Modeling Languages In Mathematical Optimization

This volume presents a unique combination of modeling and solving real world optimization problems. It is the only book which treats systematically the major modeling languages and systems used to solve mathematical optimization problems, and it also provides a useful overview and orientation of today's modeling languages in mathematical optimization. It demonstrates the strengths and characteristic features of such languages and provides a bridge for researchers, practitioners and students into a new world: solving real optimization problems with the most advances modeling systems.

This book Algebraic Modeling Systems – Modeling and Solving Real World Optimization Problems – deals with the aspects of modeling and solving real-world optimization problems in a unique combination. It treats systematically the major algebraic modeling languages (AMLs) and modeling systems (AMLs) used to solve mathematical optimization problems. AMLs helped significantly to increase the usage of mathematical optimization in industry. Therefore it is logical consequence that the GOR (Gesellschaft für Operations Research) Working Group Mathematical Optimization in Real Life had a second meeting devoted to AMLs, which, after 7 years, followed the original 71st Meeting of the GOR (Gesellschaft für Operations Research) Working Group Mathematical Optimization in Real Life which was held under the title Modeling Languages in Mathematical Optimization during April 23–25, 2003 in the German Physics Society Conference Building in Bad Honnef, Germany. While the first meeting resulted in the book Modeling Languages in Mathematical Optimization, this book is an offspring of the 86th Meeting of the GOR working group which was again held in Bad Honnef under the title Modeling Languages in Mathematical Optimization.

AMPL, developed at AT&Ts Bell Laboratories, is a powerful, yet easy-to-use modeling environment for problems in linear, nonlinear, network, and integer programming. Users can formulate optimization models and analyze solutions using common algebraic notation; the computer manages the interface to advanced optimizers. In less advanced programming software, students must write out every variable and constraint explicitly. AMPLs powerful display commands encourage creative responses to modeling assignments..The AMPL Student Edition is a full-featured version of the AMPL and optimizer software that accepts problems up to 300 variables and 300 constraints. AMPLs modeling approach can handle real-world problems. AMPL student models easily scale up to optimization problems of realistic size. AMPL Student Edition comes with both the MINOS and CPLEX solvers. Beginners need only type solve to invoke an optimizer, but advanced students have full access to algorithmic options because the AMPL Student Edition works just like the professional editions that run on computers from PCs to Crays. Classroom skills transfer directly to the job environment.

Here is a collection of nonlinear optimization applications from the real world, expressed in the General Algebraic Modeling System (GAMS). The concepts are presented so that the reader can quickly modify and update them to represent real-world situations.

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.

This book presents a structured approach to formulate, model, and solve mathematical optimization problems for a wide range of real world situations. Among the problems covered are production, distribution and supply chain planning, scheduling, vehicle routing, as well as cutting stock, packing, and nesting. The optimization techniques used to solve the problems are primarily linear, mixed-integer linear, nonlinear, and mixed integer nonlinear programming. The book also covers important considerations for solving real-world optimization problems, such as dealing with valid inequalities and symmetry during the modeling phase, but also data interfacing and visualization of results in a more and more digitized world. The broad range of ideas and approaches presented helps the reader to learn how to model a variety of problems from process industry, paper and metals industry, the energy sector, and logistics using mathematical optimization techniques.

A supplemental textbook introducing mathematical programming using the commercial software package, designed to be used in conjunction with a full text explaining the optimization theory and algorithmic details used in mathematical programming. The second edition incorporates developments in the software since 1992. Annotation copyrighted by Book News, Inc., Portland, OR.