Ebook: Mathematical Modeling and Optimization: An Essay for the Design of Computer-Based Modeling Tools

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.

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The book proposes concepts and a general framework for computer-based modeling. It puts forward a modeling language as a kernel representation for mathematical models. It explores fundamental features of models and defines the notion of mathematical model and other related concepts. It gives a comprehensive overview of the modeling life cycle. The most frequently used methodologies of modeling management systems actually available are reviewed and a new framework in computer-based modeling is proposed. The book not only gives a theoretical foundation of modeling, but presents a concrete implementation using the modeling language LPL. It includes many concrete applications. All models and the complete software can be downloaded from the Web free of charge.
Audience: This book is intended for modeling tool designers, as well as students and teachers in mathematical modeling, and for real-live model `practitioners'.

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The book proposes concepts and a general framework for computer-based modeling. It puts forward a modeling language as a kernel representation for mathematical models. It explores fundamental features of models and defines the notion of mathematical model and other related concepts. It gives a comprehensive overview of the modeling life cycle. The most frequently used methodologies of modeling management systems actually available are reviewed and a new framework in computer-based modeling is proposed. The book not only gives a theoretical foundation of modeling, but presents a concrete implementation using the modeling language LPL. It includes many concrete applications. All models and the complete software can be downloaded from the Web free of charge.
Audience: This book is intended for modeling tool designers, as well as students and teachers in mathematical modeling, and for real-live model `practitioners'.
Content:
Front Matter....Pages i-xxii
Introduction....Pages 1-13
Front Matter....Pages 15-16
What is Modeling?....Pages 17-36
The Modeling Life Cycle....Pages 37-65
Model Paradigms....Pages 67-97
Front Matter....Pages 99-100
Problems and Concepts....Pages 101-114
An Overview of Approaches....Pages 115-154
A Modeling Framework....Pages 155-205
Front Matter....Pages 207-208
The Definition of the Language....Pages 209-233
The Implementation....Pages 235-247
Selected Applications....Pages 249-287
Conclusion....Pages 289-292
Back Matter....Pages 293-313

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The book proposes concepts and a general framework for computer-based modeling. It puts forward a modeling language as a kernel representation for mathematical models. It explores fundamental features of models and defines the notion of mathematical model and other related concepts. It gives a comprehensive overview of the modeling life cycle. The most frequently used methodologies of modeling management systems actually available are reviewed and a new framework in computer-based modeling is proposed. The book not only gives a theoretical foundation of modeling, but presents a concrete implementation using the modeling language LPL. It includes many concrete applications. All models and the complete software can be downloaded from the Web free of charge.
Audience: This book is intended for modeling tool designers, as well as students and teachers in mathematical modeling, and for real-live model `practitioners'.
Content:
Front Matter....Pages i-xxii
Introduction....Pages 1-13
Front Matter....Pages 15-16
What is Modeling?....Pages 17-36
The Modeling Life Cycle....Pages 37-65
Model Paradigms....Pages 67-97
Front Matter....Pages 99-100
Problems and Concepts....Pages 101-114
An Overview of Approaches....Pages 115-154
A Modeling Framework....Pages 155-205
Front Matter....Pages 207-208
The Definition of the Language....Pages 209-233
The Implementation....Pages 235-247
Selected Applications....Pages 249-287
Conclusion....Pages 289-292
Back Matter....Pages 293-313
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