Deterministic Operations Research: Models and Methods in Linear Optimization

John Wiley & Sons, Aug 23, 2010 - Mathematics - 632 pages
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.

What people are saying -Write a review

We haven't found any reviews in the usual places.

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