Deterministic Operations Research: Models and Methods in Linear Optimization
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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INTRODUCTION TO OPERATIONS RESEARCH
LINEAR PROGRAMMING MODELING
INTEGER AND COMBINATORIAL MODELS
INTRODUCTION TO ALGORITHM DESIGN
IMPROVING SEARCH ALGORITHMS AND CONVEXITY
GEOMETRY AND ALGEBRA OF LINEAR PROGRAMS
LINEAR PROGRAMMING DUALITY
SENSITIVITY ANALYSIS OF LINEAR PROGRAMS