Title: Optima
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Permanent Link: http://ufdc.ufl.edu/UF00090046/00007
 Material Information
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: June 1982
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Bibliographic ID: UF00090046
Volume ID: VID00007
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.


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AT "L..Y IN T E!,. FIELDS OF S(..IU ,)U. ,.;-, TTH OORY

E.L. Lawler
i I..iri, of California, Berkeley
A.H.G. I' inm ....
Erasmus nIti.-

Machine I-i..ii.Ih theory is some-
of a ,ilI. encompassing a bewil-
lr ,;, large variety of problem types,
as the most cursory examination of the
journals reveals. It is also a marvelous I ..
SiI rin' for the ai;- liHiio, designer and the
complexity analyst, in that every known
trick of combinatorial optimization can be
applied somewhere, to one problem or
another. This is an account of our explora-
tions of this ji,_ p.-! .,ground. Not inciden-
*-'-y, we shall describe a computer program
have used to help us guide our way. We
conclude with some speculations about how
similar, possibly more sophisticated, pro-
grams could be useful aids for researchers in
other fields.
When we began our collaboration
several years ago, we decided to focus our
attention "on machine scheduling problems.
I i, meant that we excluded from consid..
ration such worthy topics as *...i. i sched-
ili,, i I.,1il .. and cyclic schedul-
ing of manpower. also decided to con-
centrate on strictly deterministic models.
Even so, this left us with an enormous
number of problem types to study.
Very early on in our investigations,
we decided we needed a uniform system of
classification for the problems which had
appeared in the literature. L.I, Ih.i from the
classification scheme of Conway, Maxwell
and Miller I 1], after much debate we settled
on a scheme which suited our purposes. This
classification system is detailed elsewhere
[41, and for present purposes can be sum-
marized as (.n.IIimI.--in.i machine environ-
,t (single machine, parallel machines,
open shop, flow shop, job shop), job char-
acteristics (independent vs. precedence con-
strained, etc.), and optimality criterion
(makespan, flowtime, maximum lateness,
total tardiness, etc.).

J.K. Lenstra
Mathematisch Centrum, Amsterdam
y Kan
! in i r ,i.m.Ml

An iinmediate payoff was the consunm-
mate case with which we could commlnii
nicate problem types. Visitors to our offices
were sometimes baffled to hear exchanges
such as: Since lI r, |C is I -hard, does
that imply that 1;.,' i,'.,j |Ci is NP-hard
too?"' that's easy, rememberr" I i
I d ICj is easy and that imIplies
I |pmttn,d JiECj is easy, so what do we know
abo ut ,i .' J C ,cJ ,?" ."I..i l .n "
As this discussion indicates, one of our
objectives was to demark as clearly as
.I -iil,- the boundary line between easy
problems (solvable in polynomial time) and
NP-hard problems. But because of the huge
number of problem types and the relation-
ships between them, it was easy to become
confused. One could spend an hour trying to
determine the status of a particular problem,
only to realize that the issue had already
been resolved the problem was a generali-
zation of a known NP-hard problem and
therefore NP-hard as well. or a specialization
of a known easy problem and therefore easy
as well.
I i, idea of using the computer as an
aid began as a joke. The afternoon of Sep-
tember 22, 1975, Dick Karp, Ben Lageweg,
Gene Lawler and Jani Karel Lenstra met in
the Mathematical Center in Amsterdam to
decide on a gift to present to Alexander
Rinnooy Kan on the occasion of his upcom-
ing promotion to doctorate. Somebody
made the amusing suggestion of a bound
volume consisting of a computer tabulation
of all the thousands of problem types with a
notation for the status of each one: for
easy, for NP-hard, and ? for unresolved.
We were well aware that the problems
in our classification system admitted of a
natural partial ordering. Job shops are more
general than flow shops. Precedence con-
strained problems are more general than
Continued overleaf-

It is a great pleasure for us to welcome
the participants of the XI. International
Symposium on Mathematical Programming
on behalf of the program and organizing
committee here at the Rheinische Friedrich-
Willichns-Universitlf Boto i.
This triennial scientific meeting of the
Mathematical Programming Society is one of
the best occasions for all researchers in the
area to assemble and interchange ideas. We
expect participants from Universities, re-
search institutions, and industry from
about 40 different countries andl thus hope
to have a very productive international
conference. We are also happy that quite
a large number of researchers from i'Eastern
Europe an and I 1i,,, ',' ., I. countries arc able
to participate in the Symposium in spite of
their substantial difficulties in obtaining
convertible currency. We gratefully acknow-
ledge the financial support provided by
various public institutions and private firms,
in particular Deutschc Forschungsgemein-
sclaft, Deutscher Akademinscher Austausch-
dienst and Gesellschaft von ireunden und
F'rderern der Rheinischen Friedrich-
\\ ,11,. I, UniversitS't.
The structure of the meeting ll be
roughly the same as it was for the past
symposia. For this : ....I,. however, we
have for the first time organized 23 state-of-
the-art tutorials. These are intended to be
a combined plenary talk and comprehensive
survey lecture, and are given by leading
experts in the respective fields. We hope that
you will enjoy these presentations and that
you will profit from them. I I r.- will be
four of these lectures (two parallel sessions)
every day except on Monday when there will
be three lectures and eight on Wednesday.
The schedule of the contributed and
invited talks within a session was made in
order to avoid conflicts with other talks on
similar topics in parallel sessions. It does not
indicate a ranking.
As a tradition of Mathematical Pro-
gramming Symposia the ratio of participants
to lectures is close to one. Due to the large
See page 5

June 1982

Number 7

(;,1F' FOR ATI.E.' UNDER ...

problems with independent jobs. Maximum
lateness is a more general optimality crite-
rion than makespan. And so on. All that
was required to produce the tabulation was
to feed the computer all results in the form
of known easy problems and known NP-hard
problems (ignoring results that were clearly
dominated by others), let the computer take
account of the partial ordering, and let it
churn out a properly annotated listing.
I ,i t afternoon at the Math Center,
the group speculated on what the score
would be: how many "s, i's and ?'s would
the tabulation contain? A playful attempt
was made to obtain an estimate by gener-
ating a few random chains in the partial
order, with everyone testing his expertise
to sec how far up a chain lie could prove
easiness antd how far down NP-hardness.
(Lenstra has since made the generation of
random chains part of one of his stock
lectures, with a member of the audience
throwing a die.)
Tlie next inevitable suggestion some-
one made was: "Why not have the computer
list the maximal easy and minimal hard
problems, and the minimal and maximal
open ones as well? '..,hiiin't that give us a
clearer picture of the situation?"
;A suitable program was forthwith
written by Lageweg and an initial run was
made. The results were startling, for tihe
number of easily resolvable cases it revealed
in the listings of minimal and maximal open
problems. During the next few weeks
Iageweg, Lawler and Lenstra knocked off
many targets of opportunity. The number of
question marks in the tabulation was consid-
erably smaller when, on January _':, I.-, a
handsomely bound volume was presented to
Alexander F15].

i*i:, tlie past six years there have
been many developments, and Alexander's
volume is now thoroughly outdated. The
most impressive progress has been made in
tlie area of preemptive hli.diiiii' of p.,..l--II
machines. An elegant J':...iiih, due to
Gonzalez and Sahni (for Q rI ...... .. the
problem of iii iii., i- i. makespan in preemp-
tive -. I. i:l;C. of uniform parallel machines)
13] spawned a whole host of derivative
. i. i -. for related ,, ...1. :i
At the present time, the score for
4, .,' problem types stands at 8 I NP-hard,
Seasy and 1"1 open 17 'This particular
split is an artifact of our classification
system, but it is certainly true that several

subareas have been pretty well cleaned up.
For example, the status of almost all single
machine problems is known. 1i..1 i open
problems are still occasionally resolved, it
is safe to say that nearly all the cream has
been skimmed.

The problems which remain are :r-. .dI
rather difficult. It is .:i. -i1-l that they are
neither NP-hard nor easy, provided that P=
NP (which we believe). One of the frustra-
tions of the theory is that there is no way of
proving such a result at present. r- those
who might care to accept a challenge,
we mention two classic open !,l. i
(1) ;:1.. p' = l1Cmax' the problem of
minimizing makespan for unit-time jobs
subject to arbitrary ir.'ii. 1:i .- constraints
on three identical parallel machines: known
to be easy for two machines and NP-hard for
an arbitrary number of machines.
(2) 1 -'T,' the problem of muiiii;i.';ii- total
tardiness on a single machine: known to
adm it of a : '. II' l'Ip .. l ,il .. '; .. ; ihl
hence not NP-hard in the strong sense
(unless P = NP). Is this problem easy or is it
NP-hard in the ordinary sense?
A few words about the significance of
NP-completeness theory are in order. It is
not always true that polynomial algorithms
are good and that problems that admit of
such algorithms are easy to solve in practice.
It is perhaps even less true that NP-hard
problems are invariably hard in a practical
sense. Yet there is enough correspondence
with reality to make the notions of easy and
NP-hard more than a polite fiction. Some
NP-hard problems are really hard to solve.
For example, no one has yet solved to
optimality a certain notorious 10-mnachine
10-job job shop problem, small as this
problem instance is. (The best published
solution has a inakespan of 972 [8].
Lageweg has found a solution of The
best known lower bound is 865.)
The primary usefulness of the concept
of NP-hardness is the direction it gives to the
d1...iilrii' designer. With knowledge that a
problem is NP-hard, he can abandon any
attempt to reformulate the problem as, say,
a simple network flow problem or a 1LiJ
.,l.mLin-: problem. Instead he can concen-
trate his energies on l, '...l *ii an efficient
enuimerative optimization method or a
i, i i,,-ii :;ir, approxim action Ii; ..:.i, It is
in this way that NP-completeness theory
has probably had more impact on comibi-
natorial optimization than any other theo-
retical development of the past ten years. We
were '.1,- d. i to observe, during the NATO
Advanced Study and Research Institute on

Deterministic and -,In n., l : 1'-1.i1ii"
(Durham, Fi.i..l.nd. July 1981) [21, that the
,..!-liii ..... "carries over to computational
questions about stochastic ,: i-w in.-r as
One of our hopes when we began
, ,.i. i was that we might be able to deter-
mine the boundary line between easy
and NP-hard problems sufficiently closely
that we could gain meaningful insight into
the properties that make a scheduling
problem of one type or the other. Il we
have been able to do to some extent. When
dealing with a practical scheduling problem
(which is invariably NP-hard), we found it
increasingly easy to detect the particular
features of the problem which were respon-
sible for its computational intractability,
since they would correspond to the crucial
ingredients of an NP-hardness proof. ;I h.
features then suggested certain relaxations
that should be made to obtain lower bounds
for a branch-and-bound procedure, or
directions that could be taken in designing a

Now to return to a discussion of the
computer program and the -: ...i...0. we have
received from it. ,, the program has
provided an orderly form of record \...-.i r
for research results. Confusions and
sights have been .i .,il, reduced. Seco,.i,
the 'i, .- rI has .-I '. 1 us focus our re-
search. Listings of minimal and maximal
open 1.... "ni, have made it easy to choose
the most interesting and important ones to
work on. And finally, the automatic score-
'..,-. in, has been motivational and intro-
duced a healthy competition into our
A frivolous idea which occurnred o us
was that the computer might be pro-
gramnned to produce another type of score,
namely the minimum number of open
problems whose resolution would resolve all
remaining open problems. Alas, we found
that the calculation of this score is itself an
NP-hard problem 6]. We have made no
attempt to devise an algorithm for its
We !.... that computer programs
similar to ours could be i.p,,i :, ,.:a well
to other well-structured areas of '.ii J.
and research. Certainly allied areas of
combinatorial .ri.i. i. such as location
theory and, more ambitiously, algoriit
Si !,.: theory are ,.,.i.,i,. Even the i. .
area of mathematical .'.ii..i. ir": might be
S. ..!... i. as well as inventory theory,
queueing theory, or even .... .1: chemistry.
It would not )be difficult to create a

GIFT FC'i. A, i KA .1 [i . .

sort of automated encyclopedia. Given such
... fl..r thle field of mathematical
. ............ thle user could make queries
of the formi: li n is known about a
problem with such-and-such objective funic-
tion and so-and-so constraints'?"' The system
might answer: "Nothing has been reported
on this specific problem, but these results
have been obtained for more general and
more special cases. Moreover, the ..il. 11
computer codes are available . .'' The
program would be knowledgeable of prob-
lem relationships which might be unknown_
to the user, even if their usefulness would be
contingent on future theoretical develop-
ments. For example, it would know that
maximization of a posynomtial in bivalent
variables is equivalent to the inil-cut prob-
lem of network :I. theory.
There are other :.,- of i,. ', ..
answering facilities it would be useful to
have. For example, for a book on scheduling
theory we are writing, we should like to
state a few simple rules that will enable the
reader to comprehend the status of large
subclasses of problems. It would be nice to
be able to verify these rules by a !..i. tIhe
iten questions of the form: "Are there
.-sy problems i,.,,'.. .. the 'ip,. i the
scheduling of .1.i. I machines which do nol
Have the .!I. ':i.' of minimizing 'i i...
or "Are there any -.r.bl. 11, which are
known to be NP-hard when preemption is
pennitted but easy when it is n.:'-'"
At some future date. it may be possible
to have computers search for problem trans-
formations themselves. At this lime, such an
undertaking appears to be beyond the
capabilities of artificial intelligence,. i .....I.l
this development come to pass, the coim-
puter would truly he an automated research

1. I.W. Conway, W.L[. Maxwell, L,.W.
SII (1967) Theory of ..,.' .
Addison-Wesley, P'. I.,,I MA.
2. M.A.II. Dempster, J.K. Lenstra, A.H.
G(. I i K...... Kan ((ds.) (1982) Deterministic
and Stochastic Scheduling, leidel, Dord-
3. T'. Gonzalez, S. Sahni (1978) Preemnp-
e Scheduling of Utnifornm .... ....I
-,sterns. J. Assoc. Comput. Mach. 25,
4. R.L. Graham, E.L. Lawler, J.K.
Lenstra, A.H.G. Rinnooy Kan (1979)
Optimization and Approximation in Ieter-

miniistic Sequencing and Scheduling: A
Survey. / nn. )iscrete Math. 5, 287- "'-'
. B . E. L. Lawyer. J.K.
Lenstra (1976) Machine Scheduling Prob-
lems: Comnputations, Complexity and
( i . ..... I. I t I. 30, M athemi atisch
Centritn, Amsterdam (out of print).
6. H.J. I .. E.L. Lawler, J.K.
Lenstra, A .I. 1 .......... Kail (1981)
Computer Aided Complexity Classification
of (Comibinatorial Problems. Report BW 137,
Ma th ematisch (Cen tru m, Amsterdam.
7. B.J,. I .. .L. Lawler, J.K.
Lenstra, A.Ht.G. Rinnooy Kan ([981)
Computer Aided Complexity Classification
of )Deerministic Scheduli ng Problems. Re-
porti IX 1 ". Mateateatisch (entrum,
8. G. McMahon, M. Florian (1975) ()n
Scheduling '. ....iy 'I ,,V and Due
Dates to i........ Vlaximum Lateness. Oper.
R es. 23, . i .. _..

Computer Codes for Selected Network
Optimization : i:.h,-m

!il purpose of this note is to report
on a collection of computer codes that are
designed to handle certain network opti-
mization problems that arise frequently
in modeling and in practice. I I-. selected
codes have special relevance to transporta-
tion and i i,,n, .... problems especially in
the area, of routing and scheduling. Since
some of the problems frequently emerge as
building blocks in more complex models, we
believe that a collection of codes (in sub-
routine form) of this sort could be extreme-
ly useful to other network researchers.
Each algorithm coded is listed below
in onet of five categories. All codes are in
FOIIRTiAN and are user-oriented in nature.
The description of each algorithm includes a
complete specification of input and output
characteristics and the computer environ-
ment of the subroutine. Moreover, along
with each code is a brief directory that
sunimarizes its purpose, applications, and
performance characteristics. ()Ouri hope is that
this will make the .1.,l .. ,ni particularly
accessible t tthe novice as well as the
We do not claim that the codes repre-
sent tlhe most efficient means of solving
the related problems and, furthermore, we
have made no special effort to fine-tunel
them. 0' do feel, however, that they pro-
vide easy-to-use and reasonably-effective
tools for solving the selected network

problems, especially when a lmaj'or coding
effort is not warranted. As such, we antic-
ipate that this collection will be of benefit to
a variety of alplications-oriented users.
The collection of codes is available as
"Listing, and Documentation for Selected
Network Optimization Computer Codes,'"
Management Science and Statistics Working
Paper No. 81-003, ( .11, of Business and
Management, University of Maryland at
College -' I

List of Network Optiiization Algorithms

I. iE 'TIRAVI I :; S/ I i \N
a) Arbitrary Insertion TSP Ifeuristie -
b) ( i, . Insertion TSP I1.
c) Farthest Insertion I' lheuristic -
F I: I: I .
d) Nearest Neighbor Heuristic -
e) Nearest Insertion TSP Heuristi -

a) Modified Clark-Wrighlt A\lgorithm for
Vehicle Routing CRVRP
b) Traveling Salesnian Alorithni for
Directed Networks 1, I
c) Tinie-Constrained Traveling Salesman
Algoritin I' I -I'
d) Traveling Purchaser Algorithm TPP

Ill. 1 ii)RTEST PATi PRCI I i I
a) Bellman's Algorithm BELLI,
b) D;iI i, s Algoritinhm DIJKST
c) Floyd's Algorithm FLOYD
d) Modified El... .i's Algorithm F3
e) Papes Algorithi I i'APE

a) Minimum Spanning Tree Algorithm -
b) Prim's Minimumn Spanning Tree
Algorithm 'I:' I

a) Maxiimum I I.. Algorithm -
b) Dilworth's Chain Decomposition
Algorithm DILS

-A. Assad, B. Golden, L. Bodin,
M. Railt and t D)11ah


Maintained by the Mathematical :'.... .. 111 .. .. y ( i, )

This Calendar lists meetings specializing in mathematical ,. .... ,ii._ or one of its subfields in the
general area of optimization and applications, whether or not the Society is involved in the meeting.
( 1 1.. .- meetings are not necessarily "open".) Any one knowing of a forthcoming meeting not listed here
is urged to inform the Vice t I i.im ,1 of the Society, Dr. Philip Wolfe, IBM Research 33-221, POB 218,
Yorktown Heights, NY 10598, U.S.A; Telephone 914-945-1642, Telex 137456.
...n- of these meetings are sponsored by the ... -..ly as part of its world-wide support of activity
in mathematical programming. n.lI i certain _,t ..i.. the Society can offer l-..- y, mailing lists and
labels, and the loan of money to the organizers of a 11 .i.. meeting. For further information address
the ( I il1 ii i of the Executive Committee, Dr. A. C. ,In i, Mobil Corporation, 150 East 42d Street,
New York, New York 10017, U.S.A.; Telephone 212 -7678.
Substantial portions of meetings of other societies such as SIAM, !.;'., and the many national C':
societies are devoted to mathematical pif .iiiiii,,' and their schedules should be consulted.

August 23-28: Eleventh International Symposium on Mathematical ', ....iuI,; .: in Bonn, '* i. al
i,'.li',-I of Germany. Contact: Institut fur ikonometrie und Operations Research Universitat
Bonn, I .,. ii i... 2, 5300 Bonn 1, Federal Republic of Germany; Telex ..- 17 unibo b,
Telephone (02221) 7 '1- Official triennial meeting of the MPS. (Note: The International
Congress of Mathematicians will be held August 1 1-19 in Warsaw, i', I n,! )

October 25-27: Sparse Matrix Symposium 1982, I ,,i,.i.i Glade, Tennessee, U.S.A. The Symposium
will address the construction and analysis of algorithms and mathematical software for sparse
matrix calculations and associated applications, one of which is 'Optimization'. Abstract
deadline 1 July 1982. Contact: Robert C. Ward, Union Carbide Corporation, MSRD,
Computer Sciences, P. O. Box Y, i'li ,' !, Oak i_. Tennessee 3 U.S.A.;
telephone 615-574-3131.

October 20-21: i.d. Mathematical Programming Symposium I..in, Tokyo, Japan. '. 11 Advances
in Mathematical :':.,L:r ii ,l... Mathematical '".. .. .-i,n : Software, and Applications.
Contact: Professor Masao Iri (i :i.i., ,,l Organizing Committee), ... 'ny of Tokyo,
Pi,,,i .-ku, Tokyo, Japan 113, or i. i. Kaoru Tone (Chairman, r' ,,i Committee),
Graduate School for Policy Science, Saitama University, Urawa, Saitama Japan.


July 11-15: 3d IFAC/IFORS Symposium "Large Scale Systems: Theory and Applications", Warsaw.
Deadline for abstracts, 15 February 1982. Contact: Dr. Z. Nahorski, 3d IFAC/IFORS
LSSTA, Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447
,i, t, i, '"..i ld. Telex 812397 ibs pl, Telephones 364103, 368150.

July 25-29: 11th '! Ii' Conference on System Modelling and COil, ; ,li..n. Copenhagen, Denmark.
C. .lliii.. for abstracts, 31 December 1982. Contact: Professor P. Thoft-4 !' I I. 1.., Institute
of Building T. h.l..i and Structural Fnigi.,-, in ., Aalborg University Center, P.O. Box 159,
DK-9100 A.i11.. _. Denmark.
0@* *@



f Fl,: F E


NEW Y :i

The, "Friends of Optimizatioln" was a
hosely organized group of mathematical
riiograminers that held twenty-four meetings
ii> New, York City, 1971-' Donald Gold-
iBrb (Departmtent of industrial FEngineerilng
;inl Operations Research, Columbia Univer-
:iy, New York, NY 10027, U.S.A.) has
,'activated this group.
is he writes, "There are several good
4leasons for doing so. I manly active
r-:earchlers and users of optimization have
moved to the New York area since the last
') meeting and several of them have ex-
(pressed a strong interest in meeting inflor-
mally to discuss current research. Second,
lie F(OP meetings that were held from 1971
through 1976 were quite successful in help-
ing mathematical programmers in the New
York area keep in contact witi one another
k ieep abreast of advances in the fie ld.
1 there have been a number of new and
interesting developments in mathematical
, since 1976..."
I first in the new series of meetings
was held on February 4, 1-'".., at the City
University Graduate Center iln Manhattan.
W.C. Davidon of Harverford College spoke
on "C..,.', ,1. Directions for Conics."
Jorge Nocedal of the Courant Institute of
'Mathematical Sciences ( .. York Univer-
,ity) followed with another view of tile same
opic. Other recent meetings were Friday,
larch 5, I'ri '.. "Truncated Newton
Methods: Thursday, April 1, R. Bland:
"Vlinty Coloring and0 Linear P.....r ..ii.. ;
quality:" Friday, May 7, M. Grigoriadis:
"Primal, Dual, and Parametric Network
Simplex Algorithms." Write Professor Gold-
iiarb to be included in the mailing list of
The Mathematical Programming Soci-
:ty wants to encourage the development
ofl local .... Ii. of this kind. If you know of
suchi an existing group. or could use the
ty's assistance in forming one, please
,.act the Chalirman of tile executive
Committee: Dr. A.C. Williams, Mobil Cor-
poration, 1.50 East 42nd :,.. i N New York,
New York 10017, U.S.A.
!,I'l,1. Wolfe

A Nordic Symposium
Complementarity Problems a
Areasas s held at the histitu
..1 I.. I;i .. ; Sweden.
In the list of participate
approximately 60 names, one
names like A.W. Tucker, H. Ku
andi several others from the
from Europe, and even one ea
I. and ( .
Besides the sessions on X)I
1 .i variational .,, 1' ." .
point theory, there were sessi
vexity and duality and on I, i
rati: ... ;

on Linear
nd Related
te. of Tecl-

its, holding
could find
uhn, V. b -
U.S., many
clh from tlhe

and fixed
o011 oIn on-
.. and quad-

Ipoti request, tihe organizer Dr. Per
Smeds at tle department of Mathemaltics
will send a technical report with "Ex-
tended Abstracts" of the ,1l
I ,I conference was sponsored by 'Tlie
National Swedisli Board of Technical I)evel-
opment (STUi), Nordiska Forskarkurser
and I I. Swedish Institute of li
jlohan Philip


The: Optimization Days .'* were
held at the Ecole des Hautes Etudes Com-
merciales (I .... i School) on tile campus
of the Universiti de Montral, May 13 and
14, 1982. It was the tenth anniversary of
this annual meeting that grew from a local
.. i;. to one including speakers from all
parts of Canada, United States, Latin Amer-
ica, and Europe. There were more than 185)
participants, and( more than 90 papers were,
presented. Four plenary sessions were also
organized with the i.ii..- i, speakers:
Austin Blaquiere, Jean-Louis Coffin, Tom
., i:,u.n, ;: and '1..1. Sain. I in event is
sponsored by II I Control Systems Soci-
ety, Association Canadienne-Francaise pour
I'Avancement des sciences, SIAM, Mathe-
matical 1'.... ..i i. ;, Society, and Socift:t
Caiadienne de Mathimatiques Appliquies.
We gratefully acknowledge tie financial
support of the Ministere te e'Education du
Quebec, the Natural Sciences and Engi-
neering Research Council of Canada, and the
Social Sciences and Humanities Research
Council of Canada.
Next year tile Optimization Days
I' :.. will be held at the Ecole Polytechniq ue
(Engineering School) on the campus of the
University de Montreal, May 1.983.
-Jacques A. Ferland
President, Optimization Days 1'":.'

number of invited and contributed papers
and the 23 plenary state-of-the-art tutorials,
we are forced to start very early (8:15 am)
and work very hard until 6:15 pmn. '' hope
that the boat trip to Linz up the river Rhine
and back will provide the necessary relief
from the stress of tile days before.
The concert on Tuesday evening will
also give you a chance to relax while lis-
tening to the Baroque IiEnsemlble of the
(..il .,11 i. Musicuml of thie university of
Bonn. presenting (;alrieli, Frescolaldi,
Fasch. lHandel, Boisniortier and Bach.
During the buffet dinner at the recep-
tion in thile lheinisches Landesmuseum
on Monday evening you will have the
opportunity of meeting all your friends
within tih Mathematical Programming com-
munity and ,i...L' the outstanding ex-
hibits of the museum.
All events of thle meeting (except the
reception on Monday) will take place in the
main building of tlhe University of Bonn.
which is the former residential palace and
the hunting lodge of the archbishop of
We recommend that you take the
opportunity to discover some of t.he beau-
tiful places Honnl has to offer. BHoin is a
1913-year-old city with an eventful history.
The social program 11 guide you to some
of the most interesting places.
All members of tdhe .,.. i :-. conm-
mittee will ibe happy to answer your ques-
tions and help you to overcome technical
problems. I'. i.. do not hesitate to contact
them (you may identify the members of tile
organizing staff by a red dot on the name

Achim Bachel m
Martin GriZtschel
Organizing Committee

Bernhard Korte
S Co mmnittee

0" i Il'

Newsletter of the Mathematical Program-
ming Society
Donald W. Hearn, Editor
Achim Bacherm, Associate Editor
Published by the Mathematical P... i.. i, i;i,.
Society and Information Services of the
College ofFI ;... 11, University of Florida.
Composition by Lessie McKoy, and Mech-
anical Production by Dick Dale.

*'. o. :1 i 4. W '.
7; I '
A rat

i. ii. Optimization Laboratory
Department of Operations Research
Stanford, CA 94305

T.C. tIl and M.T. I 'n- "Multi-Terminal 'Flows in Outerplanar
Networks,' Sol 8-19.
It.W. Cottle, "A'pplication 'of a Block Successive Overrelavation
Method to A (Closs of' (Costrained Matrix fPoblems,'" Sol 81-20.
C.A. Tovey, "Polynomial Local Improvement Algorithms in Com-
binatorial Optimization. "Sol 81-21.
S. T McCornnlick "Opitimal Approximtion of Sparse H1essians and
its Equinmlence to a (raph Coloring* Problem, Sol 81-22.
j,.11. Friedman and M.H. 1 "An Adaptiue Importanct e Sarm-
, Procedure," Sol 81-23.
I.J. Latond, "On the Deterministic Production ,I ... Problem of
a La rge Hydroelectric System, "Sol 81-24.
P.E. Gill, W. Murray, M.A. Saunders, and M.1. Wright. A Pro-
cedure for Computing .' ... ...', I. ..'.. Intervals for Nmnerical Opti-
mization, "Sol 81-25.
G.li. I)an[tzig, "The Pilot lnergy-Elconomic Model for Policy Plin-
ning," Sol 81-26.
G.I. Dantzig, "Concerns About Large-Scale Models," Sol 81-27.

Varennes, Quebec, Canada

M.A. Hanscom, J.-J. Strodist, ... . Van Ilien, "Une approche de
Type Gradient- Rliluit en Optimization i. i i.. ...... Pour
I'ordonnanrtment Mloyen Termle de La Production ', 'electriqlue
danrs un Systmne de Production Mixte," Rapport No. 2427.

Department of Industrial and i in.- ,' ., '- I ,..
303 Well Hall
Gainesville, FL 32611

D.W. Learn and J. Vijay, "A Geometrical Solution for the Weighted
Minimum Circle Problem," 81-2.
R.L. Francis and T.J. Lowe, "Tlhe District Cover Problem on a Tree
Network," 81-1.0.
T.J. Hodgson, "On the Pallet Loading Problem, 81-11.
B.C. Tansel, R.L. Francis and T.J. Lowe, "Location on Networks:
A Survey," 81-12.
H. Hamacher, "Decomposition of Group Flows in :. 'i.,l Mat-
roids," 81-13.
I.W. Hamacher, "Min Cost Tension,"81-14.
S. Tufekci, "A Decomrposition Algorithm for Shortest Paths in a
Sparse Network," 81-16.
M.L. Chen, R.L. Francis and T.J. Lowe, "P-Centers on Bitrees,"
M. Toledo and S. Tufekci, "A Comparison of Decomposition
Algorithms on Shortest Path Problems," 82-2.
D.J. i I n i. and D.W. Earn, "On .r..r. .r Rules for Facilities
Location !l ..,-,,i,, ,"82-3.
D.W. Hearn and S. Nguyen, "Dual and Saddle Functions Related to
the Gap Function," 82-4.
H. Hamacher and S. Tufekci, "A Lexicographical Time-Cost Trade-
off Problem, '82-7.

Econometric Institute
P.O. Box 1738
3000 DR Rotterdam
The Netherlands

A.K. Lenstra. J.K. Lenstra. A.H.(;. Rinnooy Kan and T.J. Wans-
beek, '"Two Lines Least Squares, "8104/0.
C.L. Momnna and A.iH.G. Rinnooy Kan, ',, Solmble
Special Cases of the Permutation Flow-Shop Problern, "8 105/0.
i. Lageweg, E.L. Lawler, t I Lenstra and A.H.G. Rinnooy Kan,
.... r Aided Complexity .. .. of Combiunatorial Problems,"
Lageweg, E.L. Lawler, J.K. Lenstra and A.H.G. I ... Kan,
"Computer Aided Complexity lI., ,i. ..I of Deterministic. i I,.Ir
Problems." 8109/0.
W. Kribbe, "Nonlinear Programming I!. ii.,'s' Using Conjugate
Directions in Reduced Dimensions, "8110/0.
..Carlier and A.H.G. Rinnooy Kan, .,,. .t ,- .... to Non-
renciwable Resource Constraints," 81 12/0.
M.A.I1. Depster, M.L. Fisher, I L. ier Janse.n, Lageweg, II
Lenstra and A..G11. Rinnooy Kan, I..i of Heuristics for Stochastic
........... Results for Hierarchical .i,,, Pro blcems," 8118/0.
W.I1. van Darn, J.B.C. Frenk and J. Telgen, 't ... .... (Generated
Polytopes for Testing Mathelm tical i, ....I....., ..., ,... 8 '0.
M. ilendriks-Baardmnan, "Alternatives to the Simplex Met. )f
Linear programming, 121/0.
R.T'h. Wijrienga and G. van der IHock, "Linearly Dependent Actitx
Constraint Normals in Nonlinear Programming, "'8125/0.
M.L. Fisher, I Lageweg, J.K. Lenstra and A.ll.G. Rlinnooy Kan,
.... I. !, Relaxation for Job Shop -. i,. I' n .." 81 27/0.
E.L. Lawler, J.K. Lenstra and A.H.G. Rinnooy Kan, "Recent
Developments in Deterministic ir....... and .' *,,i'.. A Siurvey,"
E.L. Lawler, J.K. Lenstra and A.I. G. Rinnooy Kan, "At in the
Fields of. i,. .I1,,, I Theory," 8203/0.
J.T. Postmns, A.I.G. Rinnooy Kan and G.T. Timmenr. "Anl* i' .
Dynamic Selection Method, "8207/0.

College of Business and Management
College Park, Maryland 20742

(;olde an d Assad, "An Analytic Framework for Comparing
Heuristics," 82-002.
Gass, "What is a .., ior.. I..... Mathematical Model?" 82-003.
Bodin and Sexton, "The Multi-Vehicle Subscriber Dial-A-Ride
Problem," 82-004.
Gass and Parikh, "Credible Baseline Analysis for Multi-Model Public
Policy Studies," 82-006.
Dror, Wasil, Golden and Assad, "Comparing Forecasting Methods
Using an Expected Utility Approach," 82-009.
Stewart and Golden, "Stochastic Vehicle Routing: /I (. '-
hensive Approach," 82-010.
Assad, Yea and Golden, .i.t.,.t leI'a.. in Team competitionss:
I r. and Cromputational Results, "82-011.
Stewart and Golden, "A Lagrangean Reltxation lHeuristic for
Vehicle Routing," 82-012.

Voiume 2; 3 N 2

Vtiinnit': 23: No. 2

V. Griffin, J, Araoz and J. I'dmnonds, "PIolyhedral Poklrity 1 I..1
by a General Bilinumr Inequality. "
1B.C. Eaves and R.M. I'reuind, "Optimal '..'. of kalls and Poly-
hedra. "
'T.. Elkein. "Combining a Path Method andand Parametric Linear
Prograimmiing for the Computation of Competitive Equilibria. "
A.C. Ilo, "Worst iCase Analysis of a Class of Set Covrin /
tourist ics. "
RI) I) overspikc. "Somer Pe/rturbation Results for ti Lini'ar Com-
plinentarity Problem.i
I.-P. (Crouei? and J,.A, Irland. "Criteria for Quasi-Convexity
and selndo-C nn(m ily: ,' .. ... and (Comparisons. "
K.G. M uri and Y. Fathi, "A Critical Inde'x Alfgrithm for Nearies
Point Problemts on nt I ..I I Conets. "
M. (Gaudioso and M. F. Monaco, ".1 fBndhile Typ Approach to 1the
Unconstrained Minimization of ConM'x Nonsmooth Functions."
.E1. Burkard and I, Fincike. "On Random ()uadratic lBotlmneck
4ssi4nmtiient Problems. "

Volume .- No. I

(, IDebru and T.C. Koopmans. "Addilively ])ieomposed F'unc-
tions. "
L.Mcl.itLindl "Polyhedral IExtensi.os of Some 'Th'iorinms of Linear
Ilogramming. "
J.Hi. iMayv and iL. Smitl, "Random I'lytopes: Their I' .I.-
C(eneration, and Alggrpeate IPropertie's.,
J.K. lteid. "A ...i I oloiting iVariant of the B]artels-(olub
Decomposition for Linear Pogranmming Bases. "
A. Ben-Tal arli J. Zowe, an . . Optimality
Conditions for a Class of Nonsmtooth Minimization Problems.'
k.1i. Murphy. 11.1). Sherali and A.I. Soyster. "A Mathel atical
...... Approach for Determinini g 'I' i i i. Market Iquilil-
M.. Dyer and J,. Walker, '... t he Subproblemn in the
Lagranaian Dual of Separable Discrete Programs with Linear Constrain ts."

Voliumi 23 No. 3

C'. llair and l/.(G. Jeroslow, "Tho Value uiinction of an Intet'er
Program. "
l.Fiourer. ".Solvinii Staircase Lineiar Pro/irams by the Simplex
Method, 1: Invi'rsion."
tHerman, "hlynamically ]estricted ;. in thr Simplex
Mellithodfor Linear Programnmig., "
i,. Naarethi and J, Nioctdal. "Conijugate Direction Methods wiith
iblt .
I" T. Ichiiiori, 11. Ishii and T. Nishida. "Optimal, ...
P.E. (Gill. W. Murray. M.A. Saundcrs anid VW.11. - ih "A note on a
C ,riterion for a Non-lD riti ive . . troced-

S. Agarwal, PSharma and A.K. Mittal. "An Extension of the Efdge
Covering Problehnt, "

S- I L
-. $.. . -

Practical Methods of Optimization, Vol. 2: Constrained Optimriza-
tion. R. Fleleher. 1981, 224 pp., S31.25, John .
Generalized Cotncaity in Optimization and lEconomics, edited by
Siegfried Schaible and William Ziemnba, 1981. 767 pp. S455.00. Academic



I hereby enroll as a member of the Society for the calendar year 1982.

S..'.. address

My subscription to Mathematical Programming/ is for my personal us" and not for the benefit of any library or other institution.

I, *'" -

The dues for 1982 are:
40 Dollars ( U.S.A.)
20 Pounds (U.K.)
71 Francs (Switzerland)
200 Francs (France)
84 Marks (Fed. Rep. (ermany)
93 Guilders (Netherlands)

Pleasse snd this .i~ ,'l .. with your dues to:
The Mathematical ... ....'.ii Society
%The International Statistical Institute
428 Prinses Beatrixlaan
2270 AZ Voorburg. Netherlands

"i.i ; ',;!- .-i-:.-- D)ues are one-hafl the above rates. Have a faculty member verify your student status below and send
.iT .. 1' ''. to. : Professor John i I School of Engineering and ,. ii Science, Princeton University, Princeton,
N.J. 08544.
Faculty verifying status Institution


Thomias L. I1 iin (I; (1.I.1.) will i the inew editor of operationss Hiesearch, effective
Janiar\ I . Ronald Rardin (Georgia Tc(-i) will visil Puirl during 1982- ..
Mokhtar Bazaraa (Georgia TeIch) II lhe on leave in 1982 :' at Hurnham Van Lines, . Don
Goldfar. formerly of Cit y Colleg of New NYork, has accepted a position as Professor
of Industrial Iitineerint and Operations Research at Columbia University starting July 1,
1" ..' . Jack Ednmonds (\aterloo) will visit Cornll during l" '- . L. Lovasz (Sze'ed)
visited Cornell in May as. Andrew 1). ','. i.. Visiting Professor and will return fo(r on to two{
w'eks it each of the next five years . I. n May, Herbert Robbins ( nColumia) save thei
second Anlnual lecture Series holoring I).' Fulkerson at Cornell . Sauil (;ass (lar-
land) has conmnmtnicated news of the deathl of Dr. 1. .h. W. Jacobs, formerly associated with
I ,Al' ', ;. I SCOO()P which originated the theory of liner pro"granmming and developed its
first applications. )r. Jacobs, in particular, formulated the caterers problem (jet enrine
replacement mIodel) and the parametric objective funclioni problem.

Deadline for the next issue of 01 I I I ', is October 1, 1982.

._' ...... Alex Orden (Chicago)
bheen elected to the Chairmanship of
Society for the three year period beginning
August II A. C. Williams ( I..I.1) ;i be
treasurerr Ior the( sanme period. New al-large
Council members are E. M. L. ,1 (S(Cl-
(CO(I), jean-LoLuis Goffin ( I ;ill), Donald
Goldfarb (Coulnhia). and J. K. ILenstra
( I, 111...... ir i Centrumn ). (Council ternswill
begin August. 1982. at the Hiontt Sympo-
sium. and are for thre years.

: 1 DENT N11! 1 hI' ;

By recent action of the I" Council.
stulldent niclmlbrships arc lnov, availabIlc.
)iuei for students are one-half the regular
inmenlmbership dues, and l.e student member-
ship includes all rights and ,..,, I. of
re-/ular mienmcrshlip exceptT voting rights.
Included are subscription to the journal and
to Optima. An application form is included
in this issue. Applications (for students
otly) must o e sent to John Mulvey, ( 1 ..
man of the Membership Committee, at It,(
address given.

303 Weil Hall
College of Engineering
i 'ni'-.! i!o of Florida
Gainesville, Florida 32611


This public document was promulgated at a cost of $426.15 or
$0.61 per copy to inform researchers in mathematical programming of
recent research results.


Results of the 1982 Questionnaire

The 1982 Questionnaire was published in the issue of OPTIMA dated March I'"' By June, 1982, members
had returned 49, which are tallied below.

1. Normally the 1985 International Symposium on Mathematical Programming would be held in North
America. There has been some discussion of holding it in Japan, but there is concern about the travel
cost for many of our members. Would you plan to attend the Symposium if it were held in --
Japan: Probably yes: 25 Probably no: 22
North America: Probably yes: 47 Probably no: 0

2. The activities of our Society are expanding and we would like to invite interested members to become
more active. Please check those areas in which you might like to participate: Publications Committee,
Membership Committee, Committee on Algorithms, Establish new activities, Editorial activities,
Administrative, and Other.
Nineteen members responded of this question and we appreciate the interest expressed by these
individuals. Their offers of service have been passed on to the appropriate Officers of the Society for

3. List subjects, if any, whose emphasis in the journal you would like changed.
Give more emphasis to:
Applications (9), Computation (5), Stable Numerical Methods (2), Software (2), Nonlinear Program-
ming (2). One mention each for: Theory, Combinatorics, Book Reviews, Short Communications,
Surveys, Global Optimization, Game Theory.
Give less emphasis to:
Theory (4), Unsupported Algorithms (2), Optimality Conditions (1), Graph Theory (1).

4. If you have submitted an article to Mathematical Pir.lmiiiin' in the last two years, how did you find the
response time?
Excellent: 2 Good: 5 Fair: 8 Poor: 8

5. Do you think the Society should sponsor a new journal devoted exclusively to applications and systems?
20- Yes 25 -No
Assuming reasonable cost, would you subscribe to it?
27 Yes 12 No

6. What features would you like to see added to OPTIMA?
Software News (4), New Book List (3), Problem Column (2), Letters to Editor (1), Employment
Information (1), Contents of Relevant Journals (1), Applications News (1). (Eight members commented
that OPT-Ii was doing a great job.)

List here any services or activities that the Society is not providing that you would like to have, and any
other comments:
Information about the winners of the Dantzig & Fulkerson prize and the relevance of their work either in
OPTIMA or the JOURNAL, algorithm distribution service, package deal for the JOURNAL and the

Compiled June 15, 1982
By the Executive Committee

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