TELKOM
NIKA
, Vol. 11, No. 2, Februa
ry 2013, pp. 1024
~10
3
2
ISSN: 2302-4
046
1024
Re
cei
v
ed Se
ptem
ber 27, 2012; Revi
se
d Jan
uary 6, 2012; Accept
ed Ja
nua
ry 1
7
, 2013
Evaluation on Decomposition Granularity of
Manufacturing Task in Manufacturing Grid
Yong Yin*
1
, Chaoy
ong
Z
h
ang
2
, Jihon
g.Wang
3
1
Wuha
n Univ
ersity of Tech
nology, Wu
ha
n, China
2
Hua
z
ho
ng University of Scien
c
e a
nd T
e
ch
nolo
g
y, Wuhan, China
3
University of Wa
rw
i
ck, Cov
entry
,
UK
*Co
rre
sp
ondi
ng autho
r, email: Yiyng_h
ust@126.
co
m, zcyhu
st@mail.hust.ed
u
.
cn,
Jiho
ng.Wang
@warwi
ck.a
c
.uk
A
b
st
r
a
ct
T
a
sk deco
m
po
sition
is o
n
of
the
most i
m
p
o
rtant activiti
e
s
for manuf
acturin
g
task p
l
a
nni
ng i
n
Manufactur
i
ng
Grid.
Many ac
hiev
e
m
ents in the me
th
ods t
o
dec
o
m
p
o
se
ma
nufactur
i
ng
tasks hav
e b
e
e
n
obtai
ne
d. But
as for t
he
dec
ompos
itio
n
gr
a
nul
arity, the
study
an
d res
e
a
r
ch ar
e rar
e
.
Referrin
g
to
th
e
princi
pl
e of “strong co
hes
ion
and w
eak co
upli
n
g
”
i
n
the
softw
are engi
n
eeri
ng fiel
d, the deco
m
pos
iti
o
n
mo
de
l of
man
u
facturin
g task
is
bui
lt up,
in
w
h
ic
h a ma
n
u
facturin
g
task
is deco
m
pos
ed into differe
n
t
subtasks, and
each s
ubtask
is com
pos
ed of
various proc
essing
events.
On the bas
is
of the
m
o
del, t
he
constrai
nt a
m
ong
process
i
n
g
eve
n
ts w
i
thin the su
btask
s
is ana
ly
z
e
d.
T
hen the
ev
alu
a
tion
in
dex
on
deco
m
positi
on gran
ular
ity
of
ma
nufactur
i
ng
task is put forw
ard b
a
s
ed
on s
e
vera
l defi
n
itio
ns an
d eva
l
uati
o
n
steps for the deco
m
p
o
sitio
n
g
r
anu
larity of manufactur
i
n
g
task are listed. Final
ly, exa
m
p
l
e
s
to illustrate t
h
e
ide
a
of
t
he pa
per are giv
en. W
e
ho
pe
t
he w
o
rk
of
the
pa
per c
an
pro
m
o
t
e the st
udy
a
nd
ap
plic
ation
for
Manufactur
i
ng Grid
further.
Key
w
or
ds
:
manufacturi
ng gri
d
, manufacturi
ng task dec
ompositi
on, dec
o
m
positi
on gra
n
u
larit
y
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Manufa
c
turi
n
g
Gri
d
(M
G)
aims
at reali
z
i
ng
re
sou
r
ce
sha
r
ing,
coll
aborative de
sign an
d
colla
borative manufa
c
turi
ng, and
ach
i
eving the p
u
rpo
s
e
s
of
redu
cing m
a
n
u
facturi
ng
co
st,
increa
sing
re
sou
r
ce utilizat
ion rate an
d speedi
ng up th
e prod
uct dev
elopme
n
t [1].
In Manufa
c
tu
ring G
r
id, the
compl
e
tion
of a
compl
e
x ta
sk often
re
qui
res the
dyna
mic a
nd
colla
borative enga
geme
n
t of
multiple
re
sou
r
ce
node
s. Rea
s
on
abl
e an
d effe
cti
v
e plan
ning
of
manufa
c
turi
n
g
task ca
n
sho
r
ten th
e cycl
e of prod
uct d
e
velopme
n
t, improve th
e
task
perfo
rman
ce
and up
gra
de
the overall co
mpetitivene
ss of the enterprise. The de
comp
ositio
n of
the ma
nufa
c
turing
ta
sk is
on of
the
ba
sic a
c
tivi
ties fo
r ma
nufa
c
turi
ng ta
sk pl
ann
ing, in
whi
c
h
a
manufa
c
turi
n
g
task i
s
d
e
com
p
o
s
ed i
n
to several different su
b
t
asks a
c
cord
ing to certai
n
principles, and the
relations am
ong
these subtasks
are determined
to facilitate the
collaboration
among m
u
ltip
le resou
r
ce n
ode
s [2].
In recent yea
r
s, nume
r
o
u
s
studie
s
o
n
the
de
comp
osit
ion of the ma
nufactu
ring ta
sk
have
been
cond
ucted [3-7], an
d ma
ny excit
i
ng a
nd i
nno
vative achi
evements h
a
ve
bee
n o
b
tain
ed.
Their wo
rks can
be cla
ssi
fi
ed into the fo
llowing
cate
g
o
rie
s
, nam
ely [8-12]: Similarity coeffici
e
n
t
method
s; Array-ba
sed
met
hod
s; Gra
ph t
heoret
ic m
e
th
ods; Math
em
atical p
r
og
ra
mming meth
o
d
s
and arti
fi
ci
al intelligen
ce
-b
ase
d
method
s.
Their achie
v
ements ha
ve
explore
d
t
he dep
e
nden
cy rel
a
tionshi
p du
ring the
decompo
sitio
n
pro
c
e
ss of the manufa
c
turing ta
sk, th
e method
s to decom
po
se
and re
-comp
o
se
subta
s
ks; th
e re
co
gnition
and
analy
s
i
s
of
subt
a
sk cou
p
ling
a
nd de
co
uplin
g, the confli
ct
recognitio
n
a
nd its
re
solu
tion and
so
on [13
-
19],
whi
c
h
can
guide
users to de
comp
ose
manufa
c
turi
n
g
tasks into different su
btasks effe
ct
ively. Howeve
r, their
works
only dire
ct users
how to de
compo
s
e ma
nufactu
ring t
a
sks. As
fo
r the deco
m
positio
n granula
r
ity of th
e
manufa
c
turi
n
g
task, h
o
w to evaluat
e their de
compo
s
ition,
namely h
o
w to a
s
sess the
perfo
rman
ce
of the
de
compo
s
ition
result
s, rare
wo
rks hav
e be
en
re
p
o
rted,
so
fu
rther
exploratio
ns
shall b
e
mad
e
on releva
nt model
s, strat
egie
s
and ju
d
g
ing metho
d
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Evaluation on Decom
positi
on Gr
anularit
y of Manufact
u
ring T
a
sk in
Manufacturi
ng... (Yong Yin)
1025
In the d
e
co
mpositio
n of
manufa
c
turi
n
g
task, the
d
e
com
p
o
s
ition
granula
r
ity
plays
an
importa
nt rol
e
. For
examp
l
e, on on
e h
a
nd, too la
rge
decompo
sitio
n
granula
r
ity will in
cre
a
se t
he
compl
e
xity of single
subta
sk o
r
a
c
tivity, affecti
ng the
quality of se
rvice, an
d in turn influe
nci
ng
the execution of subsequent s
ubtasks,
weakening the flexibility
of subtask execution. On the
other h
and,
much
sm
all d
e
com
p
o
s
ition
gran
ula
r
it
y will increa
se th
e numb
e
r of
subta
s
ks, ma
ke
subta
s
k stru
cture a
nd ta
sk pl
anni
ng
more co
mp
licated. Mea
n
whil
e, small
decom
po
sition
gran
ula
r
ity wil
l
increa
se
the
co
uplin
g d
e
g
r
ee
am
o
ng
subtasks, in
crease the
time
for
co
ordi
nati
o
n
among
su
bta
s
ks, or eve
n
trigge
r co
nflicts in t
he allo
cation a
m
on
g
resource
no
des. In orde
r
to
ensure th
e completion of
subta
s
ks a
n
d
avoid the
de
lay in the co
mpletion of the man
u
fact
uring
task cau
s
ed
by unb
alan
ce
d allo
catio
n
o
f
subta
s
ks, it
is n
e
cessa
r
y t
o
stu
d
y relev
ant theo
rie
s
a
nd
method
s co
n
c
erning d
e
co
mpositio
n gra
nul
arity of the manufactu
rin
g
task.
This pa
pe
r o
n
ly focuses o
n
how to eval
uate
the perf
o
rma
n
ce of the task de
co
mpositio
n,
not the
way
to de
comp
ose. T
o
be
g
i
n with it, we give the
decompo
sitio
n
mod
e
l of
the
manufa
c
turi
n
g
tasks at first.
2. Decompo
s
ition Model
s
To be
gin the
study on
th
e de
comp
osi
t
ion gra
nula
r
i
t
y of the manufactu
ring t
a
sk, this
pape
r first d
e
com
p
o
s
e
s
a manufa
c
turing task in
to
different su
btasks,
an
d each su
btask is
comp
osed of variou
s proce
ssi
ng ev
ent
s, as sho
w
n in
Figure 1.
Figure 1. Manufactu
ring T
a
sk T De
co
m
posed into 3
Different Subt
asks
In Figure 1, manufa
c
turi
n
g
task T is d
e
c
omp
o
s
ed int
o
3 su
btasks, i.e. subtasks
A, B and
C. Gen
e
rally
one resource node i
n
M
anufa
c
turin
g
Grid
can i
n
d
epen
dently a
c
compli
sh o
n
e
subta
s
k. The
subta
s
k is
co
mposed of a
seri
es
of
processing
event
s. For
i
n
st
a
n
c
e
,
subt
a
s
k A
in
Figure 1
(
b
)
contain
s
3
proce
s
sing
eve
n
ts e,
f
and
i. Re
sou
r
ce
node
R1 can
inde
pend
ent
ly
accompli
sh th
is su
btask (T
ake the
su
bta
sk of n
u
t man
u
facturi
ng for example, the
resource
no
de
that is capa
bl
e of nut pr
ocessing
ca
n a
c
compli
sh 3
pro
c
e
ssi
ng e
v
ents, incl
udi
ng Nut
3, Nut
5
and Nut
8). Reso
urce no
d
e
with wea
k
pro
c
e
ssi
ng capa
city may
be allocated
with only on
e
pro
c
e
ssi
ng e
v
ent in a subt
ask,
e.g. subt
ask B in Figure 1.
In the pape
r,
the prin
cipl
e of “st
r
ong
coh
e
si
on an
d wea
k
cou
p
ling” in th
e software
engin
eeri
ng f
i
eld h
a
s be
e
n
taken fo
r
referen
c
e
[20]
. To b
e
spe
c
ific, the
inte
rnal
processi
ng
events
co
ntai
ned i
n
e
a
ch
subta
s
k
sho
u
l
d have
stro
n
g
cohe
sio
n
coefficient, wh
ile
the extern
a
l
cou
p
ling
relat
i
onship am
on
g subta
s
ks
should b
e
rel
a
ti
vely loose. On such
ba
si
s, this pa
per
has
adopte
d
the
activity con
s
t
r
aint mat
r
ix to analy
z
e
th
e
co
nst
r
aint relation
ship a
m
ong su
btasks.
After that, the decompo
siti
on granul
arity of m
anufa
c
turing ta
sk ha
s be
en jud
g
e
d
and eval
uat
ed
by cohe
sion
and cou
p
lin
g indicato
rs. Finally
, spe
c
ific exampl
e
s
have bee
n
given on the
decompo
sitio
n
gran
ula
r
ity of manufactu
ring task,
and
the work of th
is study ha
s b
een verified.
a
f
e
i
h
g
b
c
d
l
k
n
j
m
f
e
i
a
h
g
b
c
d
l
k
n
j
m
M
a
nuf
a
c
t
u
r
i
ng
t
a
s
k
T
S
ubt
a
s
k A
S
u
bt
a
s
k B
S
u
bt
a
s
k C
l
M
a
nu
f
a
c
t
ur
i
n
g
t
a
s
k
S
ubt
a
s
k
P
r
oc
e
s
s
i
ng
e
v
e
n
t
s
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No. 2, Februa
ry 2013 : 1024 – 1032
1026
3. Cons
traint Analy
s
is
Acco
rdi
ng th
e de
comp
osition model
of
manufa
c
turin
g
task in se
ction
2, one
manufa
c
turi
n
g
task i
s
an
o
r
de
red
set of correl
ativ
e su
btasks, an
d e
a
ch
subta
s
k
contai
ns
seve
ral
pro
c
e
ssi
ng e
v
ents. The
s
e
pro
c
e
ssi
ng e
v
ents are ex
ecute
d
und
er certai
n con
s
traint conditio
n
s.
The modifi
ca
tion of one processin
g
event will l
ead
to the chang
e in the entire status of the
subta
s
k, whi
c
h may influe
n
c
e the
execut
ion of
next
subtask. Thi
s
pro
c
e
s
s keep
s goi
ng o
n
a
n
d
on, until all
the su
btasks
are
com
p
leted. The
r
efore, the
constraint rel
a
tionship am
ong
pro
c
e
ssi
ng e
v
ents withi
n
a su
btask n
e
eds to
be
a
n
a
lyzed. A
cco
rding to
Ref
e
ren
c
e [21], t
h
e
con
s
trai
nt rel
a
tionship am
ong pr
ocessi
ng events
ca
n be divided i
n
to several types a
s
sho
w
n in
Figure 2.
Figure 2. Different Con
s
tra
i
nt Relation
sh
ip Among Pro
c
e
ssi
ng Even
ts
After the ma
nufactu
ring t
a
sk is
deco
m
posed in
to
subta
s
ks, t
here
exists
correl
ation
con
s
trai
nt am
ong p
r
o
c
e
ssi
ng event
s in
each subta
s
k.
In Figure 2,
the directio
n
s
of the
arro
ws
rep
r
e
s
ent in
p
u
t or o
u
tput relation
ship
s a
m
ong
pr
o
c
e
s
sing events. Suppo
se
su
btask T
contai
n
s
n
pro
c
e
ssi
ng e
v
ents, i.e. e1, e2,
e3, ……
en. Then o
n
e
n X n matrix can b
e
con
s
tructed. Th
e ro
ws
and column
s of the matrix represent the co
rre
l
a
tion
among p
r
o
c
e
ssi
ng event
s in the subta
s
k.
This
correlati
on is expressed by e
ij, and it s
a
tis
f
ies
formula (1).
1
i i
s
input unit, j is output unit
eij = -1
i i
s
o
u
tput unit, j is input unit
(1)
1 No input or output relatio
n
shi
p
betwee
n
i and j
Since o
ne p
r
oce
s
sing eve
n
t has n
o
co
rrel
a
tion
con
s
traint
with itself po
ssi
bly, all the
diago
nal ele
m
ents of the
matrix are “0”. S
ee Figure
3 for the matrix E with n X
n.
Figure 3. The
Matrix E With n X n
4. Ev
aluation Index
Followi
ng
se
ction
s
2 an
d
3, one man
u
facturi
ng ta
sk i
s
de
co
m
posed into a
seri
es of
subta
s
ks, a
n
d
ea
ch
subta
sk i
s
com
posed of se
veral
pro
c
e
ssi
ng events with
correlation
s
.
T
h
e
output of the previo
us
pro
c
e
ssi
ng e
v
ent is
the input of the
sub
s
eq
uent
one or
sev
e
ral
pro
c
e
ssi
ng e
v
ents. A gro
up of input a
nd output
ev
ents con
s
titutes
an event control
unit. The
con
s
trai
nt structure of eve
n
ts ha
s seve
ral a
c
tivi
ty control unit
s
. In here a fo
rm
al definition
of
con
s
trai
nt structure amon
g
proc
e
s
sing
e
v
ents h
a
s be
en
spe
c
ified,
and th
e d
e
fini
tion of
coh
e
si
on
coeffici
ent an
d the me
asurement meth
o
d
s fo
r it
s co
h
e
sio
n
have b
een
p
u
t
forward as well
[
20,
21].
Definition 1:
Activity const
r
aint structu
r
e
among p
r
o
c
e
ssi
ng event
s within a subta
sk.
The a
c
tivity constraint st
ru
cture
amo
ng
pro
c
e
ssi
ng e
v
ents within
a
subta
s
k is d
e
fined a
s
two-el
eme
n
t (T, C), and it satisfies the fol
l
owin
g co
nditions:
(1) T rep
r
e
s
e
n
ts a finite nu
mber of p
r
ocessing
events in c
o
ns
traint
s
t
ru
cture of subtasks;
(2)
C=
{(
os, is
) T x
D(T)
} is
a co
n
s
traint control
set co
mposed of
a
seri
es
of pro
c
essing eve
n
ts. It
rep
r
e
s
ent
s the input and o
u
tput relation
ship am
ong
all the pro
c
e
ssi
ng event
s in the con
s
traint
stru
ctur
e. “o
s
”
re
pre
s
e
n
ts
t
he output e
v
ent set, and
“is” re
pre
s
e
n
ts the inp
u
t event set. T
he
con
s
trai
nt co
ntrol set (o
s, is) b
e
long
s to
the co
n
s
trai
n
t
structu
r
e
sp
ace
com
p
o
s
e
d
of pro
c
e
ssi
ng
events. As o
ne exam
ple
sho
w
n
in Fi
g
u
re
4,
the i
n
put processin
g
ev
ent
s a,
b an
d c hav
e a
1
2
1
3
1
2
1
3
2
2
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comm
on o
u
tp
ut pro
c
e
s
sing
event d. Thi
s
a
c
tivity
control relation
shi
p
ca
n be
exp
r
esse
d a
s
d
{
a
,
b, c}
by co
ntrol units. F
o
r
a
nother examp
l
e in Fi
g
u
re
4,
the input
pro
c
e
ssi
ng eve
n
ts e
and f h
a
ve
a com
m
on o
u
tput pro
c
e
ssing event h,
and the o
u
tp
ut of
g is also h. So this a
c
tivity control
unit
can b
e
expre
s
sed a
s
{(h
{e
, f}), (h {g})}.
Figure 4. Examples of Acti
vity Control Unit
Definition 2:
Effective subt
ask.
Suppo
si
ng there
exist
s
an a
c
tivi
ty constraint stru
cture
(T
,
C) of a
subt
ask, any
co
n
s
traint
sub
s
e
t
t C i
s
call
e
d
an
effectiv
e subta
s
k of
this const
r
ai
n
t
st
ru
ct
ur
e.
Definition
3: Effective subt
ask sequ
en
ce. Prov
ided t
hat an a
c
tivity con
s
traint
structu
r
e
(T, C)
of a subtask exist
s
, one two-ele
m
ent (Q,
F) i
s
the effectiv
e subta
s
k se
quen
ce of thi
s
con
s
trai
nt structure, and it m
eets the foll
owin
g co
nditions:
(1) F
o
r any
c
C, whe
n
c
t, then t
Q always exists. Q i
s
a colle
ction
of effective subtasks,
and Q
P(C);
(2) F
o
r a
n
y
t,u
Q, wh
en p
s
is, (os,is)
t, (p
s, qs
)
u, (u, t)
F. F
Q X Q i
s
a con
s
trai
nt
stru
cture ba
sed on Q;
Definition
3 h
a
s
provid
ed a
colle
ction
co
mposed
of se
veral in
put ev
ents. “c” is th
e ba
sic
control unit; i
s
an
d q
s
are
the input eve
n
t sets; o
s
a
n
d
ps
are th
e
output event
sets. Both
“t”
and
“u” are effe
ctive subta
s
ks. Con
d
ition
(1) in
dicate
s
that all the
control
un
its in
th
e ac
tivit
y
con
s
trai
nt st
ructure
sho
u
ld
app
ear at le
ast o
n
ce
in
subtasks, whil
e Condition
(2)
stre
sse
s
t
h
e
correl
ation
a
m
ong su
btasks.
In anoth
e
r words,
th
e input
eve
n
t of a
cont
rol u
n
it in t
he
sub
s
e
que
nt subtask is th
e
output
event
of control un
it in the pr
evi
ous subta
s
k.
This con
d
ition
has e
n
sure
d the co
rrectn
es
s of subta
s
k seque
nce.
In Manufa
c
tu
ring G
r
id, ea
ch subta
s
k is
comp
l
e
ted b
a
s
ed o
n
certai
n con
s
traint structu
r
e
according to
corre
s
p
ondin
g
wo
rki
ng flo
w
. The
out
pu
t of a pro
c
e
s
sing
event m
a
y be the in
p
u
t of
the next one.
Duri
ng the i
n
tera
cting p
r
oce
s
s
bet
we
en the inp
u
t and the o
u
tp
ut, many reu
s
ed
activity units will be produced. Th
ose units may appear twi
c
e or
move
in constraint control.
The
reu
s
ed
coh
e
sion co
efficient
of processin
g
event is def
ined a
s
follows [21].
Definition 4: Reu
s
e
d
coh
e
s
ion
coefficie
n
t of proce
s
sing event
s. With re
spe
c
t
to the
effective con
s
traint ta
sk “t
” based on a
c
tivity c
onstraint stru
cture
(T,
C), the reused cohe
si
on
coeffici
ent of its pro
c
e
s
sing
events is [20
]
:
(2)
Reu
s
e
d
co
he
sion
coeffici
e
n
t of a pro
c
e
ssi
ng
event i
s
the ratio be
tween the
nu
mber of
reu
s
ed
pro
c
e
ssi
ng event
s
and total p
r
o
c
e
ssi
ng even
ts. It can refl
ect the p
r
op
o
r
tion of re
use
d
pro
c
e
ssi
ng e
v
ents in total pro
c
e
ssi
ng e
v
ents in the constraint stru
cture.
Definition 5:
Correl
ated co
hesi
on coefficient
among p
r
ocessin
g
events.
For the
effective
con
s
trai
nt su
bset “t” in th
e unit con
s
traint
stru
cture
,
the correlat
ed co
he
sion
coeffici
ent
)
(
t
among p
r
o
c
e
ssi
ng event
s is define
d
as f
o
llows [20]:
(3)
)
(
t
1
|
|
0
t
1
|
|
}
,
)
}
({
)
}
({
|
)
,
{(
)
,
(
t
ps
os
qs
ps
is
os
t
qs
ps
t
is
os
c
b
d
a
h
e
f
g
0
|
|
)}
}
({
,
)
,
(
|
{
)}
,
(
)
,
(
),
}
({
)
}
({
,
)
,
(
,
)
,
(
|
{
t
is
os
u
t
is
os
T
u
qs
ps
is
os
qs
ps
is
os
u
t
qs
ps
t
is
os
T
u
)
(
t
0
|
|
0
t
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In the above f
o
rmul
a, “
” is t
he sum of n
o
n
-em
p
ty interse
c
tion
s amo
ng on
e control unit
and othe
rs. The co
rrelat
ed coh
e
si
on
co
efficient
among
p
r
o
c
essing
event
s i
s
a
coeffi
cient
measuri
ng th
e relation
ship
amo
ng
co
ntrol unit
s
in
th
e con
s
traint
stru
cture. It h
a
s
refle
c
ted
the
gene
ral level
of correlatio
n amon
g adj
ace
n
t co
ntrol
units. According to the
definition
s
, the
coh
e
si
on coe
fficient insid
e
a subta
s
k is there
b
y define
d
as follo
ws.
Definition 6:
coh
e
si
on coe
fficient insid
e
subta
sk. Giv
en an effectiv
e con
s
traint subset o
f
subta
s
k activi
ty constraint stru
cture (T,
C), its cohe
si
on co
effici
ent
is the pro
d
u
c
t of correl
ated
coh
e
si
on coe
fficient and re
usa
b
le cohe
si
on
co
efficient
of processin
g
events [20]:
)
(
)
(
)
(
t
t
t
c
(4)
Definition 1
~
6 have described the
co
hesi
on
rel
a
tionship amo
n
g
pro
c
e
ssi
ng
events
within ea
ch
subtask that is decom
po
sed
from the ma
nufactu
ring ta
sk.
Ho
wever,
with re
spe
c
t to the rel
a
tion
shi
p
amon
g su
b
t
asks, the fun
damental
prin
ciple to
decompo
se a
manufactu
ri
ng task is to ensure
ce
rtai
n indepe
nde
nce of ea
ch
subta
s
k, nam
ely
wea
k
co
uplin
g
amo
ng su
btasks. The cou
p
ling co
e
fficient bet
ween
su
btasks i
s
d
e
fined
as
follows
.
Definition 7:
Cou
p
ling coefficient
a
m
ong s
ubta
sks.
Supp
ose there are n kind
s
of
cou
p
ling
relat
i
onship am
on
g su
btasks, in whi
c
h
the i
n
fluen
ce
coef
ficient of the
kth in n i
s
k
, s
o
the cou
p
ling
coeffici
ent be
tween
subta
s
k Si and Sj is defined a
s
fol
l
ows:
0
1
1
,
ij
n
k
k
j
i
k
j
i
r
r
r
(5)
In formula (5
), we have:
1 Subta
s
ks Si and Sj meet the kth co
upling relatio
n
=
(6)
0 Su
btasks Si and Sj don’t meet the kth co
uplin
g relation
n
k
k
1
1
(7)
In further ste
p
, as one
sub
t
ask i
s
of autoco
r
re
lation b
y
itself, its coupling
coeffici
ent is:
0
1
,
1
1
,
ij
n
k
k
j
i
k
j
i
r
j
i
c
r
(8)
Combi
ng the
definition 6
and 7, th
e
ev
aluation i
ndex, nam
ely the decom
positio
n
gran
ula
r
ity co
efficient, can
be ded
uced:
)
(
t
c
r
(9)
5. Ev
aluation Steps
On the ba
si
s of the evalu
a
tion index in
se
cti
on 4, a
c
cordi
ng to t
he pri
n
ci
ple
of “strong
coh
e
si
on an
d wea
k
cou
p
ling” fo
r de
comp
ositio
n of manufactu
ring task, the step
s for the
evaluation of
decompo
sitio
n
gran
ula
r
ity of one m
anuf
acturi
ng task
is listed a
s
fol
l
ows [22].
1)
Whe
n
de
co
m
posi
ng the
m
anufa
c
turin
g
t
a
sk,
the ta
sk
to be de
co
m
posed i
s
rega
rded
a
s
on
e
subta
s
k (i.e. t
h
is ma
nufa
c
turing ta
sk i
s
accompli
sh
ed
by one
re
so
urce no
de
). F
i
rst of all, the
pro
c
e
ssi
ng
e
v
ents of th
e
manufa
c
turi
n
g
task
before
decompo
sitio
n
are d
e
termi
ned
acco
rdin
g
to definition 1
;
2)
Acco
rdi
ng to
sectio
n 2
and 3 of th
e pape
r,
the
activity correlation matri
x
E of this
manufa
c
turi
n
g
task i
s
de
rived;
k
j
i
r
,
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Evaluation on Decom
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Manufacturi
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1029
3)
Con
s
trai
nt structure (T, C)
of this manufacturi
ng ta
sk i
s
obtaine
d according t
o
the activity
correl
ation m
a
trix;
4)
The de
comp
osition coefficient
of the manufactu
ri
ng task i
s
calcul
ated according to
definition 4
~
7
in sectio
n 4;
5)
Then th
e ma
nufactu
ring
ta
sk i
s
de
comp
ose
d
into 2
subtasks. Retu
rn to
step
s (2
), (3
) an
d (4),
and calculate
the decom
po
sition coeffici
ent
of each
subtask ag
ain;
6)
The followi
ng
rules
can be
used to evaluat
e the decompo
sition granula
r
ity of manufa
c
turi
n
g
t
a
sk:
Rule
No.1: If the de
compo
s
ition
coeffici
ent
of man
u
fa
cturin
g ta
sk before
decompo
sitio
n
is larg
er than that of the effe
ctive subta
s
ks afte
r decom
p
o
sit
i
on, that is, the
manufa
c
turi
n
g
task is in
tight con
s
traint
stru
ctu
r
e, the deco
m
posit
io
n granula
r
ity of the
manufa
c
turi
n
g
task i
s
a
p
p
rop
r
iate, a
n
d
the initia
l
con
s
trai
nt st
ructure of m
a
nufactu
ring
task
sho
u
ld be ma
intained.
Rule
No.2: I
f
the de
com
positio
n coef
ficient
of the ma
nufa
c
turing
task
b
e
fore
decompo
sitio
n
is
sm
aller than th
at of th
e effect
ive
su
btasks after
decompo
sitio
n
, it indicates a
wea
k
cohe
sio
n
exists am
o
ng the intern
al activi
ty units of the initial task, and th
e manufa
c
turi
ng
task h
a
s lo
ose con
s
trai
nt structu
r
e. It is stro
n
g
ly re
co
mmend d
e
co
mposi
ng the task furthe
r.
7)
If the man
u
fa
cturin
g ta
sk n
eed
s to
be
de
comp
os
ed
wit
h
differe
nt g
r
anula
r
ities,
re
turn to
ste
p
s
(2),
(3)
and
(4), de
com
p
o
s
e the task
on
ce a
gain, a
n
d
cal
c
ulate th
e
decompo
siti
on coefficie
n
t
of subtasks after decomp
o
sition. The
gran
ula
r
ity with the minimum value of
is the
optimal ch
oice of manufact
u
ring ta
sk d
e
c
omp
o
sitio
n
.
In the follo
wi
ng pa
rt of the
pape
r, exam
ples
to de
mo
nstrate
the
d
e
com
p
o
s
ition
pro
c
e
s
s
of a manufact
u
ring ta
sk
with prop
er g
r
an
ularity are giv
en.
6. Examples
Providing th
at a ma
nufa
c
turin
g
ta
sk
T is
to
be
decompo
se
d, whi
c
h
co
ntains 14
processi
ng events, i.e. a,b,
c,d,e,f,g,h,i,j,k,l,m and n, as shown in Figure 5.
Figure 5. Manufactu
ring T
a
sk T to be Decom
p
o
s
ed
Followi
ng ste
p
(1), T is tre
a
ted as on
e subta
s
k. Accordin
g to se
ction 3, the correl
a
tion
con
s
trai
nt ma
trix of proce
s
sing eve
n
ts in
m
anufactu
rin
g
task T i
s
ob
tained a
s
in Figure 6.
Figure 6. Correlation
Con
s
traint Matrix o
f
T
The set of the
processin
g
e
v
ents in ma
nufac
t
uring task
T is
as
follows
:
a
f
e
i
h
g
b
c
d
l
k
n
j
m
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1030
T=
{a,b,c
,d,e,f,g,h,i,j,k
,l,m,n
}
(10)
In terms of formul
a (10
)
, we get the constr
aint co
n
t
rol set of manufa
c
turin
g
task T in
Figure 6:
C={f(a), g(b), h(c
,
d), i(e,
f), j(g), k(g, h), l(
i, j), m(j, k
)
, n(l, m)}
(11)
Acco
rdi
ng to
formula
(2
), the re
used
co
h
e
si
on
coefficient of
pro
c
e
ssi
ng e
v
ents in
manufa
c
turi
n
g
task T
can
be achieved:
7
4
14
8
)
(
t
(12
)
Next by formula (3
), the co
hesi
on coefficient
of all the pro
c
e
ssi
ng e
v
ents in task T is:
72
19
8
*
9
2
3
3
3
3
1
1
2
1
)
(
t
(13)
Then i
n
the
light of fo
rmula
(4), th
e cohe
sion
coeffici
ent in
side
the
su
btask of
manufa
c
turi
n
g
task T (In h
e
re, T is de
co
mposed into
only one subt
ask)
can be a
c
qui
red:
15
.
0
7
4
*
72
19
)
(
)
(
)
(
t
t
t
c
(14)
As T is
onl
y decom
po
sed into o
n
e
subta
s
k, its cou
p
ling
co
efficient r=1.
So the
decompo
sitio
n
gran
ula
r
ity coeffici
ent for manufactu
rin
g
task T
can
be derive
d
ou
t.
67
.
6
15
.
0
1
)
(
t
c
r
(15
)
It can b
e
see
n
that, if man
u
facturi
ng ta
sk T i
s
de
co
m
posed into
o
n
ly one
subta
sk, the
decompo
sitio
n
g
r
anul
arity
coeffici
ent i
s
very large,
so
the ta
sk ne
e
d
s to
be
furth
e
r
de
comp
osed.
Suppo
se the
manufa
c
turi
ng task T i
s
decompo
se
d
into two
subt
asks
T1 a
nd
T2 a
s
sho
w
n
in
Figure 7.
Figure 7. T is De
comp
osed
into Two T1
and T2
Figure 8. Correlation
Con
s
traint Matrix
Insid
e
Subtask T1 an
d Sub
t
ask T
2
h
a
g
b
f
c
e
d
l
k
n
j
m
i
f
e
i
h
g
b
c
d
l
k
n
j
m
a
+
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TELKOM
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046
Evaluation on Decom
positi
on Gr
anularit
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u
ring T
a
sk in
Manufacturi
ng... (Yong Yin)
1031
Subtask
T1
contains
4 proc
es
s
i
ng event
s
,
i.e.
a,e,f,i;
s
ubtask
T2
contains
10 proc
ess
i
ng
events, i.e. b
,
c, d, g, h, j,
k, l, m, n. See Fig. 8
for correl
atio
n co
nst
r
aint
matrix of the
s
e
pro
c
e
ssi
ng e
v
ents insi
de subtask T1 an
d subta
s
k T2.
Acco
rdi
ng to the correlatio
n con
s
trai
nt matrix
of pro
c
e
ssi
ng even
ts in subta
s
ks T1 and
T2, their co
nstraint cont
rol
set are
as foll
ows:
C1=
{
f(a), i(e,
f)}
C2=
{ g(b)
, h(c
,
d),, j(g), k(g, h), l(
j), m(j, k
)
, n(l,
m)}
(16)
The reu
s
ed
cohe
sion
coeff
i
cient
s of pro
c
e
ssi
ng eve
n
t
s in subta
s
ks T1 a
nd T
2
can
be
achi
eved indi
vidually according to formul
a (2):
2
1
4
2
)
(
1
t
5
3
10
6
)
(
2
t
(17)
The co
he
sion
coefficie
n
ts
of all the pro
c
e
ssi
ng even
ts in subta
sks T1 an
d T2
can be
acq
u
ire
d
by formul
a (3
):
1
2
2
1
*
2
1
1
)
(
1
t
21
8
42
16
6
*
7
2
3
2
3
3
1
2
)
(
2
t
(18
)
Then in the li
ght of formula
(4), we g
e
t the
coh
e
si
on coefficient in
si
de su
btasks T1 and T2:
5
.
0
1
*
2
1
)
(
)
(
)
(
1
1
1
t
t
t
c
23
.
0
21
8
*
5
3
)
(
)
(
)
(
2
2
2
t
t
t
c
(19
)
As
sho
w
n
in
Figure 7,
su
b
t
ask T1
an
d
T2 i
s
o
n
ly co
upled
by n
o
d
e
i a
nd l,
an
d their
cou
p
ling
coef
ficients
r1 an
d r2 a
r
e 0.5.
So
the deco
m
positio
n gra
nularity coefficient
s
1
and
2
of subta
sk T
1
and T2 are a
s
follows:
1
5
.
0
5
.
0
)
(
1
1
1
t
c
r
17
.
2
23
.
0
5
.
0
)
(
2
2
2
t
c
r
(20
)
It can
be
see
n
that, after t
he ma
nufa
c
tu
ring ta
sk T i
s
de
comp
osed
into
subta
s
k
T1 an
d
T2, the deco
m
positio
n gra
nularity co
efficient
s of
both T1 and T2 h
a
ve decrea
s
e
d
. Therefo
r
e,
it
is app
rop
r
iate
to decomp
o
se manufa
c
turi
ng task T into
subta
s
ks T1
and T2.
Of cou
r
se,
manufa
c
turi
n
g
task T ca
n also be d
e
com
p
o
s
ed i
n
to different
kind
s of
subta
s
ks i
n
di
fferent ways.
After decomp
o
sin
g
ma
n
u
fa
cturin
g ta
sk
T
into differe
nt subta
s
ks
ea
ch
time, we
cal
c
ulate th
e d
e
com
p
o
s
ition
gran
ula
r
ity coeffici
ent
of subta
s
ks
according to th
e
step
s in
se
ction 5, an
d the de
com
p
o
s
iti
on
with th
e minimum
gran
ula
r
ity value of
is the
optimal de
co
mpositio
n of the manufa
c
tu
ring task.
7. Conclusio
n
Manufa
c
turi
n
g
grid ha
s provided man
u
f
acturin
g
ent
erp
r
ises with
a global pla
tform for
sha
r
ing
ma
nu
facturin
g
re
so
urces,
and
it i
s
a
key ste
p
t
o
de
com
p
o
s
e
the m
anufa
c
t
u
ring
task i
n
to
subta
s
ks wit
h
p
r
op
er gra
nularity.
Ref
e
rri
ng to
the
pri
n
ci
ple
of “stron
g
co
h
e
sio
n
a
nd
weak
cou
p
ling
”
in software e
ngin
eerin
g field, this pap
er h
a
s
esta
blish
e
d
the model for evaluating t
h
e
decompo
sitio
n
gran
ularity
of the manufactu
ri
ng t
a
sk, explore
d
the desig
n step
s for the
decompo
sitio
n
granul
arity, and
put fo
rward exa
m
pl
es to
illu
strat
e
the i
dea
of the p
ape
r.
This
study is
ba
se
d on the
assumption that
each re
so
ur
ce nod
e on
m
anufa
c
turin
g
grid i
s
capa
bl
e of
executin
g the subta
s
ks d
e
com
p
o
s
ed
according
wi
th approp
riate
granul
arity. Mean
while, this
pape
r ha
s
evaluated th
e decomp
o
sition gra
nul
a
r
ity only through the
subtasks afte
r
decompo
sitio
n
, i.e.
to passively co
mpare
and
evaluate the
appro
p
riate
ness of different
decompo
sitio
n
gra
nula
r
ity throug
h subt
asks afte
r de
comp
ositio
n. Since a m
a
n
u
facturi
ng ta
sk
can b
e
deco
m
posed in variou
s ki
nd
s of appro
a
che
s
, it will be a very meanin
g
ful research
to
actively guid
e
the decom
positio
n of manufa
c
turi
n
g
task by com
b
ining thi
s
e
v
aluation met
hod
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and ce
rtain o
p
timization
al
gorithm
s whil
e
taki
ng
the
constraint of
reso
urce
nod
e
into a
c
count
as
well.
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