Linear programming and related techniques

382 Pages·1971·14.103 MB·English

by  C. van de Panne

NORTH-HOLLAND/
AMERICAN ELSEVIER
linear programming
and related techniques
C. van de PANNE
THOMAS J. BATA LIBRARY
TRENT UNIVERSITY
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LINEAR PROGRAMMING AND RELATED TECHNIQUES

LINEAR PROGRAMMING AND
RELATED TECHNIQUES
C. van de PANNE
University of Calgary, Alberta, Canada
1971
NORTH-HOLLAND PUBLISHING COMPANY - AMSTERDAM - LONDON
AMERICAN ELSEVIER PUBLISHING COMPANY, INC. - NEW YORK
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© North-Holland Publishing Company - 1971
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system, or transmitted, in any form or by any means, electronic, mechanical, photo¬
copying, recording or otherwise, without the prior permission of the copyright owner.
Library of Congress Catalog Card Number 75-157018
North-Holland ISBN 0 7204 2049 0
American Elsevier ISBN 0 444 10115 2
Publishers:
NORTH-HOLLAND PUBLISHING COMPANY - AMSTERDAM
NORTH-HOLLAND PUBLISHING COMPANY, LTD. - LONDON
Sole distributors for the U.S.A. and Canada:
AMERICAN ELSEVIER PUBLISHING CO., INC.
52 VANDERBILT AVENUE, NEW YORK, N.Y. 10017
Printed in The Netherlands
PREFACE
The origin of this book can be traced to lovely Stratford-upon-Avon,
where in 1964 I was asked to explain to executives of Turner and Newall
Ltd., the essence of linear programming. Linear algebra, which I had used so
far when teaching linear programming was of no avail, so that I had to start
from scratch. The result can be found, not greatly changed, in Chapter 2.
Later on, I extended the same approach in lectures for nonspecialist classes
in Operations Research, which served as a basis of this book.
The book is designed as an introductory text for students in economics
and business administration. It is my opinion that linear programming is an
indispensable tool for the economist. Firstly, it provides economists with a
very useful decision technique; since economics is mainly analytically orien¬
tated this serves as a necessary complement. Students in economics are fre¬
quently frustrated by the surfeit of analysis in economics. Secondly, linear
programming can also be used in economic analysis as is shown in Chapter 10.
One of the advantages is that in this case numerical examples can be easily
worked out. For students of business administration linear programming
stands apart from other techniques of operations research by giving an evalua¬
tion of the values of machines, plants, sales constraints and other bottle¬
necks, so that these can be directly related to the values used in the account¬
ing system.
The methods presented in this book are not new and the number of books
on the same subject is not exactly small. The main advantage of this book is
thought to consist in the approach used for the explanation of the various
methods. Linear programming is explained in such a manner that the essen¬
tials are covered without use of linear algebra. I hope to have demonstrated in
this book that this is possible. Furthermore, transportation methods, network
methods and integer programming are treated in a manner which follows
naturally from general linear programming; in this respect the book can claim
some novelty.
It is obvious that the book relies on developments of the subject as they
are found in the literature. However, in a book of this kind it is of great
importance to have examples and exercises which are both nontrivial and
V
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Preface
VI
manageable. Whereas most of the examples and exercises of this book are
new, some have been taken from other sources.
The material of the book is suitable for a half year course or a full year
course. In the first case it is likely that some material such as that on integer
programming must be left out. It is my experience that, in order to obtain a
full understanding of the methods, it is indispensable that the students work
out a reasonable number of problems manually. Usually students find at first
the material difficult and the problems time-consuming, but before the course
is finished they usually agree that the methods are not difficult but merely
complicated.
Thanks are due to students in Birmingham, Groningen, Lafayette (Ind.)
and Calgary who, having to go through this material, improved it by their
comments, and to my secretaries in the places aforementioned, who typed
various versions of the manuscript. Finally, I am grateful to Mr. Victor G.
Taylor on whose thesis the example of crude oil distribution is based.
Calgary, December 1970