Optimization Modelling : A Practical Approach

Although a useful and important tool, the potential of mathematical modelling for decision making is often neglected. Considered an art by many and weird science by some, modelling is not as widely appreciated in problem solving and decision making as perhaps it should be. And although many operations research, management science, and optimization books touch on modelling techniques, the short shrift they usually get in coverage is reflected in their minimal application to problems in the real world. Illustrating the important influence of modelling on the decision making process, Optimization Modelling: A Practical Approach helps you come to grips with a wide range of modelling techniques. Highlighting the modelling aspects of optimization problems, the authors present the techniques in a clear and straightforward manner, illustrated by examples. They provide and analyze the formulation and modelling of a number of well-known theoretical and practical problems and touch on solution approaches. The book demonstrates the use of optimization packages through the solution of various mathematical models and provides an interpretation of some of those solutions. It presents the practical aspects and difficulties of problem solving and solution implementation and studies a number of practical problems. The book also discusses the use of available software packages in solving optimization models without going into difficult mathematical details and complex solution methodologies. The emphasis on modelling techniques rather than solution algorithms sets this book apart. It is a single source for a wide range of methods, classic theoretical and practical problems, data collection and input preparation, the use of different optimization software, and practical issues of modelling, model solving, and implementation. The authors draw directly from their experience to provide lessons learned when applying modelling techniques to practical problem solving and implementation difficulties. Table of Contents List of Figures List of Tables List of Mathematical Notations Preface Acknowledgments Authors Section I: Introduction to Optimization and Modeling Chapter 1. Introduction Chapter 2. The Process of Optimization Chapter 3. Introduction to Modelling Section II: Modelling Techniques Chapter 4. Simple Modelling Techniques I Chapter 5. Simple Modelling Techniques II Chapter 6. Modelling Large-Scale and Well-Known Problems I Chapter 7. Modelling Well-Known Problems II Chapter 8. Alternative Modelling Section III: Model Solving Chapter 9. Solution Approaches: An Overview Chapter 10. Input Preparation and Model Solving Chapter 11. Output Analysis and Practical Issues Chapter 12. Basic Optimization Techniques Section IV: Practical Problems Chapter 13. Models for Practical Problems I Chapter 14. Models for Practical Problems II Chapter 15. Solving Practical Problems Index Mathematical modeling is an essential part of most optimization problem-solving processes. To reduce the gap between the solutions obtained from mathematical models and the real-world solutions to practical problems, appropriate modeling techniques must be applied along with efficient solution approaches. "Optimization Modelling" presents different modeling techniques, illustrated by various examples. A range of well-known theoretical and practical problems are analyzed, and the use of optimization packages is demonstrated for mathematical models. Including numerous case studies, the book also addresses practical aspects and challenges of problem solving and solution implementation