Mathematical Modeling and Optimization

1. Front Matter

   Pages i-xxii

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2. Introduction

   1. Introduction

      • Tony Hürlimann

      Pages 1-13

3. Foundations of Modeling

   1. Front Matter

      Pages 15-16

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   2. What is Modeling?

      • Tony Hürlimann

      Pages 17-36

   3. The Modeling Life Cycle

      • Tony Hürlimann

      Pages 37-65

   4. Model Paradigms

      • Tony Hürlimann

      Pages 67-97

4. A General Modeling Framework

   1. Front Matter

      Pages 99-100

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   2. Problems and Concepts

      • Tony Hürlimann

      Pages 101-114

   3. An Overview of Approaches

      • Tony Hürlimann

      Pages 115-154

   4. A Modeling Framework

      • Tony Hürlimann

      Pages 155-205

5. LPL — An Implemented Framework

   1. Front Matter

      Pages 207-208

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   2. The Definition of the Language

      • Tony Hürlimann

      Pages 209-233

   3. The Implementation

      • Tony Hürlimann

      Pages 235-247

   4. Selected Applications

      • Tony Hürlimann

      Pages 249-287

   5. Conclusion

      • Tony Hürlimann

      Pages 289-292

6. Back Matter

   Pages 293-313

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Computer-based mathematical modeling - the technique of representing and managing models in machine-readable form - is still in its infancy despite the many powerful mathematical software packages already available which can solve astonishingly complex and large models. On the one hand, using mathematical and logical notation, we can formulate models which cannot be solved by any computer in reasonable time - or which cannot even be solved by any method. On the other hand, we can solve certain classes of much larger models than we can practically handle and manipulate without heavy programming. This is especially true in operations research where it is common to solve models with many thousands of variables. Even today, there are no general modeling tools that accompany the whole modeling process from start to finish, that is to say, from model creation to report writing. This book proposes a framework for computer-based modeling. More precisely, it puts forward a modeling language as a kernel representation for mathematical models. It presents a general specification for modeling tools. The book does not expose any solution methods or algorithms which may be useful in solving models, neither is it a treatise on how to build them. No help is intended here for the modeler by giving practical modeling exercises, although several models will be presented in order to illustrate the framework. Nevertheless, a short introduction to the modeling process is given in order to expound the necessary background for the proposed modeling framework.

• Mathematica
• mathematical modeling
• modeling
• optimization
• information and communication, circuits

• Institute for Informatics, University of Fribourg, Switzerland

  Tony Hürlimann

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