E-Book Overview
Mathematical programming has know a spectacular diversification in the last few decades. This process has happened both at the level of mathematical research and at the level of the applications generated by the solution methods that were created. To write a monograph dedicated to a certain domain of mathematical programming is, under such circumstances,especially difficult. In the present monograph we opt for the domain of fractional programming. Interest of this subject was generated by the fact that various optimization problems from engineering and economics consider the minimization of a ratio between physical and/or economical functions, for example cost/time, cost/volume,cost/profit, or other quantities that measure the efficiency of a system. For example, the productivity of industrial systems, defined as the ratio between the realized services in a system within a given period of time and the utilized resources, is used as one of the best indicators of the quality of their operation. Such problems, where the objective function appears as a ratio of functions, constitute fractional programming problem. Due to its importance in modeling various decision processes in management science, operational research, and economics, and also due to its frequent appearance in other problems that are not necessarily economical, such as information theory, numerical analysis, stochastic programming, decomposition algorithms for large linear systems, etc., the fractional programming method has received particular attention in the last three decades.
E-Book Content
Fractional Programming
Mathematics and Its Applications
Managing Editor:
M. HAZEWINKEL Centre/or Mathematics and Computer Science, Amsterdam, The Netherlands
Volume 409
Fractional Programming Theory, Methods and Applications
by
I.M. Stancu-Minasian Centre for Mathematical Statistics, The Romanian Academy, Bucharest, Romania
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-13: 978-94-0 10-6504-7
e-ISBN-1 3: 978-94-009-0035-6
DOl: 10:1007/ 978-94-009-0035-6
Published by Kluwer Academic Publishers, P.O. Box, 3300 AA Dordrecht, The Netherlands. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed
by Kluwer Academic Publishers,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands. This is a complete revised and updated translation of the original work M~ttxk d~ R~zplvan a Probl~melor d~ Programare FracIionarii Editura Academiei Romine, Bucharest © 1992. Translated from the Romanian by Victor Giurgiutiu.
All Rights Reserved ®1997 Kluwer Academic Publishers No part of the material protected by this copyright notice may be reproduced or utilized in any fonn or by any means, electronic or mechanical, including photocopying, recording or by any infonnation storage and retrieval system, without written pennission from the copyright owner
TABLE OF CONTENTS
Introduction
1
1
Fractional Programming Applications
6
1.1 1.2
7 8 9
1.3
1.4 1.5
1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 2
Blending Problems Optimal Cutting Stock Problems Information Theory Optical Processing ofInformation Minimum-Risk Problems in Stochastic Programming Macroeconomic Planning The Production Efficiency Problem Cluster Analysis Optimal Paths in Graph Theory Repartition Problems Transportation Problems with Several Objective Functions Investments Allocation Problems Geographical Repartition of Investments Game Theory Pro