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In this paper. we address the backlog sequencing problem in a flow-shop
CON\VIP
production
conlrol
conlrolled by a
system with the objective to mini mise the makespan We
characlerise the problem and analyse its similarities and ditlerences with the permutation
110\\-shop problem
A comparison of same well-known
and a simple and fast dispatching rule is proposed
heuristics.
the proposed
rule
Regarding the more simple and laster
outperforms
those commonly
used für the
problem!
permutation flow-shop
Key\vords:
dispatching
flow-shop heuristics is carried out.
Scheduling, Sequencing, Flow-Shop. Constant Work in Process (CONWIP).
Heuristics, Dispatching Rules
ZUSAMMENFASSUNG
In diesem Arbeitspapier wird das Reihenfolgeproblem fur die Einsteuerung von Aufträgen in
ein Fenigungssystem
(backlog
wenn das System durch
(CONstanl
sequencing) bei Reihenfenigung
eine 'Konstanles
Work In Process = CONWIP)
rung der maximalen Durchlaufzeit
rakterisien
Seine Ähnlichkeiten
Reihenfenigung
mit konstanter
Shop) werden analysien
Arbeitsvolumen
gefuhn wird
(Flow-Shop)
in der Fenigung'-Steuerung
Als Zielfunktion
(C...J angenommen
behandelt,
wird die Minimie-
;
und Unterschiede zum klassischen Reihenfolgeproblem bei
Auftragsfolge
auf allen Maschinen (Permutation-Flow-
Bekannte Heuristiken fur den Permutation-Flow-Shop
werden auf
den CONWIP-Flow-Shop
übertragen und verglichen
regel wird vorgeschlagen
Wird diese Regel mit einfachen und schnellen Heuristiken fur den
Permutation-Flow-Shop
!
Das Problem wird zunächst cha-
verglichen.
Eine einfache und schnelle Prioritäts-
schneidet sie in Simulationsuntersuchungen
besser als
letztgenannle ab
1. Introduction
The production
control
system CONWIP
-acronym für CONstant Work In Process-
(Spearman el '1/. 1989) is a pull system thaI appears to share the benefits of Kanban while
being applicable in a wider range ofsituations
The key poinl ofCONWIP
is that it does not
limit the single station's WIP or its butTer size, hut the total WIP in the system Several
studies (eg
Spearman el al. 1989, Lambrecht and Seagert ]990. Chang and Yih
Gstettner and Kuhn
1996. and Bonvik
"I al.
1994,
1997) indicate thaI in certain production
scenarios. this conlrol system is prelerable to others
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011 Ihis general CONWIP
sequencing problem, very litlle
work has been reportcd
I)lll:nyas
(1994)
sludies Ihe most suilable dispalching rules tor a CONWIP
nel\\ork
queues
TarditT (1995) designs an MRP-C based Iramework
lilIe by USillg
tor sequencing in a
C'ONWIP system Finally, Herer and Masin (1997) lormulate a mathematical programming
version of the problem of sequencing the back log in a CONWIP
of minimising
system with the objeclive
total costs
In this paper we address the backlog sequencing problem in a CONWIP
CONWIP
framework
described by Spearman I!f al (1990).
sincc Ihe back log is generaled by an MPS (Master
accoum customers demand. so the composilion
Ihe production
period
system in Ihe
sequencing is a slatic issue,
Production
Schedule) taking imo
of the backlog is known at the beginning of
It is supposed thaI the number of cards to be employed in the system
has beeIl fixed within the previous WQS module. and thus there is no way to schedule the
emrance of jobs into the system once the jobs are arranged in the backlog This means thaI a
.job in the backlog will enter whenever there is a card available given it has been sequenced
first in the queue in front ofthe system.
In Ibis context, a plausible objective für sequencing the backlog seems to be minimising
the makespan because:
(I) Meaning ofthe backlog in a CONWIP system: thaI is, the set ofjobs
to be processed within
the next production
assigned to a specific job, the completion
priorities
period
thaI are going
Thus, unless a high priority
is
of all jobs is a major issue If different
are assigned to the jobs. a relevant objective could be minimisation of the
weighted tlow time
(2) According
to Schonberger
(1984) and Spearman I!f al. (1990),
period für a pull system in general -and particularly
be divided
into a regular production
the production
für a CONWIP
system -must
time in which the production
quota can be
achieved and a catch-up time which provides a time-buffer to reach the production
quota if, due to unforeseen circumstances (eg
materials),
machine breakdowns or lack of raw
it cannot be accomplished within the regular production
time
Usually,
the catch-up period is used für housekeeping, preventive maimenance, etc In this
context, makespan minimisation
has the effect of ensuring the production
be reached within the regular production
basis für a reduction ofthe
time On the long run, it also provides a
regular production time and für shor1eninglead limes
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illlermcdiale
butrers) and the zero or no-wait sequencing problem
In the two lalter Ihe
iJllermediate butTers are zero, but the no-wait sequence problem is even more restriclive in
the sense thaI the staning time of a job on the first machine has to be chosen such thaI the
job does not have to wait für its processing on any machine The unconstrained sequencing
problem has been studied extensively, and a good reference für zero and no-wait problems
is pro\ided by Hall and Sriskandarajah (1996)
Ht1we\'er, the intermediate case in which butrers are different from zero and not infinite
has been addressed by relatively
Cunningham
Logendran
1975, Reddi
despite it is considered
(Wismer
few researchers für very specific purposes (Dutta and
1976, Papadimitriou
and Sriskandarajah
and Kanellakis
J993, and Sharadapriyadarshini
1980, Leisten
and Rajendran
the most realistic situation in many manufacturing
1972, and Reddi and Ramamoonhy
considered in principle
-
(o be more difficult
1972)
1990,
} .'
1997),
environments
Besides, this type of problems is
than the extreme cases (Mon on and Pentico
1993)
With the exception
of Dutta and Cunningham, who develop a dynamic programming
procedure to generate optimal
solutions with the objective of minimising
completion limes for the two-station
the maximum
problem with limited butTers, the rest ofthe papers are
mainly devoted to the development ofheuristics
für the problems
Maybe the most complete work in this direction is done by Leisten, who compares
several
heuristics
für
the
m-station
flow-shop
sequencing
problem
with
different
intermediate buffer sizes The tested heuristics include buffer-constrained specific (including
Dutta and Cunningham,
Reddi, and Papadimitriou
and Kanellakis and two new heuristics
suggested in the paper) as weil as F .,LormuIC""" heuristics
heuristic (Nawaz
It turns out thaI the NEH
ef GI. 1983), employed foT the unconstrained buffeT problem. performs
weil according to the objective of minimising makespan. These results suggest thaI same
well-known
F..lvrmIIIC
, heuristics
may be suitable also für the CONWIP
problem. which is connected to the buffer-constrained
sequencing
problem with respect to regarding
buffer capacities within the system However, in contrast to fixed buffer sizes between each
two machines, the CONWIP
problem supposes a fixed number of jobs within the entire
system being either processed on a machine or waiting for their next operation
3.
The structure
of the problem
To obtain a first insight info the CONWIP-problem,
the empirical distributions
of all
possible makespans obtained by complete enumeration of I 000 instantes of seven machines
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patterll~
For instance, the CONWIP
six cards curve nearly lits the Ilow-shop
makespan
di~t ribution
However,
second pattern
jobs
from a practical
out look it seems there should be a focus primarily onto the
thaI is when the card count is neither very low nor close to the number of
The first problem
is easy to salve and even a 'bad' sequence does not have as much
impact on the system performance
For the laffer case, we can use numerous techniques
developed für the F;'!fJrmIIICmn., problem
additional problem
Besides of discussing the second pattern itselt: an
therefore arises from determining the borderline between the second
pattern. ie the 'real' CONWIP-problem,
and the third pattern, ie
.
,
1
li .
the ordinary permutation
tlow shop case
150
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ftow-shop
CONWIP -2 cards
CONWIP -3 cards
---CONWIP-4cards
-CONWIP.5cards
,
'.
900
1100
1300
1500
makespan
Figure 2: Empirical
In figure 2, the distributions
are shown
The distributions
distributions ofthe optimal makespans
of the optimal makespan für the I 000 problem instances
are almost symmetric
While
für six cards instances, the
optimal values of the makespan coincide with those obtained für the permutation flow-shop,
the situation is different when the number of cards is lower
A more exhaustive analysis by
inspection of the vectors of the optimal job sequences confirms thaI these vectors, within
this small numerical
problem,
study, are identical für the six cards problem and für the flow-shop
and almost the same in most of the instances of the five cards problem as
compared with the flow-shop
problem
However, the analysis reveals thaI, in general, the
vl:ctor of the optimal solutions für two, three and four cards are different as compared with
thosc obtained für the ordinary permutation flow- shop case
8
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1970, arId Dannenbring 1977) In
lolal, (he tesl-bed contains 180 instances
The tested heuristics are those due to Palmer (1965), Gupta (1971), CDS (Campbell el
"i
1970), RA or Rapid Access (Dannenbring 1977),and the previously mentionedof NEH
Thc Ihree latter perform makespancalculation in several consecutive steps, so the card
numher limitation must be explicitly laken into account We will call them CONWIP-CDS,
CONWIP-RA and CONWIP-NEH to indicate thaI in the evaluation of partial schedules,the
!,.'
available number of cards has beenlaken into account For the Palmerand Gupta heuristics,
,.i
no specific adaptation is required, since both are based in the construction of indices, taking
;':
into account exclusively the processinglimes of thejobs.
Besides the above mentioned heuristics, we also test the PF (Profile Fitting) heuristic,
introduced by McCormick et al (1989) and proposed in Pinedo (1995) für the flow-shop
with limited intermediate storage problem In this heuristic, the first job of the sequenceis
the one with the smallest sum of processinglimes This job generatesa ~
determined
by ils departure limes from every machine The next job to be sequencedis chosenamong
the remainingjobs in order to fit the profile ofthe previous job (that is, to minimise the idle
and blocking time in the machines during the processing of this job) The procedure is
repeated until all jobs are arranged This heuristic has been also adapted für a CONWIP
system in the calculations of the profiles of the jobs taking into account the availability of
cards,so in the following it will be namedCONWIP-PF.
T 0 compare the relative efficiency of the heuristic, an upper bound of each instancehas
beeIl found by long runs (about 10 000 objective function evaluations) of a standard
simulated annealingalgorithm The quality of the solutions is representedby the percentage
deviation of this upper bound In table 1, the mean percentage deviation from the best
known solution of each type of problem is presented
The results shown in table 1 reveal that the NEH heuristic is by rar the most suitable
among the tested heuristics. The poor performance of the CONWIP-RA heuristic is
.,
'~.
surprising to a certain extent, since it is usually considereda rather suitable heuristic für the
FmVJrml/IC..,.,
problem when short computation limes are required (Taillard, 1990) This
reinforccs the idea al ready expressedin section :; thaI suitable methodsfor the f;"VJrmlllr.."
problem may not work weil für f;"lcCJllwip!('"""
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;
Thcrcll,re,
also 1'or the CONWIP-problem
performance of the CONWIP-NEH
setting it can be analysed whether the excellent
heuristic is based on the large number of evaluatiolls,
tlJe initial sequence of jobs generated in phase one, or on the combination ofboth
Therefore,
in an additional experiment, we try to evaluate the contribution
of the initial
order of jobs to the CONWIP-NEH
heuristic's performance To do this, we have run the
('ONWIP-NEH
heuristic's phase 2 star1ing from a randomly generated initial order of jobs,
replacilJg the initial order generation according to sums of processing limes
I
'
The results
indicate to what extent the final sequence in a NEH heuristic is caused by the initial order of
.,
the jobs (phase I) and how much is due to the evaluations of the par1ial sequences (phase
., r
2)
.1
Problem size
IIlm/N"r
10/10/IJ5
CONWIP-NEH
NEH
4.619
9136
6.452
10/10/08
1919
2997
2553
15/10/05
7.U7"
16115
8172
15/10/08
6175
13.353
6267
1;/111/10
1;/10/12
4251
3811
;8;9
3811
4339
4.587
20/10/10
5683
IU 845
5573
20/10/15
5523
;523
3608
20/10/18
;.;23
;;23
3608
i
311/111/10
;57;
8843
;941
i
311/111/2"
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3518
4670
3U/I0/2;
3;23
3.;23
4675
2837;
36753
30641
20/20/1;
13.7;2
21.832
14697
20120/18
10.165
10.207
10.545
311/20/10
6704
13093
8.034
30/20/20
3 746
52%
4620
30/20125
3;18
3518
4309
Mean:
6.858
9.986
7,-105
20/20/10
Table 2 Mean percentage deviation ofthe
RANDOM-NEH
i
:
~
best solution für the heuristics
~
t
..
Besides, the NEH
permutation tlow-shop
heuristic is by rar the best constructive
sequencing problem (Taillard
heuristic known
für the
~
1990), although its main shor1coming
is the time required to arrive to the solution. compared with other heuristics This is because
the NEH heuristic is O(/? m), while Gupta's. RA and Palmer's are O(lIlog(lI)
CDS is 0(11 m2 + m 1110g(lI) )
As mentioned before, in CONWIP
+ 11m), and
sequencing, it is not
12
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Note thaI this can be achieved by placil1g the shortest proces~ing time job at the
beginnil1g of the sequence or at the end Col1sequently, two possible s~quences might be
originated
in this manner. beil1g one the inverse of the other
In the proposed 'Centre'
dispatching rule, we evaluate both of them al1d we chose the one with the best value of the
makespan
For instance, if the ascending order of the sums of their processil1g limes of a cenain
problem instance with six jobs is (1,2,3,4,5,6),
schedules (1,3,5,6,4,2) and (2,4,6,5.3,1)
the results of the di~patching rule are the
-.
The rationale für this procedure is as follows
in a CONWIP
system it is imponant thaI
the jobs entering in the first places have a shon processing time, since the cards thaI are
1
"
-J
attachcd to them must be used für funher jobs This is a critical condi\ion für the first jobs,
since a delay of the first jobs is propagated along the sequence On the other hand, entering
the jobs with higher processing times at the end causes the makespan 10 be enlarged, and
most of the time gained within processing the first jobs is spoiled by large processing limes
at the end of the schedule
Thus für a CONWIP
system, the location of a job with high
processing time is less harmful with respect to the makespan of the sequen~.if
middle ofthe
sequence.
,IlIlIfNT
Palme.
C.:nl.e
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10/10/115
Gupta CONWIP.RA
it is in the
14849
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Taille 3 Mean percentage deviation ofthe
14
gIRO
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best solution für the dispatching rules
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might bc seen as a contirmation
dillcrent
thaI 1'..,VJrmlll( '..." and 1';'It.'/J/lwipl( '...:, are, in general,
problems, as it is derived from the results obtained in section 3
As lar as simple heuristics are concerned, CONWIP-RA
to ofter very good
clearly outperformed
the behaviour
results with short computation
by the other heuristics
of the NEH
heuristic,
heuristic, which is considered
limes in the I'~,v)rmlll( '..." problem, is
For more elaborate heuristics, it appears thaI
which
otTers the best results among the tested
heuristics, is partly due to the numerous partial evaluations of sequences, and partly due to
the fact that same problem instances are not WIP-constrained
..
Finally. a simple dispatching rule is devised for the CONWIP sequencing problem This
rule has proven to be panicularly
suitable for those instances with lower card count
I
In
-t
these situations, the rule also clearly outperforms the more common fast heuristics used for
the F;'VJrmIIIC""" problem
The study presented here can be extended detinitely: As rar as the relation of n, m and
NT as weil as the structure of the processing limes are concemed, the border li ne between
simple flow
shop behaviour
of a problem
relevance of the CONWIP
constraints
dispatching
the CONWIP
developed
rules exploiting
or a problem instance respectively
can be explored
problem
Additionally,
and the
heuristics
and
structure in more detail might be
We plan work on these aspects However, the study presented here gives a first
insight into the structure ofthe sequencing problem ofCONWIP
problem settings
References
Berkley, B. J., 1992, A review of the Kanban production
Prcldllction and Operations Management, I, 393-411
control
research literature
Bonvik, A M, Couch, C, and Gershwin, S, B, 1997, A comparison of production-line
control mechanisms /11/ernational Jolln/al (1 Prod/lction Research, 35, 789-804
Campbell, H G, Dudek, R A, and Smith, M, L, 1970, A heuristic algorithm for the n-job,
m-machine sequencing problem Management oS'cience,16, B630-B637
.
Chang, T M, and Yih, Y" 1994, Generic kanban system for dynamic environment
Intemalional.fo/lrnal
0/ Prod/lction Research, 32, 889-902
Dannenbring, D G" 1977, An evaluation of flow-shop sequence heuristics ManaXl!nlel/1
~;
St.'il!nt.'e,23,1174-1182
Dar-EI, E M, Herer, Y T, and Masin, M, 1992, CONWIP-based production lines with
multiple bottlenecks
performance and design implications Technical report, Israel
Institute ofTechnology,
Duenyas, 1,1994,
Haifa, Israel,
A simple release policy for networks ofqueues with controllable
input
O,Jeralic)/l,\" '~e,\"l!arch, 42, 1162-1171
Dudek,
R
A,
and Teuton,
0
F,
1964, Development of m stage decision
rule for
scheduling n jobs through m machines (J,Jl!rat;c)/l,\"l?e\"l!arch, 12, (3)
16
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I{.:ddi. S S. and I{amamoorthy. C V, 1972. On the flow-shop sequencing problem with
no wail in process ()IJt!ratilJllal'~ex('ar('h
<!'Iar/erl>', 23, 323-331
I{ccves, (' I{, 1995. A genetic algorithm for tlowshop sequencing ('vmIJllter' ()per(l/itlll(11
1<"""11"', 22, )-1 ';
Schonberg.:r, I~ J, 1984, ~I/vrhl .Ia.'" m(l/IlljiIL'/llril"l,': /he le.\:'lIlIX llr ,impliL'I/) , appl;,'J
(NY,
Thc Free Press)
Sharadapriyadarshini, B, and Rajendran, C. 1997, Scheduling in akanban controlted Ilowshop wilh dual blocking mechanism and missing operations for part-types Illtema/iV/lal
,!clllmal llf PrlJd/lc/io/l/~e.~em'ch,
Spearman, M
architecture
L,
Hopp,
W
J.
35, 3133-3156
and Woodrufl:
for Constant Work-ln-Process
0
L.,
(CONWIP)
""al/1!fact//rillga/ldOperatio/l.~Ma/lageme/lt,
1990, A hierarchical
production
control
..
system~, :JlI//mal llf
2,147-171
Spearman. M L., Woodruff. 0 L., and Hopp, W J, 1989, CONWIP a pult alternative to
kanban fII/ema/io/lal Jollrnal 01 Prodllctio/l Research, 28, 879-894
Spearman. M L, and Zazanis, M A,
comparisons
1992, rush and pult production syste~s
issues and
OperatiO/l.5 Research, 40, 521-532
Tailtard, E, 1990, Same efficient heuristic methods for the flow-shop
l~lIrlllJt!a/l,!ll/lr/lall?f
Operatio/lal Research, 47, 65-74
Tailtard, E, 1993, Benchmark for basic scheduling
()peratilmal Re.~earch, 64, 278-285
problems,
sequencing problem
El/ropea/l
Tardiff, V,
1995, Detecting scheduling infeasibilities in multi-stage,
production environments, PhD Thesis, Northwestern University, USA
Wismer, 0 A, 1972, Solution of the flow-shop
queue ()peratiO/l.5 Research, 20, 689-697
Jol/r/lal
finite
lI/
capacity
sequencing problem with no intermediate
WoodrutT, 0 L., and Spearman, M L., 1992, Sequencing and batching for two classes of
jobs with due dates and set-up limes Jo//r/lal
l?f Prodl/c/io/l
a/ld Operativ/ls
Ma/lageme/l/,
1, 87-102
Zegordi, S.H, Itoh, K, and Enkawa, T, 1995, Minimizing makespan for flow-shop
scheduling by combining simulated annealing with sequencing knowledge E//ropea/l
Jo/trllal llf Operatio/lal Research, 85, 515-531
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1111
wail in process ()/lerOli(llloll?exeor(..h (j1(O/"lerf}', 23, 323-331
Il.ccves, C' I~, 1995, A genetic algorithm tor tlowshop sequencing
I(""'"r,"',
22, 5-11
Schonbergcr, I~ J, 1984, UI(lrl,/ L'I""
(NY, The Free Press)
('(Inllllller,
()p,'mli(l/kll
1//001/(/LI("(llril,x Ihe 1",",'(111,'(Ir ,il//pli('II)" ,'ppli,',}
Sharadapriyadarshini, B, and Rajendran, C, 1997, Scheduling in akanban controlled tlowshop \vith dual blocking mechanism and missing operations für part-\ypes /l11"/"IIOli(l/Iol
,IVIIrIIOI v( Pr(idIIClioll/?e,\"earch, 35, 3133-3156
Spearman. M L, Hopp, W J, and Woodrutl:
D L., 1990, A hierarchical control
architecture für alld
Constant
Work-ln-Process
Nlolll!(aClllrillg
OperaliO/I.\"
Mallagemelll, (CONWIP)
2,147-171 production systems, '.J(mmol v(
Spearman, M
L, Woodrutf,
kanban IIIlenlaliol/al
D L., and Hopp, W J, 1989, CONWIP
Jollrl/al
01 ProdllCliol/
a pull alternative to
Research, 28, 879-894
Spearman, M L., and Zazanis, M A, 1992, rush and pull production systelrls: issues and
comparisons Operaliol/,\" Research, 40, 521-532
Taillard, E, 1990, Some efficient heuristic methods für the flow-shop
1;;,lr(I/iL'OI/.!ollrl/al C?(Operaliol/al Re~'earch, 47, 65-74
Taillard, E, 1993, Benchmark für basic scheduling
Operoliol/al Re,\"earch, 64, 278-285
Tarditf, V,
production
problems,
sequencing problem
E/lropeal/
1995, Detecting scheduling infeasibilities in multi-stage,
environments, PhD Thesis, Northwestern University, USA
Wismer, D A, ] 972, Solution of the flow-shop
queue ()peraliol/,~ Research, 20, 689-697
Jo/lrl/al
finite
(if
capacity
sequencing problem with no intermediate
Woodrutf, D L., and Spearman, M L., 1992, Sequencing and batching für two classes of
jobs with due dates and set-up times Jo/lmal 01 Prod/lcliol/
al/d Opera!iul/,~
Mallaxemel/l,
1,87-102
Zegordi, S.H, Itoh, K, and Enkawa, T, 1995, Minimizing makespan für flow-shop
scheduling by combining simulated annealing with sequencing knowledge Ellropeal/
Jvllrllal o( Operaliol/al Re~'earch, 85, 5] 5-531
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