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Author: David J. Rader
Publisher: John Wiley & Sons
ISBN: 1118627350
Category : Mathematics
Languages : en
Pages : 631
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Book Description
Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problem; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development. Treating real-world examples as mathematical problems, the author begins with an introduction to operations research and optimization modeling that includes applications form sports scheduling an the airline industry. Subsequent chapters discuss algorithm design for continuous linear optimization problems, covering topics such as convexity. Farkas’ Lemma, and the study of polyhedral before culminating in a discussion of the Simplex Method. The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method. Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm. The final chapters present network optimization and integer programming problems, highlighting various specialized topics including label-correcting algorithms for the shortest path problem, preprocessing and probing in integer programming, lifting of valid inequalities, and branch and cut algorithms. Concepts and approaches are introduced by outlining examples that demonstrate and motivate theoretical concepts. The accessible presentation of advanced ideas makes core aspects easy to understand and encourages readers to understand how to think about the problem, not just what to think. Relevant historical summaries can be found throughout the book, and each chapter is designed as the continuation of the “story” of how to both model and solve optimization problems by using the specific problems-linear and integer programs-as guides. The book’s various examples are accompanied by the appropriate models and calculations, and a related Web site features these models along with MapleTM and MATLAB® content for the discussed calculations. Thoroughly class-tested to ensure a straightforward, hands-on approach, Deterministic Operations Research is an excellent book for operations research of linear optimization courses at the upper-undergraduate and graduate levels. It also serves as an insightful reference for individuals working in the fields of mathematics, engineering, computer science, and operations research who use and design algorithms to solve problem in their everyday work.
Author: David J. Rader
Publisher: John Wiley & Sons
ISBN: 1118627350
Category : Mathematics
Languages : en
Pages : 631
Get Book Here
Book Description
Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problem; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development. Treating real-world examples as mathematical problems, the author begins with an introduction to operations research and optimization modeling that includes applications form sports scheduling an the airline industry. Subsequent chapters discuss algorithm design for continuous linear optimization problems, covering topics such as convexity. Farkas’ Lemma, and the study of polyhedral before culminating in a discussion of the Simplex Method. The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method. Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm. The final chapters present network optimization and integer programming problems, highlighting various specialized topics including label-correcting algorithms for the shortest path problem, preprocessing and probing in integer programming, lifting of valid inequalities, and branch and cut algorithms. Concepts and approaches are introduced by outlining examples that demonstrate and motivate theoretical concepts. The accessible presentation of advanced ideas makes core aspects easy to understand and encourages readers to understand how to think about the problem, not just what to think. Relevant historical summaries can be found throughout the book, and each chapter is designed as the continuation of the “story” of how to both model and solve optimization problems by using the specific problems-linear and integer programs-as guides. The book’s various examples are accompanied by the appropriate models and calculations, and a related Web site features these models along with MapleTM and MATLAB® content for the discussed calculations. Thoroughly class-tested to ensure a straightforward, hands-on approach, Deterministic Operations Research is an excellent book for operations research of linear optimization courses at the upper-undergraduate and graduate levels. It also serves as an insightful reference for individuals working in the fields of mathematics, engineering, computer science, and operations research who use and design algorithms to solve problem in their everyday work.
Author: Katta G. Murty
Publisher: Pearson College Division
ISBN: 9780130565174
Category : Mathematics
Languages : en
Pages : 581
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Book Description
Basic text on deterministic optimization methods. Techniques of modeling real world decision making problems, modeling examples that illustrate the use of modeling techniques, and a variety of problem classes are presented. Various types of algorithms with explanations of how each algorithm works and what conclusion can be drawn from its output, and a review of Matrix Algebra and Geometry and a chapter on Heuristic Methods.
Author: Richard Johannes Boucherie
Publisher: World Scientific
ISBN: 9811239363
Category : Mathematics
Languages : en
Pages : 512
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Book Description
This attractive textbook with its easy-to-follow presentation provides a down-to-earth introduction to operations research for students in a wide range of fields such as engineering, business analytics, mathematics and statistics, computer science, and econometrics. It is the result of many years of teaching and collective feedback from students.The book covers the basic models in both deterministic and stochastic operations research and is a springboard to more specialized texts, either practical or theoretical. The emphasis is on useful models and interpreting the solutions in the context of concrete applications.The text is divided into several parts. The first three chapters deal exclusively with deterministic models, including linear programming with sensitivity analysis, integer programming and heuristics, and network analysis. The next three chapters primarily cover basic stochastic models and techniques, including decision trees, dynamic programming, optimal stopping, production planning, and inventory control. The final five chapters contain more advanced material, such as discrete-time and continuous-time Markov chains, Markov decision processes, queueing models, and discrete-event simulation.Each chapter contains numerous exercises, and a large selection of exercises includes solutions.
Author: Changhyun Kwon
Publisher: Changhyun Kwon
ISBN: 1798205475
Category : Technology & Engineering
Languages : en
Pages : 262
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Book Description
Last Updated: December 2020 Based on Julia v1.3+ and JuMP v0.21+ The main motivation of writing this book was to help the author himself. He is a professor in the field of operations research, and his daily activities involve building models of mathematical optimization, developing algorithms for solving the problems, implementing those algorithms using computer programming languages, experimenting with data, etc. Three languages are involved: human language, mathematical language, and computer language. His team of students need to go over three different languages, which requires "translation" among the three languages. As this book was written to teach his research group how to translate, this book will also be useful for anyone who needs to learn how to translate in a similar situation. The Julia Language is as fast as C, as convenient as MATLAB, and as general as Python with a flexible algebraic modeling language for mathematical optimization problems. With the great support from Julia developers, especially the developers of the JuMP—Julia for Mathematical Programming—package, Julia makes a perfect tool for students and professionals in operations research and related areas such as industrial engineering, management science, transportation engineering, economics, and regional science. For more information, visit: http://www.chkwon.net/julia
Author: Ronald L. Rardin
Publisher: Prentice Hall
ISBN: 9780132858113
Category : Mathematical optimization
Languages : en
Pages : 936
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Book Description
For first courses in operations research, operations management Optimization in Operations Research, Second Edition covers a broad range of optimization techniques, including linear programming, network flows, integer/combinational optimization, and nonlinear programming. This dynamic text emphasizes the importance of modeling and problem formulation andhow to apply algorithms to real-world problems to arrive at optimal solutions. Use a program that presents a better teaching and learning experience-for you and your students. Prepare students for real-world problems: Students learn how to apply algorithms to problems that get them ready for their field. Use strong pedagogy tools to teach: Key concepts are easy to follow with the text's clear and continually reinforced learning path. Enjoy the text's flexibility: The text features varying amounts of coverage, so that instructors can choose how in-depth they want to go into different topics.
Author: Tsan-Ming Choi
Publisher: Springer Science & Business Media
ISBN: 1461476399
Category : Business & Economics
Languages : en
Pages : 281
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Book Description
The Economic Order Quantity (EOQ) inventory model first appeared in 1913, and in its centennial, it is still one of the most important inventory models. Despite the abundance of both classical and new research results, there was (until now) no comprehensive reference source that provides the state-of-the-art findings on both theoretical and applied research on the EOQ and its related models. This edited handbook puts together all these interesting works and the respective insights into an edited volume. The handbook contains papers which explore both the deterministic and the stochastic EOQ-model based problems and applications. It is organized into three parts: Part I presents three papers that provide an introduction and review of various EOQ related models. Part II includes four technical analyses on single-echelon EOQ-model based inventory problems. Part III consists of five papers on applications of the EOQ model for multi-echelon supply chain inventory analysis.
Author: Wayne L. Winston
Publisher: Duxbury Resource Center
ISBN:
Category : Business & Economics
Languages : en
Pages : 1050
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Book Description
Author: Kurt Marti
Publisher: Springer
ISBN: 3662462141
Category : Business & Economics
Languages : en
Pages : 389
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Book Description
This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect 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 appropriate deterministic substitute 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. In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.
Author: Katta G Murty
Publisher: Springer
ISBN: 9781493910069
Category : Business & Economics
Languages : en
Pages : 0
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Book Description
This textbook is comprised of detailed case studies covering challenging real world applications of OR techniques. Among the overall goals of the book is to provide readers with descriptions of the history and other background information on a variety of industries, service or other organizations in which decision making is an important component of their daily operations. The book considers all methods of optimum decision making in order to improve performances. It also compares possible solutions obtained by different approaches, concluding with a recommendation of the best among them for implementation. By exposing students to a variety of applications in a variety of areas and explaining how they can be modeled and solved, the book helps students develop the skills needed for modeling and solving problems that they may face in the workplace. Each chapter of "Case Studies in Operations Research: Applications of Optimal Decision Making" also includes additional data provided on the book’s website on Springer.com. These files contain a brief description of the area of application, the problem and the required outputs. Also provided are links to access all the data in the problem. Finally there are project exercises for students to practice what they have learnt in the chapter, which can also be used by instructors as project assignments in their courses.
Author: Yaroslav D. Sergeyev
Publisher: Springer
ISBN: 1493971999
Category : Computers
Languages : en
Pages : 143
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Book Description
This book begins with a concentrated introduction into deterministic global optimization and moves forward to present new original results from the authors who are well known experts in the field. Multiextremal continuous problems that have an unknown structure with Lipschitz objective functions and functions having the first Lipschitz derivatives defined over hyperintervals are examined. A class of algorithms using several Lipschitz constants is introduced which has its origins in the DIRECT (DIviding RECTangles) method. This new class is based on an efficient strategy that is applied for the search domain partitioning. In addition a survey on derivative free methods and methods using the first derivatives is given for both one-dimensional and multi-dimensional cases. Non-smooth and smooth minorants and acceleration techniques that can speed up several classes of global optimization methods with examples of applications and problems arising in numerical testing of global optimization algorithms are discussed. Theoretical considerations are illustrated through engineering applications. Extensive numerical testing of algorithms described in this book stretches the likelihood of establishing a link between mathematicians and practitioners. The authors conclude by describing applications and a generator of random classes of test functions with known local and global minima that is used in more than 40 countries of the world. This title serves as a starting point for students, researchers, engineers, and other professionals in operations research, management science, computer science, engineering, economics, environmental sciences, industrial and applied mathematics to obtain an overview of deterministic global optimization.
