50 Years of Integer Programming 1958-2008 From the Early Years to th
In 1958, Ralph E. Gomory transformed the field of integer programming when he published a short paper that described his cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for intege
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Michael J¨unger · Thomas Liebling · Denis Naddef · George Nemhauser · William Pulleyblank · Gerhard Reinelt · Giovanni Rinaldi · Laurence Wolsey Editors
50 Years of Integer Programming 1958–2008 From the Early Years to the State-of-the-Art
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Editors Michael J¨unger Universit¨at zu K¨oln Institut f¨ur Informatik Pohligstraße 1 50969 K¨oln Germany [email protected] Denis Naddef Grenoble Institute of Technology - Ensimag Laboratoire G-SCOP 46 avenue F´elix Viallet 38031 Grenoble Cedex 1 France [email protected] William R. Pulleyblank IBM Corporation 294 Route 100 Somers NY 10589 USA [email protected] Giovanni Rinaldi CNR - Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti” Viale Manzoni, 30 00185 Roma Italy [email protected]
Thomas M. Liebling Ecole Polytechnique F´ed´erale de Lausanne Facult´e des Sciences de Base Institut de Math´ematiques Station 8 1015 Lausanne Switzerland [email protected] George L. Nemhauser Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA 30332-0205 USA [email protected] Gerhard Reinelt Universit¨at Heidelberg Institut f¨ur Informatik Im Neuenheimer Feld 368 69120 Heidelberg Germany [email protected] Laurence A. Wolsey Universit´e Catholique de Louvain Center for Operations Research and Econometrics (CORE) voie du Roman Pays 34 1348 Louvain-la-Neuve Belgium [email protected]
ISBN 978-3-540-68274-5 e-ISBN 978-3-540-68279-0 DOI 10.1007/978-3-540-68279-0 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009938839 Mathematics Subject Classification (2000): 01-02, 01-06, 01-08, 65K05, 65K10, 90-01, 90-02, 90-03, 90-06, 90-08, 90C05, 90C06, 90C08, 90C09, 90C10, 90C11, 90C20, 90C22, 90C27, 90C30, 90C35, 90C46, 90C47, 90C57, 90C59, 90C60, 90C90 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
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We dedicate this book to the pioneers of Integer Programming.
Preface
The name integer programming refers to the class of constrained optimization problems in which some or all of th
