Linear Programming and its Applications
This book presents a unified treatment of linear programming. Without sacrificing mathematical rigor, the main emphasis of the book is on models and applications. The most important classes of problems are surveyed and presented by means of mathemat
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H. A. Eiselt · C.-L. Sandblom
Linear Programming and its Applications
With 71 Figures and 36 Tables
123
Prof. Dr. H. A. Eiselt University of New Brunswick Faculty of Business Administration P.O. Box 4400 Fredericton, NB E3B 5A3 Canada [email protected] Prof. Dr. C.-L. Sandblom Dalhousie University Department of Industrial Engineering P.O. Box 1000 Halifax, NS B3J 2X4 Canada [email protected]
Library of Congress Control Number: 2007931630
ISBN 978-3-540-73670-7 Springer Berlin Heidelberg New York 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. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 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. Production: LE-TEX Jelonek, Schmidt & V¨ ockler GbR, Leipzig Cover-design: WMX Design GmbH, Heidelberg SPIN 12092093
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“A problem well stated is a problem half solved.” Charles Franklin Kettering
PREFACE
Based on earlier work by a variety of authors in the 1930s and 1940s, the simplex method for solving linear programming problems was developed in 1947 by the American mathematician George B. Dantzig. Helped by the computer revolution, it has been described by some as the overwhelmingly most significant mathematical development of the last century. Owing to the simplex method, linear programming (or linear optimization, as some would have it) is pervasive in modern society for the planning and control of activities that are constrained by the availability of resources such as manpower, raw materials, budgets, and time. The purpose of this book is to describe the field of linear programming. While we aim to be reasonably complete in our treatment, we have given emphasis to the modeling aspects of the field. Accordingly, a number of applications are provided, where we guide the reader through the interactive process of mathematically modeling a particular practical situation, analyzing the consequences of the model formulated, and then revising the model in light of the results from the analysis. Closely related to the issue of building models based on specific applications is the art of reformulating problems. Some of these models may at first appear not to be amenable to a linear representation, and we devote an e
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