MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
The Special Interest Group in Optimization (SIGOPT, i.e.
Fachgruppe Optimierung in German) has been created
under the auspices of the Deutsche Mathematiker
Vereinigung (DMV) with the purpose of encouraging
cooperation amongst its members, and of facilitating com-
munication between them. This call for membership is
directed to all those interested in mathematical optimiza-
tion, both in theory and practice. PAGE TWO iN
The newly founded Fachgruppe
Optimierung of the Deutsche
(DMV), known in English as
the Special Interest Group in
Optimization (SIGOPT), intends
to intensify communication
among its members. For this
purpose, SIGOPT has established
opt-net. This forum, however, is
not limited to SIGOPT, but is
open to all scientists and students
of mathematics, computer science,
economics, electrical engineering
etc. who are interested in optimi-
zation or who want to obtain
relevant information. PAGE TWO 0
PAd 2 N0 40 JULY 1993
SIGOPT provides a forum for
discussing actual and future de-
velopments in a broad variety of
disciplines associated with opti-
mization and actively supports
interdisciplinary research and
applications to industry. Mem-
bership is encouraged, particu-
larly for those who already are
members of societies such as
AMS, DMV, GAMM, GMOOR,
SIAM, as well as anyone else in-
terested in optimization. In par-
ticular, SIGOPT encourages stu-
dents and younger scientists to
become involved in research in
optimization. To cover adminis-
trative costs, members may be
asked for a small financial con-
The annual Mathematical Opti-
mization Conference is orga-
nized by its members, the first
of which will be held at Vitte/
Hiddensee in Germany in Sep-
tember 1993. In the following
three years, the conference will
be part of larger conferences: in
Berlin, as part of OR '94, orga-
nized jointly with GMOOR,
DGOR, SVOR, OGOR; in Ulm,
under the sponsorship of DMV;
and the year after under the
sponsorship of GAMM. Further
workshops will be held on spe-
cial aspects of mathematical
Opt-net Founded to Increase Communication
To facilitate communication
among members of the optimi-
zation community, the electronic
forum, opt-net, has been in-
stalled at the Konrad-Zuse-
Zentrum in Berlin (ZIB). The
main purpose of opt-net is to
provide an efficient means of
communication among its par-
ticipants. Each member of opt-
net has a unique e-mail identifi-
cation at ZIB. To receive e-mail
at a new address anywhere in
the world, the user merely sends
an e-mail message to ZIB and all
mail will be redirected to the
new address. Members also may
receive a weekly electronic di-
gest, and will be able to use a
number of other facilities.
Access to opt-net is possible
using Internet and all academic
post office networks. (For more
information on opt-net, please
see the accompanying article.)
H. TI- JONGEN
HUMBOLDT UNIVERSITY BERLIN
Opt-net has properties that you have
,I 1,1, .1. i r1. I 1 .I 1 ,J1 1'" 0 ..I' ,! l
For instance, you can search for col-
leagues who share the same interests,
have your e-mail messages for-
warded, send conference announce-
ments conveniently, give informa-
tion on papers etc.
Among other aspects, opt-net in-
* a moderated forum for discussion
(called digest) that distributes con-
tributions through a mailing list to
which you can -, b-.':. 1..
e ,,[ i-t' . .. "I L -'.i "->-r ",
a .' i, i' -. vice with "whois"
and other search facilities,
a key for an interactive access to
ZIB's electronic library, eLib, and
anopt-netarchivewiil.,i i I".. iilt
various search facilities.
Every -,b-..t .. r to opt-net has the
possibility to use the following facili-
ties actively or passively via
ZIB's eLib for mathematical software:
dialogue access to NetLib and the
Reduce NetworkLibrary (RedLib),
which has a comprehensive collec-
tion of mathematical software;
distribution service for documents
(PostScript, TeX), programs
(sources, binaries), data and re-
* automatic announcement of contri-
butions in Internet and USENET
(Archie, WAIS, IMP); and
* access to information from Internet
(Telnet, mail, ftp) and all scientific
and postal networks (via WIN,
To receive in-depth information on
opt-netjust send the following three
1,t- l-i .. lt i -t I1 -II i i 'I
,l- ,t [ ,, ,, .. lt i. i ,i I t l)e
Your message need not include any
text. The opt-net server will read your
e-mail address and the "Subject" line
'I I t I, 11 ., il -, In you the document
requested. "Help" gives you some
initial information on the functioning
of opt-net. "Story" explains what can
be done withopt-netby telling a story
and "Manual" is a compact and com-
plete reference manual containing
descriptions of all functions and com-
mands used in opt-net.
opt-net is free of
also can be used
by persons who are
not members of tlK
These three documents give you in-
formation on all services offered by
opt-net; particularly on how to reg-
ister with opt-net, how to obtain the
digest, how to send in contributions
and, of course, how to become a
member of the Fachgruppe
Optimierung of the DMV. Opt-net
will experience continuous develop-
ment if there is sufficient demand;
your proposals can contribute to this.
Above all, opt-net is intended to en-
able a convenient and efficient ex-
change of information. Which topics
of discussion and what kinds of infor-
mation will dominate opt-net in the
future remains to be seen. This will
depend on the subscribers to the net
and on the development of their in-
terests and demands. Please send
your opt-netc. ili i..iii 1., n, ..I
tn the fnllnwine addroeS' opt-
II ,.-... .n ,-I ,, ,, lh. 1 i .. .. iI . 1 i tl.,
tl,,_,._,.it,_lst-.,I ,.l t.In~trlbhl Il.=1 111
should begin with the sender's name.
The text of the contribution can be of
any shape and in principle of
any contents. If the text is of math-
ematical contents it should start with
the "Mathematics Subject
( i..--itt..ti.. i,"(M SC1991)ofitscon-
tents that Zentralblatt fuer
.! -i 1". i. I,1. and Mathematical Re-
views have agreed to use, e.g. pri-
mary: 90C05, 90C06; secondary:
All. r, il 1.1. however, will be
examined by a moderator. The mod-
erator may reject contributions sent in
if they seem to be inadequate or of
little value for the opt-net commu-
nity. The moderator of opt-netisUwe
Zimmerman (TUBraunschweig). His
e-mail address is ('op1- ,':.,'-
i I I ll, ...-. 1 't -1 0il l ,. 1 ir. -
and the Fachgruppe Optimierung of
the DMV wants to share this facility
with interested colleagues from other
Participation in opt-net is free of
charge. Opt-net also can be used by
persons who are not members of the
DMV-Fachgruppe Optimierung or of
With the creation of opt-net, a tool has
been made available that makes use
of today's technical potential and will
help its users to pursue their math-
ematical interests more efficiently.
However, opt-net cannot live with-
out members. First of all, opt-net
needs some members to start work-
ing. It takes up its technical service
today, and its inner life is to com-
mence soon. Just try and register with
opt-net; maybe you II Ih! it. A net-
work can, of course, never be better
than its members.
- M. GROETSCHEL, PRESIDENT OF THE
DMV AND VICE PRESIDENT OF ZIB
: _. :.__ N,
._~ ,....... .-. I .;.....
Call for Nominations for
Prize for Excellence in
This award is dedicated to the
memory of Martin Beale and Wil-
liam Orchard-Hays, pioneers in
computational mathematical pro-
gramming. The prize is awarded
every three years. The 1994 prize of
$1,500 and an award certificate will
be presented in August 1994, at the
University of Michigan, during the
Awards Session of the Interna-
tional Symposium on Mathemati-
cal Programming, sponsored by
the Mathematical Programming
Society. To be eligible, a paper or a
book must meet the following re-
1 It must be on computational
mathematical programming. The
topics to be considered include:
*experimental evaluations of one or
more mathematical algorithms,
*the development of quality math-
ematical programming software
of obtaining solutions to some im-
portant class of MP problems)
coupled with documentation of the
applications of the software to this
class of problem (note: the award
would be presented for the paper
which describes this work and not
for the software itself),
*the development of a new compu-
tational method that improves the
state-of-the-art in computer imple-
mentations of MP algorithms
coupled with documentation of the
experiment which showed the im-
*the development of new methods
for empirical testing of mathemati-
cal programming techniques (e.g.
development of a new design for
computational experiments, identi-
fication of new performance mea-
sures or methods for reducing the
cost of empirical testing).
2 It must have appeared in the open
3 If the paper or book is written in
a language other than English, then
an English translation also must be
4 Papers eligible for the 1994 award
must have been published within
the years 1990-93.
These requirements are intended as
guidelines to the screening commit-
tee, but are not to be viewed as bind-
ing when work of exceptional merit
comes close to satisfying them.
Nominations will be judged on the Call for Nominations for
following criteria: magnitude of the the George B. Dantzig
contribution to the advancement of Prize
computational and experimental
mathematical I,_ ... ,r,;,_ origi- Nominations are solicited for the
nalityof ideasandmethods;andclar- George B. Dantzig Prize, adminis-
ity and excellence of exposition. tered jointly by the Mathematical
Nominations must be in writing and Programming Society (MPS) and
include the titles) of the papers) or the Society for Industrial and Ap-
book, the authorss, the place and plied Mathematics (SIAM). This
date or publication and four copies of prize is awarded to one or more
prize is awarded to one or more
the material. Supporting justification individual s for original research
individual s for original research
and any supplementary materials are
which, by virtue of its originality,
welcome, but not mandatory. The o
awards committee reserves the right breadth and de is a ma-
to request further supporting mate- jorimpact on the field of mathemati-
rials from the nominees. cal programming. The contributions
Nominations should be mailed to: eligible for consideration must be
Professor Laurence A. Wolsey publicly available and may address
Professor Laurence A. Wolsey
CORE any aspect of mathematical pro-
34 Voie du Roman Pays gramming in its broadest sense.
B-1348 Louvain-la-Neuve Strong preference is given to contri-
Belgium butions by individuals under 50
The deadline for submission of years of age.
yearsnominations is Jan. 1,1994age.
nominations is Jan. 1, 1994.
............. ........ .. ..
To be awarded at the XVth International Symposium on Mathematical Programming to be held in Ann Arbor, \ l, U.S.A., Aug. 15-19,1994.
The prize will be presented at the
symposium. Past Dantzig Prize re-
cipients have been: M.J.D. Powell
and R.T. Rockafellar in 1982, E.L.
J .1,!,-..i.,,....' I .Padberginl985,
M.J. Todd in 1988, andM. Gr6etschel
and A.S. Nemirovsky in 1991.
The prize committee members are:
Michael J. Todd, Chairman; Martin
Groetschel; Ellis L. Johnson and R.
Tyrrell ik ..-. I!, II 1
Please send nominations to Michael
J. Todd, School of Operations Re-
search & Industrial Engineering, 206
Engineering & Theory Center Build-
ing, Cornell University, Ithaca, NY
14853-3801, U.S.A., or by e-mail to
tions are due by Sept. 30,1993, and
should provide a brief one- or two-
page description of the nominee's
outstanding contributions, and, if
a list of the nominee's publications.
a list of the nominee's publications.
Call for nominations for
the D. Ray Fulkerson
Prize in discrete
The specifications for the
Fulkerson Prize read:
"Papers to be eligible for the
Fulkerson Prize should have been
published in a recognized journal
, il,, - ., .1. 1,, i . ., I
ing the year of the Congress. The
extended period is in recognition of
the fact that the value of fundamen-
tal work cannot always be immedi-
ately assessed. The prizes will be
given for single papers, not a series
of papers or books, and, in the event
of joint authorship, the prize will be
The term "discrete mathematics" is
intended to include graph i ,.. -,.
networks, mathematical program-
ming, applied combinatorics and
related subjects. While research work
in these areas usually is not far re-
moved from practical applications,
the judging ofpapers will be based on
.. ,,t. il1'. ,..; ;. , ,,; ii a and sig-
The nominations for the award will
be presented by the Fulkerson Prize
Committee (Alexander Schrijver,
C I i i,,n 11.Ii j I l..t m ,1 ,i i,.ll' /a
Tardos) to the Mathematical Pro-
gramming Society and the American
Please send your nominations by
Jan. 15, 1994, to:
1098 SJ Amsterdam,
Announcement by the
Programming Society of
the A.W. Tucker Prize
The Mathematical Program-
ming Society invites nomina-
tions for the A.W. Tucker Prize
for an outstanding paper
authored by a student. The award
will be presented at the symposium.
All students, graduate and under-
graduate, are I.d.'1. Nominations
of students who have not yet received
their first university degree are espe-
cially welcome. In advance of the
Symposium, an award committee
will screen the nominations and se-
lect at most three finalists. The final-
ists will be invited, but not required,
to give oral presentations at a special
session of the Symposium. The
award committee will select the win-
ner and present the award prior to the
conclusion of the Symposium. The
members of the committee for the
1994 A.W. Tucker Prize are: Thomas
M. Liebling, Swiss Federal Institute of
Technology, Lausanne; Andrew R.
Conn, Thomas J. Watson Research
Center, Yorktown Heights; William
H. Cunningham, University of Wa-
terloo; Clovis Gonzaga, COPPE, Fed-
eral University of Rio de Janeiro; and
Jean-Philippe Vial, University of
Eligible papers may concern any as-
pect of mathematical programming;
they may be original research, an
exposition or survey, a report on com-
puter routines and computer experi-
ments, or a presentation of a new and
interesting application. The paper
must be solely authored, and com-
pleted after January 1991. The paper
and the work on which it is based
should have been undertaken and
completed in conjunction with a de-
Nominations must be madein writ-
ing to the chairman of the awards
Thomas M. Liebling
Swiss Federal Institute of Technology
Department of Mathematics
by a faculty member at the institution
a degree when the paper was com-
pleted. Lettersof nomination must be
accompanied by four copies each of:
the student's paper; a separate sum-
mary of the paper's contributions,
written by the nominee and not more
than two pages in length; and a brief
biographical sketch of the nominee.
Nominations must be sent to the
chairman no later than Dec. 31,1993.
(Postmark on letter recommended.)
5AG1 1 N 40' J II;II93
Vol. 58, No. 3
E. Balas, S. Ceria and G.
Cornuejols, "A lift-and-project
i. ; :' plane algorithm for mixed
E. Balas and M. Fischetti, "A lift-
ing procedure for the -i i,. ,i. I, ;.
:, ... I/:. salesman polytope and a
large new class of facets"
L. Qi and J. Sun, "A non-smooth
version of Newton's '.. t,!..
K. Taji, M. Fukushima and T.
Ibaraki, "A 1..'i1i convergent
Newton method for solving
-i. 1i,1 monotone variational in-
R.M. Freund, I'.I.j. .. trans-
formations for interior-point algo-
rithms, and a superlinearly conver-
gent li. ii',.. for the w-center
P.T. Thach, "D.c. sets, d.c. func-
tions and non-linear equations"
Vol. 59, No. 1
M. Kojima, N. Megiddo and S.
Mizuno, I i,... i.. trl convergence
of large-step primal-dual interior-
point ,11 ..." tii,, for linear pro-
S. Mizuno, R. Saigal and J.B.
Orlin, "Determination of optimal
vertices from feasible solutions in
unimodular linear programming"
A.N. lusem, "On the convergence
of iterative methods for symmetric
linear .." ''.i 1,, ,tii it!, problems"
S. Dempe, "Directional i;rlt. .-
tiability of optimal solutions under
SI,; I's condition"
J.A. Ventura and D.W. Hearn,
"Restricted simplicial decomposi-
tion for convex constrained prob-
S. Chopra and M.R. Rao, i't.
partition ;"'. ., I .
A. Tamir, "A strongly polynomial
:1 .! 1,1; ,, for mininum convex
separable quadratic cost flow prob-
lems on two-terminal series-parallel
Vol. 59, No. 2
M.J. Todd, "Combining phase I
and phase II in a potential reduction
algorithm for linear i".'. 'i i ', .
Y. Ye, O. Giiler, R.A. Tapia and
Y. Zhang, "A quadratically con-
vergent O( nL)-iteration 'i ..,'i",
for linear programming"
P. Gritzmann and V. Klee, "Com-
putational complexity of inner and
outer ,:. of polytopes in finite-
dimensional normed spaces"
J.C. Bean and R.L. Smith, "Condi-
tions for the discovery of solution
P. Tseng, "Dual coordinate ascent
methods for .i... i I. I ii, convex
A.S. Nowak and T.E.S.
Raghavan, "A finite-step algo-
rithm via a bimatrix game to a
single controller non-zero-sum sto-
E.R. Panier and A.L. Tits, "On
combining, ,.-,i.i,.'. descent and
superlinear convergence in inequal-
ity constrained optimization"
Vol. 59, No. 3
W.P. Adams and H.D. Sherali,
"Mixed integer ';hr:.. ,. program-
C. Dang, "The D2-triangulation for
simplicial homotopy algoritlhms for
computing solutions of non-linear
V. Jeyakumar and X.Q. Yang,
"Convex composite multi-objective
K. Tone, "An active-set strategy in
an interior-point method for linear
M. Kojima, S. Mizuno and A.
Yoshise, "A little theorem of the
big cW in interior-point algo-
K. Murota, i i.. I ,, ,,I decompo-
sition of symmetric discrete -., ,1. ,
by matriod and group theories"
L.U. Uko, "Remarks on the gener-
alized Newton method"
D. Bienstock, M.X. Goemans and
D. Simchi-Levi, "A note on the
prize -collecting traveling salesman
Vol. 60, No. 1
P. Tseng and D.P. Bertsekas,
"On the convergence of the expo-
nential multiplier method for con-
G. Cornuejols and F. Harche,
i ,.. i .. i,, I study of the capacitated
vehicle routing problem"
F. Barahona, "On cuts and
matching in planar graphs"
J. Sun, "A .... .. .. .proof for an
t ill, ... il ,, algorithm for convex
quadratic programming without
,...,,-,1, .. ... ... assum options"
J.L. Goffin and J.P. Vial, "On the
computation .f I. '.. .1! analytic
centers and dual ellipsoids with the
projective ri ,., lim"
J.E. Martinez-Legaz and S.
Romano-Rodriguez, "Lower sub-
.hit. t'' t,,"itr, of quadratic func-
D.K. Wagner and H. Wan, "A
polynomial-time simplex method for
the maximum k-flow problem"
Vol. 60, No. 2
M.L. Balinski and F.L. Rispoli,
0 ..,.i .. classes of transporta-
M.X. Goemans and D.J.
Bertsimis, "Survivable networks,
'.,..;.' programming relaxations
and the parsimonious property"
D. Siegel, "Updating of conjugate
direction matrices using members
of I I, ', 's I,,,, 1,"
G. Di Pillo, L. Grippo and S.
Lucidi, "A smooth method for the
finite minimax problem"
O. Gfiler and Y. Ye, "Conver-
gence behavior of interior-point
J. Rohn, "A note on ..i...,i.;iii, of
a class of linear complimentarity
T.L. Magnanti, P. Mirchandani
and R. Vachani, "The convex
hull of two core capacitated net-
work design problems"
Vol. 60, No. 3
J.B. Orlin, S.A. Plotkin and E.
Tardos, i'../ ,i. .,,;I dual net-
work simplex il,,,t ,,r, "
A.V. Karzanov and V.N.
Lebedev, "Cyclical games with
U", 1aI tt,,,; ""
J.-S. Pang and S.A. Gabriel,
"NE/SQP: A robust id.." ili for
the non-linear ,'."'i' i,,, i. ,, ; i,
L. Kuntz and S. Scholtes, "Con-
straint qualifications in
1:..r. i, ',(.. ., t,. ;i. optim ization"
M.M. Kostreva and M. Wiecek,
"Linear complementarity prob-
lems and multiple objective pro-
O.E. Flippo and A.H.G.
Rinnooy Kan, "Decomposition
in general mathematical program-
R E V I E W S
The Probabilistic Method
By N. Alon and J.H. Spencer, with an Appendix by
John Wiley and Sons
The l"'.'..' I.I- -..' method was founded and developed by Paul Erd6s. One of
the main issues is to prove that certain combinatorial objects exist, by show-
ing that the probability of i ... I.l pii ''p p h t ..l'.i ) -p P'. *
is positive. Often, this also leads to an effective randomized algorithm to find
such an object.
For example, using this method, the existence of graphs which simultaneously
have a large chromatic number and a large girth is shown, and also shown
are graphs with both a large clique number and a large coclique number.
Related is the workbyErd6s and Alfred R? i, .; -inJ, .. ,ii in.., I i,,, 1..- r-
ing that a random graph with a high enough edge probability has, e.g., a perfect
matching, or a Hamiltonian circuit.
This pioneering work formed the basis for a wealth of further research, ex-
tending the depth and power of the methods and detecting several important
and unexpected further applications in fields such as discrete mathematics,
combinatorial geometry, combinatorial optimization, algorithmics, theoretical
computer science, number theory, coding, game theory and percolation. The
application to theoretical computer science has raised an especially intrigu-
ing stream of questions and results.
The book, by Noga Alon and Joel Spencer, gives a splendid in-depth overview
of these results. Alon and Spencer are two leaders in the field, and several of
the deep results discussed in the book were obtained by the authors them-
selves. The book consists of 15 chapters and is divided into two parts: "Meth-
ods" and "Topics." Between any two chapters there is an intermezzo called
"The Probabilistic Lens," .1 i-,- .- 1m: i "gem" of one to two pages: an elegant
and short proof of some combinatorial or other result with the probabilistic
method (not always based on the previous chapter).
Part I "Methods" begins with chapters on "The Basic Method," "Linearity of
Expectation," "Alterations" and "The Second Moment," introducing the ba-
sics of the probabilistic method and applying it to graph theory (e.g. coloring,
tournaments, cliques and independent sets), hypergraphs, Ramsey theory,
number theory and combinatorial geometry.
Chapter 5, "The Local Lemma," gives 'Lovisz Local Lemma,' a very power-
ful tool. In its symmetric form, it states: Let A,...,A. be events in a probability
space. Suppose that each event Ai ,'. r ,,.in , '.. .. of a set of all other events
A but at most d,and that Pr(A) p foralli.Ifep(d+l) 1 then Pr(/ A)>0. As cor-
ollaries of the local lemma, the chapter gives theorems on hypergraphs,
Ramsey numbers, covering three-space by open unit balls, the linear aboricity
of graphs and Latin transversals. As the book mentions, "There is no known
proof of any of these results which does not use the local lemma." Moreover,
some results of Beck on converting the local lemma to an algorithmic method
Following that are chapters on "Correlation Inequalities" (like the FKG-in-
equality), with applications to linear extensions of partially ordered sets,
"Martingales," with applications to the chromatic number, and i, i. ..i--,
..lo!, (with Jason's inequalities and Brun's sieve).
Chapter 9, i ... i...- i -.. ~.. -," then -. 1.t.. the results on expanders,
which form'-., I i ..1 blocks in parallel sorting networks, and the "R6dl-
nibble," the tool designed by V. R6dl to construct dense packing of k-cliques
in an 1-uniform complete hypergraph.
Part II, "Topics," starts with Chapter 10, "Random Graphs," giving bounds
on the edge probability of a random graph so as to imply certain properties,
such as having a subgraph of a certain kind or having a certain chromatic
number. It also discusses phase transition, the phenomenon that a random graph
on n vertices with edge probability c/n has only small components if c<1, but
has one 'giant' component as soon as c>1. This phenomenon connects to
percolation and to 'freezing' in mathematical physics.
In Chapter 11, "Circuit Complexity," the famous lower bound results of A.A.
Razborov for the complexity ,t I-'.. t. i 1. -1 i t, J. J-.-, I,. *i.Theyarelower
bounds on the size of Boolean circuits of given depth determining e.g. whether
a given graph has a perfect matching or a Hamiltonian circuit. The results
belong to the few lower bounds of algorithmic complexity, and the proofs fully
exploit probabilistic methods.
Chapters 12-14 discuss "Discrepancy" (including the Beck-Fiala theorem),
"Geometry" (properties of points in Euclidean space, geometric realizations
of sign matrices, -nets and Vapnik-Chervonenkis dimension), and "Codes
andC (i '-I, i V i~ .i's theorem and balancing vector games).
The last chapter, "Derandomization," discusses how the randomized algo-
rithms in some cases can be turned to an efficient deterministic algorithm, such
as, for instance, finding fair partitions and good colorings.
The 'gems' include: the Erd6s-Ko-Rado theorem on intersecting families of
sets, Bregman's upper bound on the permanent, the number of Hamiltonian
paths in a tournament, Turan's theorem, the Weierstrass approximation
theorem, random walks, Sperner's theorem on maximal antichains, unbalanc-
ing lights and the efficient packing of convex bodies.
"The book is very well-
written, giving clear
and short arguments for
It can be read and
understood by those not
familiar with advanced
The authors mention in the preface: "'I ..' i''1 ...- I t.I. t. write an encyclo-
pedic book on the probabilistic method; too many recent interesting results
applyprobabilisticarguments, andwedonot ._-iii, i-..,' it, '.. I.I themm"
Indeed, the field now is too much extended to overview everything happen-
ing, and the authors are to be congratulated for making such a fine selection.
A topic not covered is the recent works of Dyer, Frieze, Kannan, Lovasz,
Szimonovits on random polynomial-time algorithms for approximating the
volume of convex bodies. This might be too recent and too much in a stage
of continuous refinement yet to give a balanced account.
The announcement on the cover, "with an Appendix by Paul Erd6s," seems
to serve promotional purposes mainly. This appendix forms a quite marginal
part of the book. It consists of three pages, mentioning a few problems in
Thebookisverywell-written, o Ii. 'I- n.i .. ii ,,t- f.. -- i t, ..i .
theorems. It can be read and understood by those not familiar with advanced
probability theory wherever necessary, the book gives explanation. The
book can very well serve both as a textbook in an undergraduate course or
at a graduate research seminar, and as a reference work for researchers in
dci .- i. ni,,t ..it i. 1 1 .l-.. '. i. ,i *I,' .., n ii,_ -.!,iJ theoreticalcom puter
- A. SCHRIJVER
Network Models in Optimization and
Their Applications in Practice
By F Glover, D. Klingman and N.V. Phillips
Interscience Series in Discrete Mathematics and
Optimization, John Wiley and Sons
It is unlikely that the runner who brought the victory news to the ancient
Athenians from Marathon used a shortest-path algorithm to plan his route!
In any event, network optimization problems have been prevalent through-
out time. However, it was not until the modern era of T. Koopmans and L.V.
Kantorovich in Russia and the U.S. respectively that network optimi-
zation models were formally posed in the context of practical applications.
And it was not until G.B. Dantzig's work with the simplex algorithm that
theoretically sound and .,'ii...I. j efficient methods were developed
for solving network optimization problems.
Since the early days of linear programming, the field of network optimiza-
tion has developed dramatically: Network optimization algorithms are one
to two orders of magnitude faster than general-purpose linear programming
solvers. Several important applications have been developed for industrial,
government and r.-, -i, .-,iii.- iJ i.._ Modeling tools that ease the speci-
fication of large network models also have appeared. t it i- t ir ,1. r1 i the
book by Glover, Klingman and :'-i u!! p- appeared that one could grasp the
significance of network models for practical applications. Even more impor-
tantly, however, there now is a .. .I- r .t.: book to introduce students and
practitioners to the art of network modeling. This reviewer, who learned
network modeling by .- I-..- from some of the pioneers in this field as a
graduate student, wished that this book had been written earlier.
"Readers of this
book will learn both
principles of net-
and will enrich their
real applications of
Thebook-- I- i I il .. - emphasizes modeling aspects of network
optimization. The authors take a two-pronged approach that I liked. First, they
discuss general principles for the design of network models. For example, how
do we use multiple arcs to model a goal programming problem? How do we
replicate a network to model time lags? The listof tricks the authors introduce
is long, creative and for the most part very useful. I detected only a few
contrived examples. Then, the authors present case studies of network appli-
cations in practice. These case studies illustrate the use of the general prin-
ciples in specific applications of practical significance. All of the cases also
,.l.l.t . r" .. .. .. i' 'i. ii. o. i i' I r .. 11 .. /operationsresearch
applications in practice. Some very popular cases are collected in this book,
including: Manpower planning for the U.S. military, product distribution
planning for Citgo Petroleum Corp., W.R. Grace Co.'s problem .f ...
production and distribution of chemical products and so on. Readers of this
book will learn both principles of network in... 1, '1; .: and will enrich their
understanding of real applications of network models. Most of the cases are
structured in parts: This enables students to learn how to attack complex
problems by breaking them into pieces. The authors have done an excellent
job in transferring their collective expertise onto these pages.
The book coins the term netform, meaning the network flow-based formula-
tion, in Chapter 1 and gives a brief historical background and a preview of
applications. The book does not become interesting until Chapters 2 and 3.
Here, one is introduced to several variations of network models, and their
algebraic and graphical descriptions. To the extent that one can be taught -
instead of grow into ...... I.-le. these two chapters achieve the goal. A
complete convention for network diagrams is introduced, which influences
the rest of the book, and, I suspect, will influence future developers of net-
The remaining three chapters develop more advanced topics of network
models: Chapter 4 addresses dynamic models. That is, model formulations
that capture the dynamic, time-dependent behavior of a system. A typical
example is the inventory model. Of course, it is assumed ti 11 .I,11 I i I i'data
is known with complete certainty at the beginning of the planning horizon.
This is not the authors' fault. The literature on mathematical programming
usually deals with deterministic data. But this reviewer could not leave
unmentioned the increasing importance of robust optimization models for
planning under uncertainty. Nevertheless, the authors point out the impor-
tance of uncertainty in multiperiod models. Netforms provide a convenient
framework within which one can identify the potential impact of uncertainty
and perform post-optimality, "what-if," analysis. I suspect that pointing out
this challenge will prompt further developments in how to handle uncertainty.
C0 1,' l I I I t i. d 1. 1 .. i d 1 1 -, i r - il_ : r l 11 - r - r 1 -- 1 l l r L t ,,. l r -
This class of models is very important in practical applications. Arc multipli-
ers can be used to model change of units (e.g. in transforming raw material
into finished goods for production modeling) or gains or losses (e.g. in mod-
els of cash-flow management). Negative multipliers can be used to model the
proportional use of some resources. Chapter 6 introduces network models
with discrete requirements. The introduction of 0-1 variables in a network for-
mulation, together with the use of arc multipliers, makes for a very powerful
modeling tool. Applications are illustrated from flight training scheduling in
the U.S. Air Force, the planning of cotton gin operations in the Rio Grande
Valley and others.
I ___________ _____
There is nothing "advanced" about the coverage of these topics. They all are
presented in a non-technical fashion that will not discourage novices. The
authors state that no mathematical sophistication beyond college algebra is
required, and they are right. But this simplicity of presentation does not take
anything away from rigor.
I do not share the authors' view that this book can be used as the basis for a
one-semester course. I would rather use it together with a book on network
algorithms to teach both the science and the art of network optimization. This
is a more likely usage of the book in most courses on network optimization
that this reviewer is familiar with. I also suspect that this book will be used
t,. ,1 1, ,t.. . C.. I ', 11,11. 1 11 i .1r .'.. r i pplications,even
in courses where network optimization is not the primary focus.
This book contains an impressive bibliography at the end of every chapter.
The index is mediocre. The quality of the I!l.r I .1 ..r.- is excellent and so is
the authors' sense of when to use them. One omission of the book is the treat-
forms over the last decade. While such problems have been treated
algorithmically in recent books, the authors have missed an opportunity to
give us a modeling treatment as well. This, together with the cursory treat-
ment of uncertainty, are my major complaints. Otherwise, the book coverage
is extensive. I highly recommend it as a useful addition to the library of prac-
titioners and academic modelers, and for classroom teaching in courses on
network optimization. I also would encourage faculty of mathematical pro-
gramming courses in both engineering and business schools to consider
using this book for its excellent application cases.
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I U'.t- I i_ *
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