By Josef Kallrath (auth.), Josef Kallrath (eds.)

This quantity provides a special mix of modeling and fixing genuine international optimization difficulties. it's the in simple terms e-book which treats systematically the foremost modeling languages and platforms used to resolve mathematical optimization difficulties, and it additionally presents an invaluable evaluation and orientation of cutting-edge modeling languages in mathematical optimization. It demonstrates the strengths and attribute beneficial properties of such languages and gives a bridge for researchers, practitioners and scholars right into a new international: fixing actual optimization issues of the main advances modeling systems.

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Additional resources for Modeling Languages in Mathematical Optimization

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Mixed integer, combinatorial, or discreteoptimization involve variables restricted to integer values, for example counts (numbers of containers, ships), decisions (yes-no), or logical relations (if product A is produced then product B also needs to be produced). The constraints can be a wide range of mathematical relationships: algebraic, analytic, differential or integral. They may represent mass balances, quality relations, capacity limits, and so on. The objective function expresses our goal: minimize costs, maximize utilization rate, minimize waste, and so on.

In the mid 1970's, the senior vice president Hollis B. Chenery wanted to support economies with the best economists and techniques in the world. This included, of course, mathematical optimization, and he was famous for requesting that people put their arguments in terms of mathematical language and rigor. What a refreshing atmosphere that must have been compared to nowadays where responsible managers usually avoid making any clear statement in public. So it is not a surprise that together, Meeraus and Bisschop were able to get the necessary financial support through an internal research project.

So, today, we can observe that from the very few roots of modeling languages there have arisen many languages with different designs and focus. As we have seen during the symposium in Bad Honnef, the field is still active, some of the founders are still around and come up with new ideas which make the world of mathematical optimization more interesting. 4 Conventions and Abbreviations The following table contains in alphabetic order the abbreviations used in this book. t. t. 3. 5 on Semi-Infinite Programming.

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