Deterministic Operations Research: Models and Methods in Linear Optimization

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John Wiley & Sons, Aug 23, 2010 - Mathematics - 632 pages
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Thoroughly classroom-tested over the past eight years, this book focuses on the study of linear optimization (both continuous and discrete), and it also emphasizes the modeling of real problems as linear optimization problems and designs algorithms to solve them.

Topics in linear programming, network optimization, and integer programming are discussed, and three aspects of deterministic operations research are emphasized: modeling real-world problems as linear optimization problems; designing algorithms (both heuristic and exact methods) to solve these problems; and using mathematical theory to improve the understanding of the problem, to improve existing algorithms, and to design new algorithms. These three aspects are important for both researchers and practitioners of operations research. Such topics are not always in the forefront of operations research textbooks, and while it is true that many books highlight optimization modeling and algorithms to solve these problems, very few, if any, explicitly discuss the algorithm design process used to solve problems.

This book successfully fills this gap in the literature and incorporates these components into the study of linear and integer programming, currently the two most-used optimization models in business and industry. Each chapter of the book is designed to be 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. This enables the reader (and instructors) to see how solution methods can be derived instead of just seeing the final product (the algorithms themselves). Numerous examples and problems as well as relevant historical summaries can be found throughout the text. Each chapter contains at least 20 problems per chapter, with some chapters having many more problems. 

 

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Contents

INTRODUCTION TO OPERATIONS RESEARCH
1
LINEAR PROGRAMMING MODELING
21
INTEGER AND COMBINATORIAL MODELS
85
Exercises
152
INTRODUCTION TO ALGORITHM DESIGN
159
IMPROVING SEARCH ALGORITHMS AND CONVEXITY
197
GEOMETRY AND ALGEBRA OF LINEAR PROGRAMS
238
LINEAR PROGRAMMING DUALITY
317
ALGORITHMIC APPLICATIONS OF DUALITY
389
NETWORK OPTIMIZATION ALGORITHMS
449
INTRODUCTION TO INTEGER PROGRAMMING
489
EXACT METHODS
514
MODERN
556
Exercises
574
REFERENCE
597
INDEX
603

SENSITIVITY ANALYSIS OF LINEAR PROGRAMS
351

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About the author (2010)

David J. Rader Jr., PhD, is Associate Professor of Mathematics at Rose-Hulman Institute of Technology, where he is also the editor of the Rose-Hulman Institute of Technology Undergraduate Mathematics Journal. Dr. Rader currently focuses his research in the areas of nonlinear 0-1 optimization, computational integer programming, and exam time timetabling.

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