Mathematical OptimizationDepartment of Astronomy
Prof. Dr. Kallrath
Game Theory


This page contains useful references on Business Optimization and Mathematical Optimization Techniques.

bookBooks and Articles

Wolsey, Integer Programming

Jacquet-Lagrèze, Programmation Linéaire - Modélisation et mise en oeuvre informatique

Kallrath, Gemischt-ganzzahlige Optimierung: Modellierung in der Praxis

Kallrath and Wilson, Business Optimisation Using Mathematical Programming

Williams, Model Building in Mathematical Programming

Integer Programming

Laurence Wolsey

Wiley Interscience, 1998, ISBN 0-471-28366-5

What you would expect from one of the world's leading experts on IP. A superb, accessible guide to modern developments in integer programming. A must-have.

Gemischt-ganzzahlige Optimierung: Modellierung in der Praxis

Josef Kallrath

Vieweg 2002, ISBN 3-528-03141-7

Dieses Buch beschreibt und lehrt ausgehend von praktischen Fragestellungen, wie in der Industrie, vornehmlich der Prozessindustrie, aber auch anderen Gewerben, gemischt-ganzzahlige Optimierung eingesetzt wird, wie Probleme modelliert und erfolgreich gelöst werden. Es verbindet Modellbildung und algorithmische Aspekte aus den Bereichen kontinuierlicher und gemischt-ganzzahliger, linearer und nichtlinearer und globaler Optimierung. Betrachtet wird auch der Einfluss dieser Methodik in der heutigen Industriegesellschaft insbesondere auf dem Hintergrund von Supply Chain Management. Ausgehend von praktischen Problemen wird in methodisch wissenschaftlicher Weise der Modellbildungs- und Lösungsprozess mit Hilfe vieler Fallstudien veranschaulicht, und es wird gezeigt, welche Techniken in der Praxis verwendet werden und welche Schwierigkeiten dort auftreten. Es stellt in diesem Sinne ein Bindeglied dar zwischen den ehere algorithmisch-theoretisch ausgerichteten Fachbüchern mathematischer Optimierung und den methodisch weniger in die Tiefe gehenden Werken, die sich auf die Beschreibung der Anwendungen konzentrieren. Das Buch ist für Leser gedacht, die sich dafür interessieren, "wie" Mathematik angewendet wird.

Business Optimisation Using Mathematical Programming

Josef Kallrath and John Wilson

Macmillan 1997, ISBN 0-333-67623-8

This book provides a practical and theoretical introduction to business optimisation using mathematical programming - linear programming, integer programming and other approaches. The focus of the book is primarily on models, model applications and individual case studies rather than algorithmic details. However, because the success of solution of complex problems requires efficient problem solving methods, models and algorithms are kept closely connected in the book. The book emphasises the importance of model formulation and makes extensive use of case studies which are either directly based on real applications or are simplified versions of realistic problems. Throughout the book problems are solved using the mathematical programming software XPRESS-MP and a full description of the use of this system is included. A CD-ROM containing a version of XPRESS-MP and models of solved problems is included with the book.

A review of the book:

"It is clear that the authors have experience in using mathematical programming for solving real problems and are keen to pass on their knowledge and expertise. I shall certainly recommend this book to students who are undertaking a project involving mathematical programming, but beyond that, many practitioners will find this book useful to bring their knowledge up to date and to help them produce solvable models"

Journal of the Operational Research Society

This book is difficult to buy from Amazon. Although Amazon keeps telling that the book is out-of-print, Macmillan, or now PalmGrave are able to deliver the book. Therefore, to order the book visit the webpage:

Model Building in Mathematical Programming Third Edition Revised

H. P. Williams Faculty of Mathematical Studies, University of Southampton, UK

Wiley, 1993, ISBN 0471 94111 5

This extensively revised and updated edition discusses the general principles of model building in mathematical programming and shows how they can be applied by using twenty simplified but practical problems from widely different contexts. Suggested formulations and solutions are given in the later part of the book, together with some computational experience to give the reader a feel for the computational difficulty of solving that particular type of model.

Aimed at undergraduates, postgraduates, research students and managers, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations.

By emphasizing the importance of the building and interpreting of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject.

The mathematical programming system MPSX has been replaced by XPRESS-MP in this revised edition.

Note to N American purchasers of this book: Wiley have told us:

Phone your credit card order on 1-800-225-5945
Mail your order to: Wiley Professional Books by Mail, John Wiley and Sons, Inc. Dept 063, Somerset, NJ 08875-9977

Reviews of previous editions

"Such a text, and this is the only one of the type I know of, should be the basis of all instruction in Mathematical Programming." Journal of the Royal Statistical Society

"...strongly recommended to everyone who is involved in formulating practical problems by models that can be solved by mathematical programming... an excellent introduction... for students of business administration and... people who want to see the utility of operations research." European Journal of Operational Research

"...a valuable support for those who are researching in the area of optimization." Optimization Journal

" especially valuable for students and managers. It also may direct research students seeking new algorithms to fruitful grounds." Journal of Systems Analysis Modelling Simulation

"...particularly useful because model building is discussed in detail and is accompanied by explicit solutions. It will be appreciated very much by practitioners who already have knowledge in the field of mathematical programming." Mathematical Programming Society Newsletter

If you are in N. America, this book is stocked by Wiley's New York office and so can be ordered directly from them. Call Wiley's New York Customer Service department on 1-800-225-5945 to order the book, quoting the ISBN 0471 94111 5. Should you have any problems, email

Programmation Linéaire - Modélisation et mise en oeuvre informatique

Eric Jacquet-Lagrèze, Economica, 1998.

Bien que technique relativement ancienne, la programmation linéaire fait l'objet d'un regain d'intérêt dans les entreprises. La construction d'un programme de vols d'une compagnie aérienne, la planification de des horaires de chauffeurs de bus, l'ordonnancement des véhicules sur des chaînes de montage ne sont que des exemples significatifs d'applications de la programmation linéaire.

Ce livre met l'accent sur la modélisation des problèmes et donne un aperçu sur leur résolution avec des outils informatiques actuels. On montre comment utiliser le solveur d'Excel ainsi que des outils beaucoup plus puisants tels que XPPRESS-MP. Ce dernier permet un prototypage rapide de problèmes complexes de grande taille, ainsi que leur résolution avec l'un des meilleurs solveurs du marché.

Eric Jacquet a créé en 1983 Euro-Décision, société spécialisée dans la mise en oeuvre, dans des projets informatiques, de techniques d'optimisation des ressources. Il est également Directeur de Recherche à l'Université de Paris Dauphine.

Copyright © 2007, Josef Kallrath, 30th Dec 2007