Title: Optima
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Title: Optima
Series Title: Optima
Physical Description: Serial
Language: English
Creator: Mathematical Programming Society, University of Florida
Publisher: Mathematical Programming Society, University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: January 1985
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12th International Symposium on Mathematical Programming at MIT

The Programming of (Some) Intelligence:

Opportunities at the OR/AI Interface
Robert G. Jeroslow, Georgia Institute of Technology

N recent years "artificial intelli-
gence" (AI) and, more specifically, the
"expert system" (ES) approach within
the AI area have captured the popular
imagination. Here in this article I shall be
very topical and trendy. First, however, I
want to be clear about the intellectual
issues involved.
For about three years now, I have
been studying some of the mathematical
aspects of the process of taking a "real-
world" situation and representing it
(when possible) by a mixed-integer
(linear or convex) program in binary
integers. Much of this work began as joint
with James K. Lowe.
The mathematical form in which
my own inquiries have recently converged
lies in elucidating the relationship be-
tween formulation settings. I am inter-
ested in studying this 'modelling process'
because of the possibilities for extending
the use of OR models in a decision
support context.
Let us conceptualize the matter
this way. There is some domain 2, a
subset of the Cartesian product of X and
D, where X is the "spatial component"
(i.e. is a subset of some Euclidean space)
and D is the "logical component" (i.e.,
the rest). Here X and D may themselves
also be Cartesian products. On S2 there is
a set of "predicates" (also called "rela-
tions") P1, P2.... A predicate Pj is simply
a subset of G2.
Each of the predicates P. has a
"negation" P., which is simply its set-
theoretic complement in G2:-P: = 2\Pj.
Here is what we seek: we wish to

"imbed" the entire structure 2 and its
predicates P1P2,... into a space-the
non-spatial D along with the spatial part
X in a way that "preserves" the spatial
part X in terms of optimization. After all,
mathematical programming algorithms
generally operate in Euclidean space, so
we have to first get the structure there!
More specifically, we wish to find
subsets Imb (2) and Imb (P.), Imb(-Pj)
(all j) of some Euclidean space, with a
number of properties: 1) The Imb()2)
and Imb(P.), Imb(-P) are representable
using constraints of a mixed-integer type
in binary variables and have a common
recession cone; 2) Imb (P.) U Imb(-P.)
= Imb(2) and Imb (P.)'Imb (-P.)=i;
and 3) for any logical form involving
only the propositional connectives of
'or' (abbreviated as 'V'), 'and' ('A'),
'implies' ('-*') and 'not' ('7') and any
linear criterion vector 'c', we have

(*) inf cx I(x,d)e}=(min cx I(x,y)
e Imb()}
WE now explain (3) and (*) in some
detail. It allows conditions like =(P1 but
not (P2 and not P5)) and (not P3 or P5).
So here Imb()= Imb(P1) n (Imb(7P2) U
Imb(P5))n(Imb(-P3)UImb (P5)).
Under rather broad conditions
imbeddings exist, so optimization over 2
can be done entirely by spatial techniques
from mathematical programming e.g.,
branch-and-bound (that is the significance
of (*)).
Curiously enough, even for familiar
logical implications frequently done by
MIP in the past, there turn out to be new
spatial imbeddings which appear to be
more advantageous.

August 5-9, 1985
Contributed Paper Titles April 1, 1985
Abstracts May 15, 1985

Symposium Secretary
Operations Research Center
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 USA
(617) 253-3601

Society Seeks Host for 13th
The Mathematical Programming
Society is beginning its planning for the
Thirteenth International Symposium on
Mathematical Programming, which it pro-
poses be held about the last week in
August, 1988, somewhere in the world
other than North America. It wishes
hereby to invite all parties who might
act as hosts to this event to make their
interest known to the Society's Symposi-
um Advisory Committee.
The Society's practice with regard
to the Symposia has been to give the
host committee considerable autonomy
in the whole affair. The Society has some
guidelines for conducting the
Symposium, traditions it wishes to main-
tain, and a large body of experience on
which the host can draw. (The committee
-to page 4

From a practical perspective, one is
more concerned with the linear relaxa-
tion of the imbedding Imb(). This is
what guides the branch-and-bound search
tree. A good deal can be said about the
p,,iblk imbedding and the strength of
the associated relaxation. Generally, there
are "a lot" of them and one wants those
with "undominated" relaxations, relative
to the size of the (linear or convex)
system. A study of these relaxations
requires further and systematic develop-
-to page 2


The Programming of (Some) Intelligence: Opportunities at the OR/AI Interface

ment of that part of the "-Jiim...it..i
1i-rldlJ. that Egon Balas and I have
worked on.
Many "expert systems" need only
a small fragment of the modelling poten-
tialities sketched above.
When the "expert" in an ill-
structured area describes his/her heuristic
rules by means of "productions," they
are cast in the form:

(I) If Ai with MB xi (i= 1,..,t) then
B with MB y.

In (I), the Ai and B describe conditions
such as: "The patient has pneumonia"
The measures of belief (MBs) xi and y are
real numbers (usually in [0,1]) and y is a
function of the xi: y = f(x1,..., xt).
Certain initial values of the MBs
are given, in addition to the rules (I).
These may come from diagnostic tests
run on a specific patient. In contrast,
the production rules (I) represent general
Many different functions f have
been suggested; one is the minimum: y=
f(x ,...,xt)= min xi. Then the belief in B
is the maximum of all such y, over all
rules (I) which conclude B, together with
the original MB of B; and the chaining
process of taking minima (in(I)) and then
maxima, is repeated. When the con-
fidence in some conclusion like B (which
is a function j(y,y') of the MB y of B and
the MB y' of -B) is "suitably high," the
truth of B may be "concluded."

THIS summarizes my own treatment
of MBs and "confidence factors" (CFs)
calculated as j(y,y'). For me the MB y of
B is a measure of the strength of evidence
in favor of B, ignoring contrary evidence;
while the MB y' of 7B summarizes only
the evidence against B. In this treatment
MB is like a "myopic barrister," the two
barristers make cases y and y' which go to
a "jury" j(y,y').
Incidentally, even for zero-one
valued MBs, the above treatment and
existing treatments will not recover
boolean propositionall) logic. Note that
the two rules A-1B and 1A-+B assure that
B is true (as AV-A is true). However,
starting with zero MBs for A and -IA,
one will not get an MB of "one" for B in
existing treatments.
There are variations in how the
rules like (I) are used. In other treatments
the computation of the MBs and confi-
dence are done differently.

For the minimum function y =
minx1 ,...,t}, one can obtain a represent-
ation of its epigraph using linear mixed-
integer constraints in binary variables.
Using this representation, the end result
of a complete chaining process can be
obtained from solving a mixed-integer
program (MIP). Other monotone, repre-
sentable functions are also treated by
The technical advantage of the
"myopic barrister" approach lies in its
ability to obtain, from one MIP, the
limits of a very long finite (or even
infinite) process of repeated chaining
provided these limits exist and are not
less than the initial MB values.
At the present time, the use of
MBs lacks a consistent and sound axio-
matic foundation for their use. Such a
foundation may well be feasible and was
done earlier for the use of probability in
Of course, when the CFs are not
present, an "expert tviim" becomes a
conventional satisfiability problem. From
empirical results on many randomly-
generated problems (with t less than
seven), it emerged in experiments run by
Jim Lowe that the usual integer program-
ming techniques were very effective.
I have gone into detail regarding
some of my own current research in order
to indicate how issues in the "OR/AI
interface" can often be made exact and
subject to a mathematical development. I
am developing "machinery" to explore
some topics which appeal to me.

Al is a very broad area which yields
to many different mathematical appro-
aches and techniques. There will be
multiple ways of using OR in AI and
vice versa. Since the terrain of the
"AI/OR interface" is largely uncharted,
there are also "opportunities" to make
mistakes. The kind of work involved is
for the more entrepreneurial among us.
I believe that we in mathematical
pi ..i.iiaimirig have much to learn from
,lu., it m many of the techniques used in
AI. I believe also that we can benefit
from the broader modelling traditions of
There are many points of potential
commonality. I shall quickly cite a few.
The alpha/beta trees of AI (with
node evaluation functions) are a natural
extension of the 'or' trees of OR (with
linear or combinatorial node relaxa-

tions), and may prove the appropri-
ate tool for highly advanced decision-
support systems in which competitive
reactions are seriously treated.
The "constraint propagation" tech-
niques can be viewed as broad generaliza-
tions of our constraint preprocess-
ing routines. These techniques take into
account interactions between constraint
reformulations and minimally suggest
dynamic reformulation in the search tree.
These techniques are also relevant to
postoptimality analysis in which whole
constraints may be added or dropped.
The very broad concept of a
"control structure" in AI is a significant
extension of the kinds of "swapping" we
have considered in large-scale systems,
where only a part of a problem can be
treated at a time. However, it goes well
beyond this issue and includes the possi-
bilities of different processing mech-
anisms for different aspects of a model,
independent of the size issue. The "con-
trol structure" orientation subsumes the
concept of heuristic strategies for node
development in branch-and-bound.
We will stop here with our partial
enumeration of commonalities in tech-
niques. Most of AI is not technically
oriented, however.

THE "mainstream" of AI is con-
cerned with human and machine cogni-
tion, vision, language p,.:i. li,', know-
ledge representation, and learning, as well
as robotics, control structures, etc;
basic philosophical issues can arise. These
issues will be argued by those with
very broad interests.
Certainly, the development of
"expert systems" was driven primarily
by needs for decision support and not by
technical considerations. The "philos-
ophy" of ES is set out in [6]. The
emphasis is on knowledge acquisition and
representation in specific domains of
human expertise for which conventional
quantitative models were not deemed
appropriate (although, from the above,
they can be).
In some respects, ESs resemble a
"manual" of information on the domain
studied, differing from conventional
manuals in the organization and re-
presentation of the knowledge and the
higher computational complexity of the
linkages between I .i 1i." of knowledge.
The tradition of "knowledge engi-
neering" includes great respect for the

Robert G. Jeroslow

wisdom and standards of experts in a
domain area. It also includes much
patience and care, as well as large alloca-
tions of time in developing "prototype"
applications. Some of the OR consultants
will invest similar amounts of effort in
developing a consulting product.
In terms of techniques and method-
ology the differences between AI and OR
may be largely this. Technical OR derives
from applied mathematical analysis,
linear algebra, graph theory, and axio-
matics of combinatorial structures. Tech-
nical AI derives largely from applied
logic. The remaining differences seem to
be details.

HERE are the primary reasons why I
believe that a technical focus on inference
engines and representation will play a
useful and major role in at least the
decision-support context:
(1) Knowledge representations, in
expert systems or in other "'.[,:-lignt"
systems, need to have adequate inference
engines to be used, i.e., good inference
engines are a bottleneck: (2) The avail-
ability of improved techniques for in-
ference engines and for representations
will encourage more ambitious and far-
reaching applications; (3) There is evi-
dence to believe (and it is my current
belief) that the most respected inference
engines for AI (these are predicate-
logic-based resolution procedures) will
not be as efficient in the less ambitious
decision-support context as will be adapt-
tations of OR techniques aided by logic
il.rit lini (4) I am willing to conjecture
that the use of human-protocol based
heuristics, such as "means-ends analysis,"
and other techniques motivated by
conscious processing procedures, will lie
largely in the control structure of
advanced decision support systems. The
bulk of the actual processing will be
carried out by technical algorithms, many
from mathematical programming and
many from other branches of applied
The enhanced modelling possibili-
ties of the AI tradition, some of which is
captured in ESs, is obviously of great
attraction to those colleagues in areas like
applied OR, industrial engineering, pro-
duction, marketing, finance, accounting,
etc. As many of them slowly turn to AI
modelling approaches, they will need our

Regarding solely the current ES
approach within the broad and rich AI
traditions, let me make a guess. Limits
will be (have been?) found as one deals
with human experts who (at best)
approximate a reality that has a succinct
non-rule-based formulation and who may
require thousands of rules to partially
represent their knowledge. No simple
paradigm will subsume the marvel-
lous complexity of our world.
After all, one would not use an
expert system to do linear programming!
In fact, Professor Dantzig's own recollec-
tion of the origins of our field involve
precisely the need to undo some "expert
,',~Ic~I'" when one finds an excellent
mathematical method [4].
Recently I have had a number of
conversations with colleagues in OR
about software systems which incorp-
orate the multiple features of logic,
database, partial knowledge, and linear
structure. I find we generally agree about
their desirability, but, as one colleague
said, "No one knows how to build them."
Very bluntly put and (evidently) true. Of
course, we can learn how if we choose to.

Anil Nerode first brought to my
attention the technological advances of
AI in the last several years and recom-
mended a reading of [5].
I have benefitted from discussions
with Richard Platek, Janet Kolodner,
Arthur Nevins, Andrew Whinston, and
Arthur Geoffrion.
Charles Blair's visit was very valu-
able for me toward clarifying the nature
of some inference engines in current use
in expert systems.
The image of ESs as complex
manuals derived from a conversation with
Raj Gupta.
I owe particular thanks to Don
Hearn for his willingness to consider a
speculative piece for OPTIMA.

Suggestions for Readings
Either [9] or [11] are good general
AI texts. In [6] there are nontechnical
expositions of the history and philosophy
of expert systems and "knowledge engi-
neering" and a detailed application.
[6] shows the orientation toward know-
ledge acquisition, as opposed to technical
A very fine general logic text is
[10] .

I strongly recommend [2] for over-
view articles and for mid..:; Il.'.l;rli some
of the most sophisticated inference
engines. [8] goes into more detail on
resolution-based theorem proving and can
be used in connection with [10]. The
text [7] is also very useful.
The dialogues with Teresias in [5]
are very instructive, in terms of the kind
of decision support available in some
expert systems.
[1] is a general reference for the
many different approaches to AI.

S1] Avron Barr and Edward A. Feigen-
baum, The Handbook of Artificial
Intelligence, Heuris Tech Press and
William Kaufman, Inc., Stanford
and Los Altos, CA. (vol. I copy-
right 1981).
[2] W.W. Bledsoe and D.W. Loveland,
eds, "Automated Theorem Proving:
After 25 Years," Contemporary
Mathematics, vol. 29, American
Mathematical Society, Rhode Is-
land, 1983.
[3] Robert H. Bonczek, Clyde W.
Holsapple, and Andrew B. Whin-
ston, Foundations of Decision
Support Systems, Academic Press,
New York, 1982.
[4] George B. Dantzig, "Reminiscences
About the Origins of Linear Pro-
gramming," Operations Research
Letters 1(1982)43-48.
[5] Randall Davis and Douglas B.
Lenat, Knowldege-Based Systems
in Artificial Intelligence, McGraw-
Hill International, New York, 1982.
[6] Frederick Hayes-Roth, Donald A.
Waterman, and Douglas B. Lenat,
Building Expert Systems, Addi-
Sson-Wesley, Reading, Mass., 1983.
[7] Robert Kowalski, Logic for Pro-
blem Solving, North-Holland,
Amsterdam, 1979.
[8] Donald W. Loveland, Automated
Theorem Proving: A Logical Basis,
North-Holland, Amsterdam, 1978.
[9] Elaine Rich, Artificial Intelligence,
McGraw-Hill, New York, 1983.
[10] Joseph R. Shoenfield, Mathematical
Logic, Addison-Wesley, London,
[11] Patrick Henry Winston, Artificial
Intelligence, 2nd ed., Addison-
Wesley, London, 1984.



Calls for Papers:

Parallel Computing in Optimization
Institute fur Informatik
Universitlit Stuttgart
Stuttgart, Germany F.R.

The increasing number of available
computers with a parallel processor
architecture requires the development of
optimization algorithms which are able
to exploit the new technical structures.
Thus, it is planned to publish a special
volume of Computing (Springer) de-
voted exclusively to the above topic.
Papers describing algorithms, software
and applications are welcome. They will
be refereed in the usual way.
The editors of the special volume
are W. Knb'del (co-editor of Computing)
and K. Schittkowski. Three copies of
related papers should be sent to one of
the editors at the Institut fur Informa-
tik, Universitit Stuttgart, Azenbergstr.
12, D-7000 Stuttgart 1, Germany F.R.
-K. Schittkowski

12th IFIP Conference on
System Modelling and Optimization
Budapest, Hungary
September 2-6, 1985

The aim of the conference is to
discuss recent advances in the mathe-
matical representation of engineering,
socio-technical, and socio-economic sys-
tems as well as in the optimization
of their performances.
Extended abstracts of papers to be
presented at the conference should be
submitted to the secretariat by January
31, 1985. They should be approximately
two pages in length and should describe
original unpublished results by their
The conference language is English
and typescripts of a selection of complete
papers will be published in the Confer-
ence Proceedings.
The registration fee will be $80.
Dr. J. Szelezsan, John von Neumann
Society for Computer Sciences.
Budapest, 5, P.O.B. 240, H-1368
Telephone: International +361 113850.

Design and Analysis of Heuristics

This is to announce a special issue
of Management Science devoted to the
Design and Analysis of Heuristics. We
welcome contributions, both in the form
of reviews and new results, on all aspects
of this theme, including: (1) design and
classification of heuristics; (2) theoretical
performance analysis (worst case or
probabilistic); (3) empirical performance
analysis (computational experiments and
case studies).
All submissions will be refereed
according to the usual procedure. They
should be sent before September 1,1985
to the Guest Editor for this issue:
Marshall L. Fisher
The Wharton School
University of Pennsylvania
Phildelphia, PA 19104
Prospective authors are encouraged
to discuss the nature of their contribu-
tions with the Guest Editor or with the
responsible Departmental Editor of Man-
agement Science:
(January- May 1985)
Alexander H.G. Rinnooy Kan
Department of Industrial Engi-
neering and Operations Research
University of California
Berkeley, CA 94720
-A.H.G. Rinnooy Kan

Cambridge Optimization Symposium
March 21 22, 1985

A symposium will be held at Cam-
bridge University on March 21 22, 1985,
on the development and theory of algo-
rithms for nonlinear optimization calcula-
tions. Papers will be presented on recent
research, and there will be ample oppor-
tunities for information discussions. The
speakers will include L.C.W. Dixon
(Hatfield Polytechnic), R. Fletcher
(University of Dundee), S-P. Han (Univer-
sity of Illinois), M.J.D. Powell (University
of Cambridge) and Ph. Toint (University
of Namur). Offers to present papers are
invited, and the meeting is open to all
who give notice that they wish to attend.

Please address correspondence to Profes-
sor M.J.D. Powell, DAMTP, Silver Street,
Cambridge CB3 9EW, who will be pleased
to provide further information. This
symposium is supported by the London
Mathematical Society.
-M.J.D. Powell

13th Symposium from page one

members are all organizers of previous
Symposia: E.M.L. Beale, R.W. Cottle,
J.-L. Goffin, M. Groetschel, A. Orden,
and A. Prekopa.) The Symposium is
expected to be self-supporting through its
registration fees and institutional sub-
sidies. The Society can lend 'seed money'
to the Symposium or, to a limited extent,
guarantee it against loss. The host may
organize Proceedings of the Symposium
as one or more Mathematical Program-
ming Studies. Proceedings were not
compiled for all Symposia.)
There are no fixed criteria for the
selection of a site. The more important
considerations are: technical qualification
and enthusiasm of the local staff;
adequacy of the meeting facilities; avail-
ability of nearby lodging; reasonable
travel and local costs -- in short, those
factors that will lead to a productive
conference that will appeal to a wide
range of participants.
We hope that several suggestions for
the Symposium site will have been made
well in advance of August, 1985 so that
the question can be settled at the Society
Council meetings to be held in Boston.
Interested parties should communicate
with the Chairman of the Advisory
Committee (Prof. Martin Groetschel,
Lehrstuhl fuer Angewandte Mathematik
II, Universitaet Augsburg, Memminger
Str. 6, D-8900 Augsberg, F.R.
GERMANY) or the undersigned as soon
as possible on this matter, as well as on
the possibility of holding other meetings
under the sponsorship of the Society in
intermediate years.
Professor Alex Orden
Chairman, Mathematical Programming
Graduate School of Business
University of Chicago
1101 E. 58th Street
Chicago, Ill. 60637, U.S.A.



Approval Voting
by S.J. Brams and P.C. Fishburn
Birkhluser, Basel

Approval voting is a method of voting that replaces the
familiar habit of the choice of one from among a set of possible
candidates with the choice of an "approved" subset of the
candidates. No preference among the approved subset is
expressed. The winners) is (are) the candidates) with the most
The idea is fascinating, has been studied axiomatically by
various scholars, notably Brams and Fishburn, and has been
forcefully advanced by many, in particular Brams, as a kind of
best voting system that should replace the plurality system that
is so prevelant today. Regrettably, the mathematical results are
not in themselves compelling as a support to that contention. On
the other hand, plausible arguments and reconstructions of past
elections do lend strong credence to the advantageous properties
of approval voting, and one can hope for further axiomatic results
that would provide a solid foundation for that claim.
The book itself is ..ri .. a collection of the papers of
Brams and Fishburn, including definitions and the statements of
theorems, but excluding proofs and including the plausible
arguments and reconstructions. Although a convenient source for
mathematical readers interested in the subject, the absence of
proofs is a serious hindrance. Nonmathematical readers will have
as much trouble with some of the book as with a mathematics
text because the definitions and theorems are stated in the usual
mathematical style to which we are all accustomed. With this
choice of quasi-mathematical presentation, the book disappoints
both the t iilculi.! ll. ill. trained reader and the nonmathe-
*,, i -ill trained. This is a pity, for the topic is important and the
book contains a wealth of interesting results and discussion.
The subject of approval voting has nothing directly to do
with mathematical programming or optimization.
M.L. Balinski

Generalized Concavity in Optimization and Economics
Edited by S. Schaible and W.T. Ziemba
Academic Press, London
ISBN 0-12-621120-5

This book consists of papers on two strongly-connected
topics of mathematical programming: generalized convexity and
fractional programming. Since 1949 numerous authors have
defined over 20 classes of generalized convex functions which
have a wide variety of applications. Therefore, the publica-
tion of a collection of papers about this topic is of great interest.
The published contributions are surveys of current knowl-
edge and describe new research results. The relations to the
theory of duality and to stochastic systems and applications in
management science and economics especially are considered.
The papers are divided into seven sections:
1. Characterizations of Generalized Concave Functions,
2. Generalized Concave Quadratic Functions and C2-Functions,
3. Duality for Generalized Concave Programs, 4. New Classes
of Generalized Concave Functions, 5. Fractional Programming,
6, Applications of Generalized Concavity in Management Science
and Economics, and 7. Applications to Stochastic Systems.
K.-H. Elster

Mathematical Programming
Edited by R.W. Cottle, M.L. Kelmanson and B. Korte
North-Holland, Amsterdam
ISBN 0-444-86821-6

There are 21 papers in this proceedings of the International
Congress on Mathematical Programming, Rio de Janeiro, Brazil,
April 6-8, 1981. They cover an impressive variety of topics:
linear programming, integer programming, graph theory, net-
works, matroids, .. Ir.li'll,, nonlinear programming, comple-
mentarity, complexity and functional analysis. The book contains
also Professor George B. Dantzig's personal memoire "Reminis-
cences about the Origins of Linear Programming." Most of the
papers are theoretical, including surveys with very complete lists
of references, but there are some applied articles. The quality of
the papers is good.
Practitioners may find some reports stimulating for their
own job, however, many of the theoretical papers require quite a
bit of mathematical knowledge, so this book will be mainly of
interest to researchers in the field of mathematical program-
ming and its periphery.
S. Walukiewicz

Microsolve/Operations Research: An Introduction
to Operations Research with Microcomputers
by P.A. Jensen
Holden Day, Inc.
ISBN 0-8162-4501-0

The book describes several codes on two included disks
which provide a motivating and illustrating supplement to an
introductory course on operations research. The book is written
mainly as a manual containing brief introductions to the con-
sidered problems and proposing a series of examples for applica-
tion of the codes. Some examples are included as data files on the
The program disk contains codes for linear programming,
network flow programming, 0-1 programming, dynamic program-
ming, queue simulation, birth-death processes and markov chains.
All codes run under the disk BASIC language of the IBM
personal computer with 64K of RAM memory, and at least one
disk drive using PC DOS 1.1. The choice of BASIC may be
questioned though motivated by its simplicity and widespread
availability. Nowadays, all standard computer languages are
available for micros and a more structured language, e.g.
PASCAL, may be preferred for university level teaching. The slow
performance of the BASIC interpreter causes no problem when
the programs are used for modeling purposes. For solving some of
the provided examples or user-supplied moderate-sized problems,
one should use compiled versions of the programs which run
faster by a factor up to 10. To enable compilation by the IBM
BASCOM compiler for most of the programs, only some minor
modifications were necessary.
For linear programming a nice model generator allows
easy input and modification of data. Such an interactive tool is
very helpful when teaching modeling in small groups or when
preparing examples for lectures. The LP-code implements the
bounded revised simplex method which may suffice on an intro-
ductory level and which can be used to illustrate numerical
difficulties. Interactive choice of pivot steps differing from the
-to page 6


proposed standard strategy is possible. Sensitivity analysis is
For network programming a helpful model generator is
provided too. From the computational point of view, the imple-
mented primal simplex method for solving quite general tranship-
ment problems is the most sophisticated code of the package.
In! i.Irin, i r ii.li, is closely oriented along the lines of the text-
book of Jensen and Barnes on network flow programming.
Without that book a user will hardly appreciate the details of the
iteration display (may be suppressed by user).
For 0-1 programming the additive method is implemented.
Data can be easily generated using the LP model generator.
Clearly, only small-sized problems may be solved.
For dynamic programming a rather general approach is
used. A main program implements the .it..rcrir general solution
techniques. For concrete .i'rl. Iti.-i.. the user must supply a set
of specific subroutines. Included are subroutines for knapsack
problems, special path problems, replacement problems, capacity
expansion problems, deterministic inventory problems, and linear
staged problems. The subroutines are quite simple and do not
support generating, modifying, or saving of user supplied data.
For small problems a nice graphical display illustrates the per-
formance of the chosen solution technique.
Methods for the analysis of some stochastic models are
implemented in the remaining three codes. A multichannel queue
with up to 5 servers is simulated and graphically displayed for
user supplied data describing the random structure of arrival and
service times. For general birth-death processes state probabil-
ities and statistical data can be calculated from arrival (birth) and
departure (death) data. For markov chains, the code again sup-
ports generating, modifying and saving of data. Simulation of
markov processes as well as calculation of transient states and
state probability vectors are implemented.
For introductory courses on operations research, in partic-
ular when modeling is emphasized, the use of the program pack-
age may be recommended for illustrative purposes or for prepar-
ing examples. Small courses and sufficient equipment with
micros are indispensable prerequisites for effective use in class.
-Dr. U. Zimmermann

Notes on Introductory Combinatorics
by G. Pblya, R.E. Tarjan and D.R. Woods
Birkhauser, Boston-Basel-Stuttgart
ISBN 0-8176-3123-2

In 1978, George Polya and Bob Tarjan taught an intro-
ductory course on combinatorics at Stanford University. Their
teaching assistant Donald Woods prepared the class notes that
resulted in this book. The first two-thirds of the course dealt
with enumerative combinatorics, including combinations and
permutations, generating functions, the principle of inclusion
and exclusion, SIrhlni numbers and P61ya's theory of counting.
The last third covered existential and algorithmic combinatorics,
including stable marriages, cardinality matching, network flow,
Hamiltonian and Eulerian paths, and planarity.
The book gives a broad sample from the entire area of
combinatorics on a very elementary level and in a very informal
way. I taught a course from it last year to undergraduates in an
area somewhere between business administration and computer
science. I enjoyed it and I look forward to using the book again
next year.

Still, there are some difficulties. These are due mainly to
the fact that the presentation is too sloppy and not well-
structured enough. I will give two specific examples. Either
I do not understand much about Ramsey theory, or most of the
eitherr' in Chapter 9 should disappear -- or both, of course. In
the chapter of P6lya's theory of counting, after 13 pages of
unmotivated computations of cycle indices, the main theorem is
stated without proof: "You can't eat mathematics, but you can
digest it. So let's chew on a few examples." I find this hard to
swallow. I do not object to the deletion of the proof, but what
may have worked at the blackboard does not work here in print
due to lack of motivation and structure. It is a charming little
book. To make it an outstanding little book, it needs one more
round of rewriting.
Finally, the typographical presentation is an insult to
prospective readers. The most disturbing aspect of such instances
of computerized typography is that we are being .,-,hr' *..,:d to
accept them.
-J.K. Lenstra

Computer Scheduling of Public Transport
by A. Wren
North-Holland, Amsterdam, 1981
ISBN 0-444-86170-x

The chapters are papers based on presentations at the
International Workshop at Leeds in 1980. A wide variety of
methods to solve bus and crew scheduling by computer is de-
Some general papers which survey the state of the art and
the experiences with implemented scheduling problems are
followed by the chapters containing more detailed information.
The two main problematic areas concerning bus and crew
scheduling have been subdivided further by the editor into
generation of times of bus trips, route-based construction of bus
schedules, network-based construction of bus schedules, bus
crew scheduling, formation of rotating rosters, and miscellaneous
papers. But many authors discuss more than one of these areas.
To solve the optimization problems the authors use heuris-
tic methods and mathematical methods, like mathematical
programming, which in theory would guarantee optimal solu-
tions. In some cases the solution can be found by interactive
The chapter including the glossary of terms is very useful
for understanding the papers.
-G. Gershner

Studies on Mathematical Programming
Edited by A. Prekopa
Akademiai Kiado, Budapest, 1980
ISBN 963-05-1854-6

This volume contains 15 papers presented at the Third
Conference on Mathematical Programming held at MatrafUred,
Hungary, in February 1975. The authors have summarized not
only their own results but also those of other researchers. There
are :..rnir!i.r..L to almost all parts of mathematical program-
ming, especially linear, nonlinear, discrete, parametric and sto-
chastic programming.
Because the conference took place almost 10 years ago, all
papers are no longer up to date. It is a pity that so much time
passed before publication of this material.
J. Piehler


Linear Optimization and Approximation
by K. Glashoff and S.-A. Gustafson
Applied Mathematical Sciences, Vol. 45
Springer-Verlag, Berlin
ISBM 3-540-90857-9

The authors of this book are well-known for their impor-
tant theoretical and practical contributions to the field of semi-
infinite programming. The book greatly differs in many respects
from other -.. i rIi' books on linear optimization and approxima-
tion. Its main message is that semi-infinite linear programming is
an extension of ordinary linear programming having the benefits
of allowing for a broader field of applications at the cost of only
il I,. additional work. This concept mainly influences the treat-
ment of duality theory which occupies a large part of the book,
For reasons of greater clarity the presentation mainly relies on
geometrical concepts. It is a characteristic feature of the book
that it makes no reference at all to the theory of convex poly-
hedra (neither the terms "polyhedren" or "Polytope" or even
"simplex" nor the names of Rockafellar or .Grunbaum occur in
the index). This is due to the semi-infinite nature of the presenta-
One chapter is devoted to weak duality including some
elementary observations on duality state diagrams and duality
gaps. It is shown how these rather simple results can be applied
in the theory of uniform approximation, In the following chapter
the strong lu lir; theorems are derived. It is a remarkable new
feature of semi-infinite programming as compared with ordinary
linear programming that duality gaps can occur. Strong duality
theory for semi-infinite programming provides conditions guaran-
teeing that these gaps cannot happen. It turns out that these
conditions are quite natural in requiring that the problem should
be formulated properly.
The algorithmic part of the book is completely devoted to
the simplex algorithm and its adaption to semi-infinite problems
and implementation on a computer. Specifically, the task of
"stable" implementation of the basic exchange step is treated in
greater detail. In contrast to most books on linear ::-...gr. 1r .ii .
no "simplex tableaux" are used in the text. These tableaux come
from those times when students in linear programming did their
exercises manually. They are rather misleading and obscure the
facts behind this concept. This part of the book demonstrates
clearly that the authors are numerical analysts having actual
numerical experiences. For solving the semi-infinite programming
problem an algorithm consisting of three phases is proposed. In
the first phase the infinite number of restrictions of the under-
lying problem is replaced by a finite subset (discretization ) and
the resulting ordinary linear programming problem is solved by
the ordinary simplex method. The optimal solution of the dis-
cretized problem yields structural information about the optimal
solution of the semi-infinite problem in that it provides a guess
for the number of dual variables which are nonnegative for
the latter. In the last phase a ii.:.-nl!n:.ir system of equations is
derived from the owrij.lil:,. conditions by means of this struc-
tural information. This system is solved numerically using New-
ton's method. In numerous applications which were published by
the authors in different articles, this approach turned out to be
extremely i t!!,. it r especially for r,,riI-ri..... ll, sensitive problems,
as they are quite common in mathematical ,a.'pli-'i.-!., of semi-
infinite programming.
A special mathematical application is treated in the chapter
on approximation by Chebychev systems. Of great practical

importance for numerical approximation, the structure of the
optimal solution is known in advance.This simplifies greatly the
numerical algorithm.
In the last chapter some applications are presented. These
cover the topics of optimal control with distributed parameters,
operator equations of monotonic type, and air pollution abate-
ment problems.
The book is written for mathematicians. Therefore, the
presentation is mathematically rigorous. The problems treated
are from rather mathematical applications and are influenced
greatly by approximation problems. Nevertheless, the presenta-
tion is made as simple as possible by using a clear and didactic
approach. Many exercises and worked-out examples facilitate the
application of the results.
The book can be recommended as a textbook for students
of mathematics and for all mathematicians interested in this
-U. Eckhardt

Combinatorial Methods of Discrete Programming
by L.B. Kovics
Akademiai Kiad6, Budapest, 1980
ISBN 963-05-2004-4

This is partly a textbook and partly a monograph. The first
chapter is an introduction to the models and problems of integer
programming, and the chapters that follow discuss several types
of algorithms: Implicit enumeration, branch-and-bound and dy-
namic programming. Later chapters give some of the author's new
results with respect to further development of existing algo-
rithms, new procedures, heuristic methods, combinations of
different algorithms and some theoretical research. Because of
the combinatorial character of the book, cutting plane methods
are not included. The last chapter gives a survey on recent direc-
tions in discrete programming with extensive references to
the :!..!.irur. from 1974 to 1979. The book does not contain
any results in c. .iuii?..it in.il complexity even though this topic
is one of the most important developments of recent years in
discrete programming. For this the reader must be referred to
other books.
Nevertheless, this is a useful book for those who want to
acquaint themselves with this part of mathematical programming,
Specialists too will get some valuable suggestions and new ideas.
-J. Piehler

Handbook of Mathematical Economics
Volume 1, 1981; Volume 2, 1982
Edited by K.J. Arrow and M.D. Intriligator
North-Holland, Amsterdam
ISBN 0444-06054-1

The Handbook appears as the first book in the series of
handbooks in economics, the aim of-which is to provide compre-
hensive and self-contained surveys of the current state of various
branches of economics. The Handbook surveys, as of the late
1970's, the state of the art of mathematical economics. It in-
cludes 29 chapters arranged into five parts and published in
three volumes.
Volume 1 coincides with Part 1, which treats Mathematical
Methods in Economics, preceded by a brief historical introduc-
tion. Volume 2 comprises Part 2 elaborating on Mathematical
-to page 8


Approaches to Microeconomic Theory and Part 3 dealing with
Mathematical Approaches to Competitive Equilibrium. Volume
3, which is to appear, contains the remaining two parts which
cover Mathematical Approaches to Welfare Economics and
Mathematical Approaches to Economic Organization and Plan-
Though each of the chapters can be read independently,
the Handbook can assist researchers and students working in one
branch of mathematical economics to become acquainted with
other branches of the field. Most of the topics presented are
treated at an advanced level suitable for use by researchers or
by advanced graduate students in both economics and mathe-
-M. Valch

Chemical Applications of Topology and Graph Theory
Studies in Physical and Theoretical Chemistry 28
Edited by R.B. King
North-Holland, Amsterdam

Every graph theorist knows that there are some applications
of graph theory to chemistry. To see how many there are and to
appreciate the variety of applications of numerous branches of
graph theory (and topology and geometry) to chemistry, he

should read this collection of papers. To give a glimpse of the
type of applications that are discussed, I would like to men-
tion the following paper titles and catchwords: symmetry and
spectra of graphs and their chemical applications, chemical
interpretation of graph theoretical indices, global dynamics of a
class of reaction networks, the use of Riemannian surfaces in the
graph-theoretical representation of M'bius systems, the auto-
morphism groups of some chemical graphs.
It seems to me that the contacts between graph theorists
and chemists have not been too close in the past. Graph theoretic
concepts well-known in graph theory have been reinvented by
chemists, and vice versa, again and again. Parameters of interest
for chemists have been neglected by graph theorists and these -
in turn often have not been able to "sell" new theories and
results which have potential applications in chemistry to the
chemists. A paper collection ( and a symposium) of this type is
valuable in many respects. It gives chemists the chance to intro-
duce their models to graph theorists and to obtain help from the
specialists in this field. Such cooperation may result in better
chemical models, and furthermore, additional insights may
be obtained by treating the models with other (or better or new)
methods of graph theory. For the graph theorists such a book
provides a good opportunity to get into closer contact with
important real-world applications and possibly a stimulus for
further research in application-oriented areas of graph theory.
-M. Gr'otschel


Vol. 30, No. 3

P.O. Lindberg and S. Olafsson, "On the Length of Simplex
Paths: The Assignment Case."
D. de Werra, "A Decomposition Property of Polyhedra."
R. Fletcher and S.PJ. Matthews, "Stable Modification of
Explicit LU Factors for Simplex Updates. "
R. de Leone, M. Gaudioso and L. Grippo,"Stopping Criteria
for Linesearch Methods without Derivatives. "
Y. Yamamoto, "A Variable Dimension Fixed Point Algo-
rithm and the Orientation of Simplices. "
J.A. Filar, "On Stationary Equilibria of a Single-Controller
Stochastic Game."
R. Chandrasekaran and A. Tamir, "Optimization Problems
with Algebraic Solutions: Quadratic Fractional Programs and
Ratio Games."
E. Rosenberg, "Exact Penalty Functions and Stability in
Locally Lipschitz Programming."
M. Bastian, "Implicit Representation of Generalized Vari-
able Upper Bounds Using the Elimination Form of the Inverse on
Secondary Storage. "

Vol. 31, No. 1

G.B. Dantzig, A.J. Hoffman, and T.C. Hu, "Triangulations
(Tilings) and Certain Block Triangular Matrices. "
G.G.L. Meyer, "Convergence Properties of Relaxation
S.Sen and H.D. Sherali, "On the Convergence of Cutting
Plane Algorithms for a Class of Nonconvex Mathematical Pro-
grams. "

P.C. Jones, R. Saigal, and M. Schneider, "Computing
Nonlinear Network Equilibria. "
S.Agarwal, A.K. Mittal, and P. Sharma, "A Decomposition
Algorithm for Linear Relaxation of the Weighted r-covering
Problem "
B. Gavish and H. Pirkul, "Efficient Algorithms for Solving
Multi-Constraint Zero-One Knapsack Problems to Optimality."
R. Saigal and R.E. Stone, "Proper, Reflecting and Absorb-
ing Facets of Complementary Cones."

Vol. 31, No. 2

M.J. Todd, 'Fat' Triangulations, or Solving Certain Non-
convex Matrix Optimization Problems. "
T.R. Jefferson and C.H. Scott, Quadratic Geometric Pro-
gramming with Application to Machining Economics. "
A. Drud, "CONOPT: A GRG Code for Large Sparse
Dynamic Nonlinear Optimization Problems. "
D.J. White, "Vector Maximisation and Largrange Multi-
J.-S. Pang, "Asymmetric Variational Inequality Problems
Over Product Sets: Applications and Iterative Methods. "
Y. Yuan, "Conditions for Convergence of Trust Region
Algorithms for Nonsmooth Optimization."
M.C. Chang, "Generalized Theorems for Permanent Basic
and Non-Basic Variables."
M. Kojima, S. Oishi, Y. Sumi, and K. Horiuchi, "A PL
Homotopy Continuation Method with the Use of an Odd Map
for the Artificial Level."


Technical Reports & Working Papers

University of Maryland
College of Business and Management
College Park, Maryland 20742

Golden and Skiscim, "Using Simulated Annealing to Solve
Routing and Location Problems, 84-001.
Or, "A Heuristic Solution Procedure for the Inventory
Routing Problem," 84-005.
Wasil, "Evaluating the Performance of Alternative Solution
Methods for Combinatorial Optimization and Other Decision
Problems," 84-006.
Gheysens, Golden and Assad, "A Comparison of Tech-
niques for Solving the Fleet Size and Mix Vehicle Routing Prob-
lem, "84-007.
Wasil, Golden and Assad, "Comparing Heuristic Methods on
the Basis of Accuracy," 84-008.
Vohra and Washington, "Counting Spanning Trees in a
Graph of Kleitman and Golden and its Generalization," 84-009.
Ball, "An Overview of the Computational Complexity of
Network Reliability Analysis, 84-010.
Dahl, Greenberg, Sanborn, Skiscim, Ball and Bodin, "A
Relational Database Approach to Vehicle and Crew Scheduling in
Urban Mass Transit Systems, 84-011.
Golden, Assad and Dahl, "Analysis of a Large-Scale Vehicle
Routing Problem with an Inventory Component," 84-015.
Pearn, "The Capacitated Chinese Postman Problem,"
Golden and Stewart, "The Empirical Analysis of TSP
Heuristics," 84-017.
Deif and Bodin, "Extension of the Clarke and Wright
Algorithm for Solving the Vehicle Routing Problem with Back-
hauling, 84-020.
Golden, Levy and Skiscim, "Using Seed Points to Help
Solve Vehicle Routing Problems, "84-021.
Nag and Dahl, "The Effect of Cost Calculations of Stock-
outs on the Inventory Routing Problem," 84-022.
Hevner, Wu and Yao, "Query Optimization on Local Area
Networks," 84-029.
Gheysens, Golden and Assad, "The Fleet Size and Mix
Vehicle Routing Problem: A New Heuristic, 84-030.
Jarvis, Shier, Bodin and Golden, "NETPAC: A Computer-
ized System for Network Analysis, 84-031.

Georgia Institute of Technology
School of Industrial and Systems Engineering (ISyE)
Production Distribution Research Center in ISyE (PDRC)
College of Management (COM)
School of Mathematics (Math)
School of Information and Computer Science (ICS)
Atlanta, GA 30332

E. Allender and M. Klawe, "Improved Lower Bounds for
the Cycle Detection Problem," ICS, series RJ4078(45456).
J. J. Bartholdi, III and L.K. Platzman, "Heuristics Based on
Spacefilling Curves for Combinatorial Problems in the Plane,"
ISyE, series PRDC 84-08.
K.-J. Chung and M.J. Sobel, "Linear Programming Solu-
tions of the Truncated Moment Problem, COM.
M. Goetschalckx and H.D. Ratliff, "Shared Versus Dedi-
cated Storage Policies, "ISyE, series PRDC 83-08.
M. Goetscholckx and H.D. Ratliff, "Order Picking in a
Single Aisle, ISyE, series PRDC 83-10.

J.J. Jarvis and 0. Kirca, "Pick-up and Delivery Problem:
Models and Single Vehicle Exact Solution," ISyE, series PRDC
R.G. Jeroslow, "Representability in Mixed Integer Pro-
i- *. -. I: Characterization Results, "COM.
R.G. Jeroslow, "Representability in Mixed Integer Program-
ming, II: A Lattice of Relaxations, "COM.
R.G. Jeroslow, "Representability of Functions," COM.
E.Z. Prisman, "A Unified Approach to Term Structure
Estimation, "COM, series MS-84-8.
E.Z. Prisman, "Immunization as a MaxMin Strategy,"
COM, series MS-84-3.
E.Z. Prisman and U. Passy, "Saddle Function and MinMax
Problems the Quasi Convex Quasi Concave Case," COM, ISyE
and the Technion, series MS-84-5.
E.Z. Prisman and U. Passy, "A Convex Like Duality
Scheme for Quasi Convex Programming," COM, ISyE, and the
Technion, series MS-84-4.
E.Z. Prisman and U. Passy, "Secant Relations vs. Positive
Definiteness in Quasi Newton Methods," COM, ISye, and the
Technion, MS-83-4.
M. Richey, R.G. Parker, and R.L. Rardin, "An Efficiently
Solvable Case of the Minimum Weight Equivalent Subgraph
Pro blem, ISyE and Purdue.
M. Richey, R. G. Parker, and R.L. Rardin, "On Finding
Spanning Eulerian Subgraphs, ISyE and Purdue.
J. Muller and J. Spinrad, "On Line Modular Decomposi-
tion, "ICS, series GIT-ICS-84/11.
R.L. Rardin and R.G. Parker, "On Producing a Hamilton-
ian Cycle in the Square of a Bidirected Graph: An Algorithm
and Its Use, ISyE and Purdue.
R.L. Rardin and R.G. Parker, "Tree Subgraph Isomorph-
ism is NP-Complete on Series-Parallel Graph," ISyE and Purdue.
M. Richey and R.G. Parker, "Some Hard Problems Defined
on Series-Parallel Graphs, ISyE.
M.J. Sobel, "Mean-Variance T' .:. .- in an Undiscounted
J.E. Spingarn, "A Projection Method for Least Square
Solutions to Overdetermined Systems of Linear Inequalities,"
J. Spinrad, "Generalized Topological Sort and Dynamic
Cycle Detection, ICS, series GIT-ICS-84/10.
R.W. Taylor and C.M. Shetty, "Solving Transportation
Problems via Aggregation, ISyE, series PDRC 84-10.

University of Wisconsin
610 Walnut Street
Madison, Wisconsin 53705

A. Eydeland, "Globally Convergent Procedures for Solving
Nonlinear Minimization Problems, No. 2699.
W.E. Ferguson, Jr., "The Rate of Convergence of a Class of
Block Jacobi Schemes," No. 2716.
O.L. Mangasarian, "Some Applications of Penalty Func-
tions in Mathematical Programming, No. 2720.
K. Ritter, "A Dual Quadratic P' .. '..,.. Algorithm,"
No. 2733.
L. McLinden, "Stable Monotone Variational Inequalities, "
T.-H. Shiau, "An Iterative Scheme for Linear Comple-
mentarity Problems, "No. 2737. -to page 10

Technical Reports & Working Papers

Cornell University
School of Operations Research
Industrial Engineering
Upson Hall
Ithaca, New York 14853

A. Tamhane and R. Bechhofer, "A Survey of Literature on
Estimation Methods for Quantal Response Curves with a View
Toward Applying Them to the Problem of Selecting the Curve
with the Smallest q-Quan tile (ED100q), "TR 614.
R. Bechhofer and R. Kulkarni, "Closed Sequential Proce-
dures for Selecting the Multinomial Events Which Have the
Largest Probabilities, "TR 615.
P. Jackson, J. Muckstadt and L. Schrage, "Two-Period,
Two-Echelon Newsboy Problem, "TR 616.
M.J. Todd, "Modifying the Forrest-Tomlin and Saunders
Updates for Linear Programming Problems with Variable Upper
Bounds," TR 617.
T. McConnell and M. Taqqu, "Double Integration with
Respect to Symmetric Stable Processes," TR 618.
E. Slud, "Clipped Gaussian Processes Are Never M-Step
Markov, TR 619.
W. Lucas, "The Banzhaf Power Index, Tr. 620.
E. Slud, "Generalizations of the Basic Renewal Theorem
for Dependent Variables, "TR 621.
F. Avram and M. Taqqu, "Symmetric Polynomials of
Random Variables Attracted to an Infinitely Divisible Law,"
TR 622.
B. Turnbull and C. Jennison, "Repeated Confidence Inter-
vals for the Median Survival Time, TR 623.
P. Jackson, W. Maxwell and J. Muckstadt, "Determining
Optimal Reorder Intervals in Capacitated Production-Distribution
Systems, "TR 624.
R. Bechhofer, "An Optimal Sequential-Procedure for
Selecting the Best Bernoulli Process, "TR 625.

B. Burrell and M.J. Todd, "The Ellipsoid Method Generates
Dual Variables, "TR 626.
E. Slud, "Nonlinear Scaling of Sample Maxima," TR 627.
N. Erkip, "A Restricted Class of Allocation Policies in a
Two-Echelon Inventory System," TR 628.
R. Rushmeier, J. Muckstadt and P. Jackson, "A Distribu-
tion System Policy Simulator, "TR 629.
M.S. Taqqu, "Sojourn in an Elliptical Domain," TR 630.
W. Morris and MJ. Todd, "Symmetry and Positive Definite-
ness in Oriented Matroids, "TR 631.

Universitat Zu Koln
Mathematisches Institut
Preprints in Optimization
Weyertal 86-90
D-5000 Koln 41

A. Bachem and W. Kern, "Adjoints of Oriented Matroids,"
WP 84.1.
A. Bachem and R. Euler, "Recent Trends in Combinatorial
Optimization, "WP 84.2.
U. Zimmerman, "Sharing Problems, WP 84.3.
R. Euler, R.E. Burkard and R. Grommes, "On Latin
Squares and the Facial Structure of Related Problems," WP 84.4.
A. Bachem and W. Kern, "The Extension Lattice of Ori-
ented Matroids, WP 84.5.
A. Bachem and R. Kannan, "Lattices and the Basic Reduc-
tion Algorithm, WP 84.6.
S. Schubert and U. Zimmerman, "Nonlinear One Para-
metric Bo ttleneck Linear Problem," WP 84.8.
A. Bachem, "Optimization and Geometry in Discrete
Structures, "WP 84.9.
U. Zimmermann, "Submodulare Flusse: Verfahren zur
Minimerung Linearer Zielfunktionen, "WP 84.10.

Application for membership

c/o International Statistical Institute
428 Prinses Beatrixlaan
2270 AZ Voorburg, The Netherlands

Cheques or money orders should be made payable to The Mathe-
matical Programming Society, Inc. in one of the currencies
indicated below.
My subscriptions) is (are) for my personal use and not for the
benefit of any library or other institution.

[] I wish to enroll as a member of the Society. My dues payment
for 1985 which covers subscription to volumes 31-33 of
MATHEMATICAL PROGRAMMING is enclosed: Dfl. 100.00
(or $35.00 or 22.00 or Sw.Fr. 72.00 or FF 270.00 or DM

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Student Applications: Dues are one-half the above rates. Have a faculty member verify your student status below and send
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This Calendar lists noncommercial meetings specializing in mathematical programming or one of its
subfields in the general area of optimization and applications, whether or not the Society is involved.
(The meetings are not necessarily 'open'.) Any one knowing of a meeting that should be listed here is
urged to inform Dr. Philip Wolfe, JBM Research 33-2, POB 218, Yorktown Heights, NY 10598, U.S.A;
Telephone 914-945-1642, Telex 137456.
Some of these meetings are sponsored by the Society as part of its world-wide support of activity
in mathematical programming. Under certain guidelines the Society can offer publicity, mailing lists and
labels, and the loan of money to the organizers of a qualified meeting.
Substantial portions of meetings of other societies such as SIAM, TIMS, and the many national OR
societies are devoted to mathematical programming, and their schedules should be consulted.


May 6-10: Journ6es Fermat: "Mathematiques pour l'optimisation", Toulouse, France. Contact: Prof.
J.B. Hiriart-Urruty, Laboratoire d'Analyse Num6rique, Universit6 Paul Sabatier, 118, Route de
Narbonne, 31062 Toulouse Cedex, France. Telephone (61) 55-66-11.

June 11-14: 5th IFAC Workshop on Control Applications of Nonlinear Programming and Optimization,
Capri, Italy. Contact: Professor G. Di Pillo, Dipartimento di Informatica e Sistemistica,
University degli Studi di Roma 'La Sapienza', Via Eudossiana 18, 00184 Roma, Italy. Tele-
phone (39) 6-484441.

August 5-9: Twelfth International Symposium on Mathematical Programming in Cambridge, Massachu-
setts, U.S.A. Contact: Professor Jeremy Shapiro, Sloan School of Management, Massachusetts
Institute of Technology, Cambridge, MA 02139, U.S.A. Telephone 617-253-7165. Official
triennial meeting of the NIPS.


Farewell at Bad Windsheim Participants at the NATO ASI on Computational Mathematical Programming enjoy
a barrel of beer at the farewell party. The conference was held July 23 to August 2, 1984 at Bad Windsheim,
Germany F.R. Left to right: Y.Yuan, J. Burke, R. Wets, B. Milli (background), D. Kraft and P. Gill.
Photo by A. Idnani.

Gallimaufry TIM

Narendra Karmarkar (AT&T Bell Laboratories) delivered a special ii ATHEMAICAL ROGRAMMING SOCIMNEWSLUTER
plenary seminar on his new linear programming method at the ORSA/ Donald W. Earn, Editor
TIMS Dallas meeting in November. The session was attended by over Achim Bachem,Associate Editor
1000 and received considerable coverage by the Dallas press and TV.... Published by the Mathematical Program-
Michael Ball (Maryland) is visiting the Departments of Combinatorics ming Society and Publication Services of
and Optimization and Management Sciences at the University of Water- the College of Engineering, University of
loo during the 1984-85 academic year. .. .George L. Nemhauser will be a Florida. Composition by Lessie McKoy,
visiting professor at Georgia Tech during the 1985-86 academic year. .. Graphics by Lise Drake.
The Committee on Algorithms has initiated a system to match traveling
lecturers with institutions interested in inviting speakers. The system Books for review should be sent to
covers the entire world. It is being computerized by Ashok Idnani, the Book Review Editor, Prof. Dr.
Computer Science Department, Pace University, Pleasantville, New Achim Bachem, Mathematiches
York 10570. He may be contacted for further information. . .The Institute der Universitdt zu K61n,
Sixth Mathematical Programming Symposium, Japan will be held in Weyertal 86-90, D-5000 Ktiln,
Tokyo November 7-8, 1985. Contact Masao Iri, Faculty of Engineering, W. Germany.
University of Tokyo, Bunko-Ku, Tokyo 113 or Hiroshi Konno, Tokyo
Institute of Technology, Meguro-Ku, Tokyo 152. Journal contents are subject to
Deadline for the next OPTIMA is May 1, 1985. change by the publisher.

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