations research, decision theory, optimization theory, linear algebra, interval analysis and fuzzy sets. The book will also be useful for the researchers in the respective areas. The first part of the book deals with decision making problems and procedures that have been established to combine opinions about alternatives related to different points of view. Procedures based on pairwise comparisons are thoroughly investigated. In the second part we investigate optimization problems where objective functions and constraints are characterized by extremal operators such as maximum, minimum or various triangular norms (t-norms). Matrices in max-min algebra are useful in applications such as automata theory, design of switching circuits, logic of binary relations, medical diagnosis, Markov chains, social choice, models of organizations, information systems, political systems and clustering. The input data in real problems are usually not exact and can be characterized by interval values.

Anticipatory Optimization for Dynamic Decision Making

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Publisher : Springer Science & Business Media
ISBN 13 : 146140505X
Total Pages : 192 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Anticipatory Optimization for Dynamic Decision Making by : Stephan Meisel

Download or read book Anticipatory Optimization for Dynamic Decision Making written by Stephan Meisel and published by Springer Science & Business Media. This book was released on 2011-06-23 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The availability of today’s online information systems rapidly increases the relevance of dynamic decision making within a large number of operational contexts. Whenever a sequence of interdependent decisions occurs, making a single decision raises the need for anticipation of its future impact on the entire decision process. Anticipatory support is needed for a broad variety of dynamic and stochastic decision problems from different operational contexts such as finance, energy management, manufacturing and transportation. Example problems include asset allocation, feed-in of electricity produced by wind power as well as scheduling and routing. All these problems entail a sequence of decisions contributing to an overall goal and taking place in the course of a certain period of time. Each of the decisions is derived by solution of an optimization problem. As a consequence a stochastic and dynamic decision problem resolves into a series of optimization problems to be formulated and solved by anticipation of the remaining decision process. However, actually solving a dynamic decision problem by means of approximate dynamic programming still is a major scientific challenge. Most of the work done so far is devoted to problems allowing for formulation of the underlying optimization problems as linear programs. Problem domains like scheduling and routing, where linear programming typically does not produce a significant benefit for problem solving, have not been considered so far. Therefore, the industry demand for dynamic scheduling and routing is still predominantly satisfied by purely heuristic approaches to anticipatory decision making. Although this may work well for certain dynamic decision problems, these approaches lack transferability of findings to other, related problems. This book has serves two major purposes: ‐ It provides a comprehensive and unique view of anticipatory optimization for dynamic decision making. It fully integrates Markov decision processes, dynamic programming, data mining and optimization and introduces a new perspective on approximate dynamic programming. Moreover, the book identifies different degrees of anticipation, enabling an assessment of specific approaches to dynamic decision making. ‐ It shows for the first time how to successfully solve a dynamic vehicle routing problem by approximate dynamic programming. It elaborates on every building block required for this kind of approach to dynamic vehicle routing. Thereby the book has a pioneering character and is intended to provide a footing for the dynamic vehicle routing community.

Multi-criteria Decision Making Methods

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Publisher : Springer Science & Business Media
ISBN 13 : 1475731574
Total Pages : 307 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Multi-criteria Decision Making Methods by : Evangelos Triantaphyllou

Download or read book Multi-criteria Decision Making Methods written by Evangelos Triantaphyllou and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Criteria Decision Making (MCDM) has been one of the fastest growing problem areas in many disciplines. The central problem is how to evaluate a set of alternatives in terms of a number of criteria. Although this problem is very relevant in practice, there are few methods available and their quality is hard to determine. Thus, the question `Which is the best method for a given problem?' has become one of the most important and challenging ones. This is exactly what this book has as its focus and why it is important. The author extensively compares, both theoretically and empirically, real-life MCDM issues and makes the reader aware of quite a number of surprising `abnormalities' with some of these methods. What makes this book so valuable and different is that even though the analyses are rigorous, the results can be understood even by the non-specialist. Audience: Researchers, practitioners, and students; it can be used as a textbook for senior undergraduate or graduate courses in business and engineering.

Multicriteria Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 3540276599
Total Pages : 329 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Multicriteria Optimization by : Matthias Ehrgott

Download or read book Multicriteria Optimization written by Matthias Ehrgott and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Collection of results of multicriteria optimization, including nonlinear, linear and combinatorial optimization problems - Includes numerous illustrations, examples and problems

The Optimization Edge: Reinventing Decision Making to Maximize All Your Company's Assets

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Publisher : McGraw Hill Professional
ISBN 13 : 0071748334
Total Pages : 289 pages
Book Rating : 4.0/5 (717 download)

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Book Synopsis The Optimization Edge: Reinventing Decision Making to Maximize All Your Company's Assets by : Stephen Sashihara

Download or read book The Optimization Edge: Reinventing Decision Making to Maximize All Your Company's Assets written by Stephen Sashihara and published by McGraw Hill Professional. This book was released on 2011-02-25 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why downsize when you can OPTIMIZE? "At McDonald’s our focus has always been on providing maximum value to customers through ‘optimal’ quality and tight cost management, which is why Optimization has become such a pivotal concept for us. Steve Sashihara’s book brings the concept to life.” —Kenneth M. Koziol, Corp. Senior Vice President, Innovation and Design, McDonald’s Corp. “Steve Sashihara convincingly demonstrates how the application of advanced quantitative techniques can significantly improve day-to-day decision making, which is what we have done at Quad/Graphics.” —Dave Blais, Executive Vice President, Quad/Graphics “The Optimization Edge is a powerful book that will change the way organizations make decisions and manage their assets.” —Frances Hesselbein, President and CEO, Leader to Leader Institute; Recipient, Presidential Medal of Freedom “At UPS, the ‘optimization edge’ has given us a competitive advantage. It enables us to solve problems of great complexity seamlessly and with increased velocity, resulting in smarter decisions and ultimately bringing greater value to our customers.” —Chuck Holland, Vice President of Industrial Engineering, UPS About the Book: In these challenging economic times, more and more companies have turned to “cut-back management” to ensure their survival. But how do some manage to outshine their competitors—and even grow—during downturns? How does Google outsearch the other search engines? How does McDonald’s McClobber the competition? More important, how can you increase your company’s profits without downsizing? The answer is Asset Optimization. This groundbreaking approach to decision making utilizes the latest advances in mathematics and computer software. Optimization expert Steve Sashihara shows you how to squeeze every ounce of value from your company, even under “perfect storm” conditions. You’ll learn how to: Drive up your company’s value—even in a downturn Re-allocate your resources—for maximum performance Streamline your company—and stay ahead of the competition Optimize your assets—for long-term growth A proven, practical, and workable alternative to “corporate anorexia,” Optimization is your best option for dealing head-on with marketplace volatility and resource scarcity. This step-by-step guide offers concrete, ready-to- use tools drawn from decades of superior business practices—the best-kept secrets of global successes such as Amazon, Google, Marriott, McDonald’s, Intel, SAS, and UPS. You’ll learn what Optimization is, what best practices you can immediately put to use, how to use Optimization to speed up and improve decision making, and how to integrate Optimization into your organization’s culture. If you want to thrive in any economy—and grow your company in the future—forget about downsizing. Get The Optimization Edge.

Combinatorial Optimization Problems in Planning and Decision Making

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Publisher : Springer
ISBN 13 : 3319989774
Total Pages : 518 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Combinatorial Optimization Problems in Planning and Decision Making by : Michael Z. Zgurovsky

Download or read book Combinatorial Optimization Problems in Planning and Decision Making written by Michael Z. Zgurovsky and published by Springer. This book was released on 2018-09-24 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on the next fields of computer science: combinatorial optimization, scheduling theory, decision theory, and computer-aided production management systems. It also offers a quick introduction into the theory of PSC-algorithms, which are a new class of efficient methods for intractable problems of combinatorial optimization. A PSC-algorithm is an algorithm which includes: sufficient conditions of a feasible solution optimality for which their checking can be implemented only at the stage of a feasible solution construction, and this construction is carried out by a polynomial algorithm (the first polynomial component of the PSC-algorithm); an approximation algorithm with polynomial complexity (the second polynomial component of the PSC-algorithm); also, for NP-hard combinatorial optimization problems, an exact subalgorithm if sufficient conditions were found, fulfilment of which during the algorithm execution turns it into a polynomial complexity algorithm. Practitioners and software developers will find the book useful for implementing advanced methods of production organization in the fields of planning (including operative planning) and decision making. Scientists, graduate and master students, or system engineers who are interested in problems of combinatorial optimization, decision making with poorly formalized overall goals, or a multiple regression construction will benefit from this book.

Evolutionary Multi-Criterion Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 3540709274
Total Pages : 972 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Evolutionary Multi-Criterion Optimization by : Shigeru Obayashi

Download or read book Evolutionary Multi-Criterion Optimization written by Shigeru Obayashi and published by Springer Science & Business Media. This book was released on 2007-02-12 with total page 972 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2007, held in Matsushima, Japan in March 2007. The 65 revised full papers presented together with 4 invited papers are organized in topical sections on algorithm design, algorithm improvements, alternative methods, applications, engineering design, many objectives, objective handling, and performance assessments.

Reinforcement Learning and Stochastic Optimization

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Publisher : John Wiley & Sons
ISBN 13 : 1119815037
Total Pages : 1090 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Reinforcement Learning and Stochastic Optimization by : Warren B. Powell

Download or read book Reinforcement Learning and Stochastic Optimization written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2022-03-15 with total page 1090 pages. Available in PDF, EPUB and Kindle. Book excerpt: REINFORCEMENT LEARNING AND STOCHASTIC OPTIMIZATION Clearing the jungle of stochastic optimization Sequential decision problems, which consist of “decision, information, decision, information,” are ubiquitous, spanning virtually every human activity ranging from business applications, health (personal and public health, and medical decision making), energy, the sciences, all fields of engineering, finance, and e-commerce. The diversity of applications attracted the attention of at least 15 distinct fields of research, using eight distinct notational systems which produced a vast array of analytical tools. A byproduct is that powerful tools developed in one community may be unknown to other communities. Reinforcement Learning and Stochastic Optimization offers a single canonical framework that can model any sequential decision problem using five core components: state variables, decision variables, exogenous information variables, transition function, and objective function. This book highlights twelve types of uncertainty that might enter any model and pulls together the diverse set of methods for making decisions, known as policies, into four fundamental classes that span every method suggested in the academic literature or used in practice. Reinforcement Learning and Stochastic Optimization is the first book to provide a balanced treatment of the different methods for modeling and solving sequential decision problems, following the style used by most books on machine learning, optimization, and simulation. The presentation is designed for readers with a course in probability and statistics, and an interest in modeling and applications. Linear programming is occasionally used for specific problem classes. The book is designed for readers who are new to the field, as well as those with some background in optimization under uncertainty. Throughout this book, readers will find references to over 100 different applications, spanning pure learning problems, dynamic resource allocation problems, general state-dependent problems, and hybrid learning/resource allocation problems such as those that arose in the COVID pandemic. There are 370 exercises, organized into seven groups, ranging from review questions, modeling, computation, problem solving, theory, programming exercises and a “diary problem” that a reader chooses at the beginning of the book, and which is used as a basis for questions throughout the rest of the book.

Optimization Theory, Decision Making, and Operations Research Applications

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Author :
Publisher : Springer
ISBN 13 : 9781489985965
Total Pages : 0 pages
Book Rating : 4.9/5 (859 download)

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Book Synopsis Optimization Theory, Decision Making, and Operations Research Applications by : Athanasios Migdalas

Download or read book Optimization Theory, Decision Making, and Operations Research Applications written by Athanasios Migdalas and published by Springer. This book was released on 2014-12-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings consist of 30 selected research papers based on results presented at the 10th Balkan Conference & 1st International Symposium on Operational Research (BALCOR 2011) held in Thessaloniki, Greece, September 22-24, 2011. BALCOR is an established biennial conference attended by a large number of faculty, researchers and students from the Balkan countries but also from other European and Mediterranean countries as well. Over the past decade, the BALCOR conference has facilitated the exchange of scientific and technical information on the subject of Operations Research and related fields such as Mathematical Programming, Game Theory, Multiple Criteria Decision Analysis, Information Systems, Data Mining and more, in order to promote international scientific cooperation. The carefully selected and refereed papers present important recent developments and modern applications and will serve as excellent reference for students, researchers and practitioners in these disciplines. ​

Introduction to Optimization-Based Decision-Making

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Author :
Publisher : Chapman & Hall/CRC
ISBN 13 : 9781351778718
Total Pages : 241 pages
Book Rating : 4.7/5 (787 download)

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Book Synopsis Introduction to Optimization-Based Decision-Making by : João Luis de Miranda

Download or read book Introduction to Optimization-Based Decision-Making written by João Luis de Miranda and published by Chapman & Hall/CRC. This book was released on 2021-12-19 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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