Stochastic Linear Programming Models, Theory, and Computation
This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via co
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Series Editor Frederick S. Hillier, Stanford University, CA, USA
Special Editorial Consultant Camille C. Price Stephen F. Austin State University, TX, USA
For further volumes: http://www.springer.com/series/6161
Peter Kall • János Mayer
Stochastic Linear Programming Models, Theory, and Computation 2nd Edition
1C
Peter Kall Professor emeritus University of Zürich Böniweg 10 CH-8932 Mettmenstetten, Switzerland [email protected]
János Mayer Institute of Operations Research University of Zürich Moussonstrasse 15 CH-8044 Zürich, Switzerland [email protected]
ISSN 0884-8289 ISBN 978-1-4419-7728-1 e-ISBN 978-1-4419-7729-8 DOI 10.1007/978-1-4419-7729-8 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010938300 © Springer Science+Business Media, LLC 2005, 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Helene and Ilona
Preface
The beginning of stochastic programming, and in particular stochastic linear programming (SLP), dates back to the 50’s and early 60’s of the last century. Pioneers who—at that time—contributed to the field, either by identifying SLP problems in particular applications, or by formulating various model types and solution approaches for dealing adequately with linear programs containing random variables in their right–hand–side, their technology matrix, and/or their objective’s gradient, have been among others (in alphabetical order): E.M.L. Beale [12], proposing a quadratic programming approach to solve special simple recourse stochastic programs; A. Charnes and W.W. Cooper [41], introducing a particular stochastic program with chance constraints; G.B. Dantzig [49], formulating the general problem of linear programming with uncertain data and G.B. Dantzig and A. Madansky [53], discussing at an early stage the possibility to solve particular two-stage stochastic linear programs; G. Tintner [326], considering stochastic linear programming as an appropriate approach to model particular agricultural applications; and C. van de Panne and W. Popp [333], considering a cattle feed problem modeled with probabilistic constraints. In addition we should mention just a few results and methods achieved before 1963, which were not developed in connection with stochastic programming, but nevertheless tu
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