Extremal Methods and Systems Analysis: An International Symposium on the Occasion of Professor Abraham Charnes’ Sixtieth Birthday Austin, Texas, September 13 – 15, 1977

553 Pages·1980·8.42 MB·English

by  K. O. Kortanek (auth.)

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Lectu re Notes
in Economics and
Mathematical Systems
Managing Editors: M. Beckmann and H. P. Kunzi
174
Extremal Methods and
Systems Analysis
An International Symposium on the
Occasion of Professor Abraham Charnes'
Sixtieth Birthday
Austin, Texas, September 13 - 15, 1977
Edited by A. V. Fiacco and K. O. Kortanek
Springer-Verlag
Berlin Heidelberg New York 1980
Editorial Board
H. Albach A V. Balakrishnan M. Beckmann (Managing Editor)
P. Dhrymes J. Green W. Hildenbrand W. Krelle
H. P. KOnzi (Managing Editor) K. Ritter R. Sato H. Schelbert
P. Schonfeld
Managing Editors
Prof. Dr. Martin J. Beckmann Prof. Dr. H. P. KOnzi
Brown University Universitat ZOrich
Department of Economics 8090 ZOrich/Schweiz
Providence, RI 02912/USA
Editors
Anthony V. Fiacco
Department of Operations Research
Institute for Management Science and Engineering
The Washington University
Washington, DC 20052/USA
Kenneth O. Kortanek
Department of Mathematics
Carnegie-Mellon University
Pittsburgh, PA 15213/USA
AMS Subject Classifications (1980): 60J50, 60J99, 90A05, 90A15,
90BlO, 90B15, 90C05, 90C15, 90C25, 90C35, 90C99, 90010,
90012,90040
ISBN-13: 978-3-540-09730-3 e-ISBN-13: 978-3-642-46414-0
001: 10.1007/978-3-642-46414-0
Library of Congress Cataloging in Publication Data
International Symposium on Extremal Methods and Systems Analysis, University of Texas
at Austin, 1977.
Extremal methods and systems analysis.
(Lecture notes in economics and mathematical systems; 174)
Bibliography: p.
Includes index.
1. System analysis··Congresses. 2. Programming (Mathematics)--Congresses.
3. Game theory--Congresses. 4. Economics, Mathematical--Congresses. 5. Charnes,
Abraham, 1917-1. Charnes, Abraham, 1917-11. Fiacco, Anthony V.III. Kortanek, K. 0., 1936-
IV. Title. V. Series.
0A402.1571977 00379-27040
ISBN-13: 978-3-540-09730-3
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© by Springer-Verlag Berlin Heidelberg 1980
214113140-543210
ABRAHAM CHARNES
In recognition of your many outstanding contributions as a scholar,
mathematician, management scientist, engineer, teacher, and friend, we
have convened the
INTERNATIONAL SYMPOSIUM ON
EXTREMAL METHODS AND SYSTEMS ANALYSIS
in your honor. We extend our sincere greetings and good wishes on the occasion
of your sixtieth birthday. It has been our good fortune to ha ve had our
professional and personal lives greatly enriched by our associations with you.
Austin, Texas
September 13-15, 1977
PREFACE
The papers appearing in this Volume were selected from a collec
tion of papers presented at the Internationa~ Symposium on Extrema~
Methods and Systems Ana~ysis on the Occasion of Professor A. Charnes'
60th Birthday, at the University of Texas in Austin, 13-15 September
1977. As coeditors, we have followed the normal editorial procedures
of scholarly journals. We have obtained invaluable assistance from a
number of colleagues who essentially performed the duties of associate
editors, coordinating most of the reviews. All papers except those
appearing in the Historica~ Perspectives section were refereed by at
least two individuals with competency in the respective area. Because
of the wide range and diversity of the topics, it would have been im
possible for us to make a consistently rational selection of papers
without the help of the associate editors and referees. We are indeed
grateful to them.
The breadth of extremal methods and systems analysis, suggested
by the range of topics covered in these papers, is characteristic of
the field and also of the scholarly work of Professor Charnes. Extre
mal methods and systems analysis has been a pioneering and systematic
approach to the development and application of new scientific theories
and methods for problems of management and operations in both the pri
vate and public sectors, spanning all major disciplines from economics
to engineering. Representative of the topical areas discussed at the
Symposium, we have categorized 29 papers under ten basic themes: His
torica~ Perspectives, Economic Mode~ing and Equi~ibrium, P~anning and
Decision Mode~s, Genera~ized Inverses and Matrices, Transportation and
VI
Networks, Game Theory, Mathematical Programming Theory, Mathematical
Programming Computations, Complementarity and Fixed Point Theory, and
Stochastic, Dynamic, and Ma2·kov Models.
We hope that you will experience some of the high quality and ex-
citement of the Symposium itself as you discover the competent and
avant-garde sampling of the themes that we have been able to represent
in this Volume. The list of titles and authors may, it is hoped, be
enticement enough to read on. This illustrious collection of papers
does indeed honor the past achievements of the science and of the man
to whom this Volume will be an enduring tribute, by no means an easy
task. The conference was widely publicized and open to the scientific
community, the result being a reliable assessment of past achieve-
ments and a vi?ionary identification of many directions of signifi-
cance and promise for the field, by highly reputable methodologists
and theoreticians and from diverse viewpoints.
We would like to take this opportunity to express our gratitude
to those professional societies who gave the Symposium their official
endorsement:
The Association of European Operational Research Soci
eties within the International Federation of Opera
tional Research Societies
The Center for Operations Research and Econometrics
(CORE), Belgium
F6ndation Nationale pour l'Enseignement de la Gestion
des Entreprises, France
Deutsche Gesellschaft fur Operations Research (DGOR)
The Mexican National Academy of Engineering
The Operations Research Society of Japan
The Society for Industrial and Applied Mathematics
The State Committee for Science and Technology, USSR
The Institute of Management Sciences
The Operations Research Society of America
We are especially pleased to acknowledge major financial support
of the Symposium from the Mathematical Sciences Section of the Nation-
al Science Foundation, as well as contributions from Analysis, Re-
search and Computation, Inc.; the Mathematics, Computers and Systems
Department at the EXXON Corporation; and Gulf Science and Technology
Company. We must also acknowledge the valuable support of the Univer-
sity of Texas, whose facilities were placed at our disposal, particu-
larly through that university's president, Lorene L. Rogers, and Dean
George Kozmetsky and Professor Darwin Klingman.
The Symposium Committee, the list of the Symposium participants,
and Symposium Volume authors, together with their affiliations, and
the list of acting associate editors appear at the end of the Volume.
Their support of the Symposium and this Volume was indispensable. Our
appreciation must also be directed to our publisher, Springer-Verlag,
who has been extremely encouraging and helpful in every phase of manu
script preparation and whose methodical and timely attention to detail
has considerably simplified our work. A final word of gratitude is
reserved for our many illustrious colleagues who took the time and ef
fort to prepare and present Symposium papers, and to those authors
herein represented who have patiently borne with us through the long
review process to the final preparation of this manuscript.
A. V. Fiacco K. O. Kortanek
The George Washington University Carnegie-Mellon University
Washington, D.C. 20052 Pittsburgh, Pennsylvania 15213
TABLE OF CONTENTS
PART I HISTORICAL PERSPECTIVES
A Biography of Professor A. Charnes and His
Scientific Work . . . . . . 2
K. O. Kortanek
Abraham Charnes--A Strategy for Research and a Record
of Results ....... ........... 10
W. W. Cooper
Publications of A. Charnes 2S
PART II ECONOMIC MODELING AND EQUILIBRIUM
Multi-page Format Economic Systems ......... S2
Sten Thore
The Need for Dynamic Extensions of General-
Equilibrium Methods ........... . 68
William P. Drews
A Few Words on Application of Optimization Methods to
Economic Problems . . . . . . . . . . . .. 8S
L. V. Kantorovich and J. V. Romanovsky
PART III. PLANNING AND DECISION MODELS
Designing Investment Strategies for Fixed-Income
Portfolios . . . . . . .. ....... 98
Morton Lane and Jerome Kreuser
Multiple Criteria Decision Making for Discrete
Alternatives with Ordinal Criteria ..... 13S
Stanley Zionts
PART IV. GENERALIZED INVERSES AND MATRICES
Generalized Inverses of Matrices and Their
Applications ................... 1 S4
Adi Ben-Israel
Cost-flow Networks and Generali zed Inverses . . . . . 187
Yuji Ijiri
x
The Weighted Generalized Inverse in Nonlinear
Programming--Active Set Selection Using a Variable-
metric Generalization of the Simplex Algorithm 197
L. Duane Pyle
Convergence Properties of Powers of Matrices with
Applications to Iterative Methods for Solving Linear
Systems . . . . . . . . . . . . . . . . . . . . . .. 231
Uriel G. Rothblum
PART V TRANSPORTATION AND NETWORKS
A Network Augmenting Path Basis Algorithm for
Transshipment Problems 250
Richard Barr, Joyce Elam, Fred Glover, and
Darwin Klingman
More on the More for Less Paradox in the Distribution
Model. . . . . . . . . . . . . . .. 275
Michael J. Ryan
PART VI GAME THEORY
The Nash Solution as a Model of Rational Bargaining. 306
Al vin E. Roth
Computing the Core of a Market Game. . . . . . . .. 312
Gerald L. Thompson
PART VII MATHEMATICAL PROGRAMMING THEORY
Second Order Theory of Extremum Problems 336
Aharon Ben-Tal
An Elementary Treatment of Lagrange Multipliers 357
R. J. Duffin
Representation of Convex Sets. . . . . . . . . . .. 374
Ulrich Eckhardt
On One-row Linear Programs 384
Christoph Witzgall
Duality in Fuzzy Linear Programming ... 415
Wilhelm Radder and Hans-Jurgen Zimmermann
PART VIII MATHEMATICAL PROGRAMMING COMPUTATIONS
Fractional Programming with Zero-one Variables 430
E. M. L. Beale
Quadratic Termination of Conjugate Gradient
Algori thms . . . . . . . . . . . 433
D. F. Shanno
XI
Rectilinear Distance Location-Allocation Problem:
A Simplex Based Algorithm . . . . . . . . . . . . 442
C. M. Shetty and H. D. Sherali
PART IX COMPLEMENTARITY AND FIXED POINT THEORY
Recent and Past Developments in the Simplicial
Approximation Approach to Solving Nonlinear
Equations-A Subjective View . . . . . . . . . 466
F. J. Gould
Global Continuation Methods for Finding All Solutions
to Polynomial Systems of Equations in N Variables. 481
C. B. Garcia and W. I. Zangwill
Worst-case Behavior of Local Fixed-point Algorithms. 498
Charles E. Blair
PART X STOCHASTIC, DYNAMIC, AND MARKOV MODELS
I
Quality Control and Free Boundary Problems 506
Avner Friedman
The Use of Stochastic Programming for the Solution of
Some Problems in Statistics and Probability. . . .• 522
Andras Prekopa
AUTHORS, PARTICIPANTS, AND AFFILIATIONS 539
ACTING ASSOCIATE EDITORS 545
THE SYMPOSIUM COMMITTEE . 545