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Author: Josef Kallrath
Publisher: Springer Nature
ISBN: 3030732371
Category : Business & Economics
Languages : en
Pages : 653
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Book Description
This book presents a structured approach to formulate, model, and solve mathematical optimization problems for a wide range of real world situations. Among the problems covered are production, distribution and supply chain planning, scheduling, vehicle routing, as well as cutting stock, packing, and nesting. The optimization techniques used to solve the problems are primarily linear, mixed-integer linear, nonlinear, and mixed integer nonlinear programming. The book also covers important considerations for solving real-world optimization problems, such as dealing with valid inequalities and symmetry during the modeling phase, but also data interfacing and visualization of results in a more and more digitized world. The broad range of ideas and approaches presented helps the reader to learn how to model a variety of problems from process industry, paper and metals industry, the energy sector, and logistics using mathematical optimization techniques.
Author: Josef Kallrath
Publisher: Springer Nature
ISBN: 3030732371
Category : Business & Economics
Languages : en
Pages : 653
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Book Description
This book presents a structured approach to formulate, model, and solve mathematical optimization problems for a wide range of real world situations. Among the problems covered are production, distribution and supply chain planning, scheduling, vehicle routing, as well as cutting stock, packing, and nesting. The optimization techniques used to solve the problems are primarily linear, mixed-integer linear, nonlinear, and mixed integer nonlinear programming. The book also covers important considerations for solving real-world optimization problems, such as dealing with valid inequalities and symmetry during the modeling phase, but also data interfacing and visualization of results in a more and more digitized world. The broad range of ideas and approaches presented helps the reader to learn how to model a variety of problems from process industry, paper and metals industry, the energy sector, and logistics using mathematical optimization techniques.
Author: Nimrod Megiddo
Publisher: Springer Science & Business Media
ISBN: 1461396174
Category : Mathematics
Languages : en
Pages : 164
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Book Description
The starting point of this volume was a conference entitled "Progress in Mathematical Programming," held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarkar's algorithm. There were thirty presentations and approximately fifty people attended. Presentations included new algorithms, new analyses of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming. Interestingly, most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear program ming were presented (Barnes-Chopra-Jensen, Goldfarb-Mehrotra, Gonzaga, Kojima-Mizuno-Yoshise, Renegar, Todd, Vaidya, and Ye). Other algorithms presented were by Betke-Gritzmann, Blum, Gill-Murray-Saunders-Wright, Nazareth, Vial, and Zikan-Cottle. Efforts in the theoretical analysis of algo rithms were also reported (Anstreicher, Bayer-Lagarias, Imai, Lagarias, Megiddo-Shub, Lagarias, Smale, and Vanderbei). Computational experiences were reported by Lustig, Tomlin, Todd, Tone, Ye, and Zikan-Cottle. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference, it was still not clear whether the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms."
Author: Shu-Cherng Fang
Publisher: Springer Science & Business Media
ISBN: 1461561310
Category : Business & Economics
Languages : en
Pages : 350
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Book Description
Entropy optimization is a useful combination of classical engineering theory (entropy) with mathematical optimization. The resulting entropy optimization models have proved their usefulness with successful applications in areas such as image reconstruction, pattern recognition, statistical inference, queuing theory, spectral analysis, statistical mechanics, transportation planning, urban and regional planning, input-output analysis, portfolio investment, information analysis, and linear and nonlinear programming. While entropy optimization has been used in different fields, a good number of applicable solution methods have been loosely constructed without sufficient mathematical treatment. A systematic presentation with proper mathematical treatment of this material is needed by practitioners and researchers alike in all application areas. The purpose of this book is to meet this need. Entropy Optimization and Mathematical Programming offers perspectives that meet the needs of diverse user communities so that the users can apply entropy optimization techniques with complete comfort and ease. With this consideration, the authors focus on the entropy optimization problems in finite dimensional Euclidean space such that only some basic familiarity with optimization is required of the reader.
Author: Stephen P. Bradley
Publisher: Addison Wesley Publishing Company
ISBN:
Category : Mathematics
Languages : en
Pages : 748
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Book Description
Mathematical programming: an overview; solving linear programs; sensitivity analysis; duality in linear programming; mathematical programming in practice; integration of strategic and tactical planning in the aluminum industry; planning the mission and composition of the U.S. merchant Marine fleet; network models; integer programming; design of a naval tender job shop; dynamic programming; large-scale systems; nonlinear programming; a system for bank portfolio planning; vectors and matrices; linear programming in matrix form; a labeling algorithm for the maximun-flow network problem.
Author: Antonio J. Conejo
Publisher: Springer Science & Business Media
ISBN: 3540276866
Category : Technology & Engineering
Languages : en
Pages : 542
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Book Description
Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.
Author: Mikulás Luptácik
Publisher: Springer Science & Business Media
ISBN: 0387895523
Category : Mathematics
Languages : en
Pages : 299
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Book Description
"Mathematical Optimization and Economic Analysis" is a self-contained introduction to various optimization techniques used in economic modeling and analysis such as geometric, linear, and convex programming and data envelopment analysis. Through a systematic approach, this book demonstrates the usefulness of these mathematical tools in quantitative and qualitative economic analysis. The book presents specific examples to demonstrate each technique’s advantages and applicability as well as numerous applications of these techniques to industrial economics, regulatory economics, trade policy, economic sustainability, production planning, and environmental policy. Key Features include: - A detailed presentation of both single-objective and multiobjective optimization; - An in-depth exposition of various applied optimization problems; - Implementation of optimization tools to improve the accuracy of various economic models; - Extensive resources suggested for further reading. This book is intended for graduate and postgraduate students studying quantitative economics, as well as economics researchers and applied mathematicians. Requirements include a basic knowledge of calculus and linear algebra, and a familiarity with economic modeling.
Author: Kiyotaka Shimizu
Publisher: Springer Science & Business Media
ISBN: 1461563054
Category : Business & Economics
Languages : en
Pages : 482
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Book Description
The analysis and design of engineering and industrial systems has come to rely heavily on the use of optimization techniques. The theory developed over the last 40 years, coupled with an increasing number of powerful computational procedures, has made it possible to routinely solve problems arising in such diverse fields as aircraft design, material flow, curve fitting, capital expansion, and oil refining just to name a few. Mathematical programming plays a central role in each of these areas and can be considered the primary tool for systems optimization. Limits have been placed on the types of problems that can be solved, though, by the difficulty of handling functions that are not everywhere differentiable. To deal with real applications, it is often necessary to be able to optimize functions that while continuous are not differentiable in the classical sense. As the title of the book indicates, our chief concern is with (i) nondifferentiable mathematical programs, and (ii) two-level optimization problems. In the first half of the book, we study basic theory for general smooth and nonsmooth functions of many variables. After providing some background, we extend traditional (differentiable) nonlinear programming to the nondifferentiable case. The term used for the resultant problem is nondifferentiable mathematical programming. The major focus is on the derivation of optimality conditions for general nondifferentiable nonlinear programs. We introduce the concept of the generalized gradient and derive Kuhn-Tucker-type optimality conditions for the corresponding formulations.
Author: Kenneth R. Baker
Publisher: John Wiley & Sons
ISBN: 1118008979
Category : Business & Economics
Languages : en
Pages : 431
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Book Description
Reflects the latest applied research and features state-of-the-art software for building and solving spreadsheet optimization models Thoroughly updated to reflect the latest topical and technical advances in the field, Optimization Modeling with Spreadsheets, Second Edition continues to focus on solving real-world optimization problems through the creation of mathematical models and the use of spreadsheets to represent and analyze those models. Developed and extensively classroom-tested by the author, the book features a systematic approach that equips readers with the skills to apply optimization tools effectively without the need to rely on specialized algorithms. This new edition uses the powerful software package Risk Solver Platform (RSP) for optimization, including its Evolutionary Solver, which employs many recently developed ideas for heuristic programming. The author provides expanded coverage of integer programming and discusses linear and nonlinear programming using a systematic approach that emphasizes the use of spreadsheet-based optimization tools. The Second Edition also features: Classifications for the various problem types, providing the reader with a broad framework for building and recognizing optimization models Network models that allow for a more general form of mass balance A systematic introduction to Data Envelopment Analysis (DEA) The identification of qualitative patterns in order to meaningfully interpret linear programming solutions An introduction to stochastic programming and the use of RSP to solve problems of this type Additional examples, exercises, and cases have been included throughout, allowing readers to test their comprehension of the material. In addition, a related website features Microsoft Office® Excel files to accompany the figures and data sets in the book. With its accessible and comprehensive presentation, Optimization Modeling with Spreadsheets, Second Edition is an excellent book for courses on deterministic models, optimization, and spreadsheet modeling at the upper-undergraduate and graduate levels. The book can also serve as a reference for researchers, practitioners, and consultants working in business, engineering, operations research, and management science.
Author: John N. Hooker
Publisher: Springer Science & Business Media
ISBN: 146141900X
Category : Business & Economics
Languages : en
Pages : 655
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Book Description
The first edition of Integrated Methods for Optimization was published in January 2007. Because the book covers a rapidly developing field, the time is right for a second edition. The book provides a unified treatment of optimization methods. It brings ideas from mathematical programming (MP), constraint programming (CP), and global optimization (GO)into a single volume. There is no reason these must be learned as separate fields, as they normally are, and there are three reasons they should be studied together. (1) There is much in common among them intellectually, and to a large degree they can be understood as special cases of a single underlying solution technology. (2) A growing literature reports how they can be profitably integrated to formulate and solve a wide range of problems. (3) Several software packages now incorporate techniques from two or more of these fields. The book provides a unique resource for graduate students and practitioners who want a well-rounded background in optimization methods within a single course of study. Engineering students are a particularly large potential audience, because engineering optimization problems often benefit from a combined approach—particularly where design, scheduling, or logistics are involved. The text is also of value to those studying operations research, because their educational programs rarely cover CP, and to those studying computer science and artificial intelligence (AI), because their curric ula typically omit MP and GO. The text is also useful for practitioners in any of these areas who want to learn about another, because it provides a more concise and accessible treatment than other texts. The book can cover so wide a range of material because it focuses on ideas that arerelevant to the methods used in general-purpose optimization and constraint solvers. The book focuses on ideas behind the methods that have proved useful in general-purpose optimization and constraint solvers, as well as integrated solvers of the present and foreseeable future. The second edition updates results in this area and includes several major new topics: Background material in linear, nonlinear, and dynamic programming. Network flow theory, due to its importance in filtering algorithms. A chapter on generalized duality theory that more explicitly develops a unifying primal-dual algorithmic structure for optimization methods. An extensive survey of search methods from both MP and AI, using the primal-dual framework as an organizing principle. Coverage of several additional global constraints used in CP solvers. The book continues to focus on exact as opposed to heuristic methods. It is possible to bring heuristic methods into the unifying scheme described in the book, and the new edition will retain the brief discussion of how this might be done.
Author: Ulrich Faigle
Publisher: Springer Science & Business Media
ISBN: 9781402008528
Category : Computers
Languages : en
Pages : 360
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Book Description
Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature. The book is equally suited for self-study for a motivated beginner and for a comprehensive course on the principles of mathematical programming within an applied mathematics or computer science curriculum at advanced undergraduate or graduate level. The presentation of the material is such that smaller modules on discrete optimization, linear programming, and nonlinear optimization can easily be extracted separately and used for shorter specialized courses on these subjects.
