I
nte
rna
t
io
na
l J
o
urna
l o
f
Adv
a
nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
1
3
,
No
.
4
,
Dec
em
b
er
2
0
2
4
,
p
p
.
9
0
0
~
9
10
I
SS
N:
2252
-
8
8
1
4
,
DOI
:
1
0
.
1
1
5
9
1
/ijaas
.
v
1
3
.
i
4
.
pp
900
-
9
10
900
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
a
s
.
ia
esco
r
e.
co
m
The pro
duc
tion
-
i
nv
entory
mo
del w
ith
impe
rfec
t,
rew
o
rk,
a
nd
scra
p it
ems
under
stocha
stic d
ema
nd
Da
na
M
a
rset
iy
a
Ut
a
ma
,
Art
ha
B
ripk
a
P
utr
i
D
e
p
a
r
t
me
n
t
o
f
I
n
d
u
s
t
r
i
a
l
En
g
i
n
e
e
r
i
n
g
,
F
a
c
u
l
t
y
o
f
En
g
i
n
e
e
r
i
n
g
,
U
n
i
v
e
r
s
i
t
y
o
f
M
u
h
a
mm
a
d
i
y
a
h
M
a
l
a
n
g
,
M
a
l
a
n
g
,
I
n
d
o
n
e
s
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
1
4
,
2
0
2
3
R
ev
is
ed
J
u
l 6
,
2
0
2
4
Acc
ep
ted
Au
g
2
8
,
2
0
2
4
In
v
e
n
t
o
ry
is
c
ru
c
ial
in
m
a
in
tain
i
n
g
a
sm
o
o
th
p
ro
d
u
c
ti
o
n
p
ro
c
e
ss
a
n
d
m
e
e
ti
n
g
c
o
n
su
m
e
r
d
e
m
a
n
d
fo
r
m
a
n
u
fa
c
tu
rin
g
c
o
m
p
a
n
ies
.
Th
is
re
se
a
rc
h
fo
c
u
se
s
o
n
p
ro
d
u
c
ti
o
n
p
ro
b
lem
s
in
v
o
lv
i
n
g
d
e
fe
c
ts,
re
wo
rk
,
a
n
d
sc
ra
p
it
e
m
s
in
sto
c
h
a
stic
d
e
m
a
n
d
.
T
h
is
re
se
a
rc
h
a
ims
to
d
e
v
e
lo
p
a
p
r
o
d
u
c
ti
o
n
-
a
v
a
il
a
b
i
li
ty
m
o
d
e
l
b
y
m
in
imiz
in
g
th
e
e
x
p
e
c
tatio
n
o
f
t
o
tal
c
o
st
(E
TC).
T
h
e
m
o
d
e
l
in
c
lu
d
e
s
fo
u
r
m
a
in
d
e
c
isio
n
v
a
riab
les
,
n
a
m
e
ly
p
ro
d
u
c
ti
o
n
q
u
a
n
ti
ty
(Q),
sa
fe
ty
f
a
c
to
r
(k
),
p
ro
d
u
c
ti
o
n
ra
te
(P
),
a
n
d
re
wo
rk
ra
te
(P
1
)
.
T
h
is
re
se
a
rc
h
u
se
s
t
h
e
Aq
u
il
a
o
p
ti
m
ize
r
a
l
g
o
rit
h
m
t
o
o
p
ti
m
ize
t
h
e
o
b
jec
ti
v
e
fu
n
c
ti
o
n
.
It
c
o
m
p
a
re
s
with
th
e
h
e
u
risti
c
p
r
o
c
e
d
u
re
a
n
d
Ha
rris
Ha
wk
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
.
T
h
e
re
su
lt
s
sh
o
we
d
t
h
a
t
th
e
A
q
u
i
la
o
p
ti
m
i
z
e
r
a
lg
o
rit
h
m
s
u
c
c
e
ss
fu
ll
y
o
p
ti
m
ize
d
th
e
p
ro
d
u
c
ti
o
n
-
a
v
a
il
a
b
il
it
y
p
r
o
b
lem
.
A
c
o
m
p
a
riso
n
b
e
twe
e
n
a
lg
o
ri
th
m
s
in
d
ica
tes
th
a
t
th
e
Aq
u
il
a
o
p
ti
m
ize
r
a
lg
o
r
it
h
m
p
e
rfo
rm
s
e
q
u
iv
a
len
t
ly
t
o
t
h
e
Ha
rris
Ha
wk
o
p
ti
m
iza
ti
o
n
a
lg
o
ri
th
m
a
n
d
o
u
tp
e
rf
o
rm
s
th
e
h
e
u
risti
c
p
ro
c
e
d
u
re
.
S
e
n
siti
v
i
ty
a
n
a
ly
sis
sh
o
ws
t
h
a
t
i
n
c
re
a
sin
g
d
e
m
a
n
d
u
n
c
e
rtain
t
y
i
n
c
r
e
a
se
s
ET
C
a
n
d
k
.
At
t
h
e
sa
m
e
ti
m
e
,
it
c
a
n
d
e
c
re
a
se
Q.
K
ey
w
o
r
d
s
:
Aq
u
ila
o
p
tim
izer
I
n
v
en
to
r
y
Pro
d
u
ctio
n
R
ewo
r
k
Sto
ch
asti
c
d
em
an
d
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Dan
a
Ma
r
s
etiy
a
Utam
a
Dep
ar
tm
en
t o
f
I
n
d
u
s
tr
ial
E
n
g
i
n
ee
r
in
g
,
Facu
lty
o
f
E
n
g
in
ee
r
in
g
,
Un
iv
er
s
ity
o
f
Mu
h
am
m
ad
iy
ah
Ma
lan
g
Ma
lan
g
,
E
ast J
av
a,
I
n
d
o
n
esia
E
m
ail:
s
p
ea
k
d
r
s
s
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
I
n
th
e
er
a
o
f
g
lo
b
aliza
tio
n
an
d
in
cr
ea
s
in
g
ly
f
ier
ce
b
u
s
in
ess
co
m
p
etitio
n
,
s
u
p
p
l
y
ch
ain
m
an
ag
em
en
t
h
as
b
ec
o
m
e
a
cr
u
cial
elem
en
t
in
co
m
p
an
y
s
u
cc
ess
[
1
]
.
T
h
e
s
u
p
p
ly
ch
ain
in
clu
d
es
r
aw
m
a
ter
ial
p
r
o
cu
r
em
e
n
t,
p
r
o
d
u
ctio
n
p
lan
n
in
g
,
an
d
in
v
e
n
to
r
y
m
a
n
ag
em
en
t
[
2
]
,
[
3
]
.
W
h
ile
ch
an
g
in
g
m
ar
k
et
d
y
n
am
ic
s
,
co
m
p
an
ies
m
u
s
t
d
ev
elo
p
ef
f
ec
tiv
e
s
tr
ateg
ies
to
m
an
ag
e
th
eir
s
u
p
p
l
y
c
h
ain
s
.
On
e
co
n
ce
p
t
th
at
b
ec
o
m
es
th
e
m
ain
f
o
cu
s
is
th
e
clo
s
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
s
u
p
p
ly
ch
ain
an
d
th
e
p
r
o
d
u
ctio
n
-
in
v
e
n
to
r
y
m
o
d
el.
T
h
e
s
u
p
p
ly
ch
ain
s
u
p
p
o
r
ts
th
e
co
m
p
an
y
'
s
s
m
o
o
th
o
p
er
at
io
n
,
f
r
o
m
p
r
o
c
u
r
in
g
r
aw
m
at
er
ials
to
d
is
tr
ib
u
tin
g
f
in
al
p
r
o
d
u
cts
to
cu
s
to
m
er
s
[
4
]
–
[
6
]
.
W
ith
u
n
ce
r
tain
t
y
in
m
ar
k
et
d
e
m
an
d
,
g
o
o
d
s
u
p
p
ly
ch
ain
m
a
n
ag
em
en
t
ca
n
h
elp
c
o
m
p
an
ies
r
esp
o
n
d
to
ch
an
g
es
m
o
r
e
q
u
ick
ly
an
d
ef
f
icien
tly
.
On
th
e
o
th
er
h
an
d
,
t
h
e
p
r
o
d
u
c
tio
n
-
i
n
v
en
to
r
y
m
o
d
el
is
th
e
f
o
u
n
d
atio
n
f
o
r
p
lan
n
in
g
an
d
m
an
ag
i
n
g
p
r
o
d
u
ctio
n
an
d
in
v
en
to
r
y
[
7
]
.
A
h
ar
m
o
n
io
u
s
r
elatio
n
s
h
ip
b
etwe
en
th
e
s
u
p
p
ly
ch
ain
an
d
th
e
p
r
o
d
u
cti
o
n
-
in
v
en
to
r
y
m
o
d
el
is
th
e
k
e
y
f
o
r
c
o
m
p
an
ies
to
m
in
i
m
ize
co
s
ts
,
in
cr
ea
s
e
ef
f
icien
cy
,
an
d
o
p
tim
ally
m
ee
t
cu
s
to
m
er
d
em
an
d
.
Acc
u
r
ate
an
d
c
o
m
p
r
eh
en
s
iv
e
m
o
d
els
m
u
s
t
b
e
d
e
v
elo
p
e
d
to
m
an
ag
e
in
v
en
to
r
y
a
n
d
p
r
o
d
u
ctio
n
in
p
r
o
d
u
ctio
n
a
n
d
s
u
p
p
ly
ch
ain
m
an
ag
em
en
t.
I
n
to
d
a
y
'
s
p
r
o
d
u
ct
io
n
s
y
s
tem
s
,
o
n
e
o
f
th
e
b
ig
g
est
o
b
s
tacle
s
is
m
an
ag
in
g
s
to
ch
asti
c
d
e
m
an
d
u
n
c
er
tain
ty
,
wh
ich
ca
u
s
es
d
em
a
n
d
to
f
lu
ctu
ate
at
r
an
d
o
m
[
8
]
.
T
h
e
p
r
o
d
u
ctio
n
-
in
v
en
to
r
y
m
o
d
el
b
ec
o
m
es
ess
en
tial
in
o
p
tim
izin
g
th
e
p
r
o
d
u
ctio
n
p
r
o
ce
s
s
an
d
s
to
ck
m
an
ag
em
en
t.
Ho
wev
er
,
i
n
p
r
ac
ti
ce
,
m
an
y
f
ac
to
r
s
ca
n
af
f
e
ct
th
e
ef
f
icien
cy
a
n
d
ef
f
ec
tiv
en
ess
o
f
th
e
m
o
d
el.
On
e
o
f
th
e
m
ain
ch
allen
g
es
f
a
ce
d
b
y
co
m
p
a
n
ies
is
th
e
p
r
ese
n
ce
o
f
im
p
er
f
ec
tio
n
s
in
p
r
o
d
u
ctio
n
g
o
o
d
s
,
r
ewo
r
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
Th
e
p
r
o
d
u
ctio
n
-
in
ve
n
to
r
y
mo
d
el
w
ith
imp
erfect,
r
e
w
o
r
k,
a
n
d
s
cra
p
items u
n
d
er
…
(
Da
n
a
Ma
r
s
etiya
Uta
ma
)
901
p
r
o
ce
s
s
es,
an
d
th
e
o
cc
u
r
r
e
n
ce
o
f
s
cr
ap
g
o
o
d
s
.
I
m
p
er
f
e
ctio
n
s
ca
n
o
cc
u
r
f
o
r
v
ar
io
u
s
r
ea
s
o
n
s
,
s
u
ch
as
p
r
o
d
u
ctio
n
d
ef
ec
ts
o
r
e
r
r
o
r
s
in
th
e
m
an
u
f
ac
tu
r
in
g
p
r
o
ce
s
s
[
9
]
,
[
1
0
]
.
T
h
e
r
ewo
r
k
p
r
o
ce
s
s
is
n
ee
d
ed
to
r
ep
ai
r
g
o
o
d
s
t
h
at
d
o
n
o
t
m
ee
t
q
u
alit
y
s
tan
d
ar
d
s
s
o
th
at
th
ey
ca
n
b
e
r
eu
s
ed
o
r
s
o
ld
[
1
1
]
–
[
1
3
]
.
Ho
w
ev
er
,
t
h
is
p
r
o
c
ess
also
r
eq
u
ir
es
ad
d
itio
n
al
c
o
s
ts
an
d
tim
e
th
at
ca
n
n
o
t
b
e
ig
n
o
r
ed
.
I
n
a
d
d
itio
n
,
s
cr
ap
is
also
a
p
r
o
b
lem
t
h
at
n
ee
d
s
to
b
e
h
a
n
d
led
p
r
o
p
er
ly
,
as
it
ca
n
r
esu
lt
in
f
i
n
an
cial
lo
s
s
es
f
o
r
th
e
co
m
p
an
y
[
1
1
]
,
[
1
4
]
.
I
n
a
d
d
itio
n
,
s
to
ch
asti
c
o
r
u
n
ce
r
tain
d
em
an
d
is
also
o
n
e
o
f
th
e
c
h
allen
g
es
in
in
v
en
to
r
y
m
an
ag
em
e
n
t
[
1
0
]
.
Flu
ctu
atin
g
an
d
u
n
p
r
e
d
ictab
le
d
e
m
an
d
g
iv
e
co
m
p
an
ies
an
ac
tiv
e
an
d
r
esp
o
n
s
iv
e
s
tr
ateg
y
to
m
ain
tain
ad
e
q
u
ate
av
ailab
ilit
y
o
f
g
o
o
d
s
with
o
u
t
ca
u
s
in
g
u
n
wa
n
ted
in
v
e
n
to
r
y
s
u
r
p
lu
s
es.
T
h
e
r
ef
o
r
e,
t
h
er
e
is
a
n
ee
d
to
d
ev
elo
p
a
p
r
o
d
u
ctio
n
-
in
v
en
to
r
y
m
o
d
el
t
h
at
co
n
s
id
er
s
im
p
er
f
ec
tio
n
s
,
r
ewo
r
k
,
an
d
s
cr
ap
,
alo
n
g
with
s
to
ch
asti
c
d
em
an
d
.
C
o
n
s
id
er
in
g
all
th
ese
f
ac
to
r
s
,
th
e
m
o
d
el
is
ex
p
ec
ted
to
ass
is
t
co
m
p
a
n
ies
i
n
o
p
tim
izin
g
in
v
en
t
o
r
y
m
an
a
g
em
en
t
d
ec
is
io
n
s
to
ac
h
iev
e
ef
f
icien
c
y
b
y
m
in
im
iz
in
g
to
tal
co
s
ts
.
Pas
t
r
esear
ch
o
n
p
r
o
d
u
ctio
n
-
a
v
ailab
ilit
y
m
o
d
els
i
n
v
o
lv
i
n
g
d
ef
ec
tiv
e
p
r
o
d
u
cts,
r
ewo
r
k
,
a
n
d
waste
h
as
attr
ac
ted
th
e
atten
tio
n
o
f
s
e
v
er
al
r
es
ea
r
ch
er
s
wh
o
c
o
n
tr
ib
u
te
to
ex
p
a
n
d
in
g
t
h
e
u
n
d
er
s
tan
d
in
g
o
f
t
h
e
co
m
p
lex
ity
o
f
th
is
p
r
o
b
lem
.
On
e
o
f
th
e
m
ain
c
o
n
tr
ib
u
to
r
s
is
Heja
zi
et
a
l
.
[
1
5
]
,
wh
o
p
r
o
p
o
s
ed
a
m
o
d
el
th
at
r
eq
u
ir
es
r
ew
o
r
k
o
n
d
ef
ec
tiv
e
p
r
o
d
u
cts
to
a
v
o
id
waste.
T
h
e
s
tu
d
y
f
o
u
n
d
t
h
at
b
y
in
te
g
r
atin
g
th
e
r
ewo
r
k
p
r
o
ce
s
s
in
to
th
e
m
o
d
el,
co
m
p
an
ies
c
an
r
ed
u
ce
th
e
am
o
u
n
t
o
f
waste
an
d
im
p
r
o
v
e
th
eir
o
p
e
r
atio
n
al
ef
f
icien
cy
.
I
n
ad
d
itio
n
,
r
esear
c
h
b
y
Sar
k
ar
[
1
6
]
,
L
i
n
an
d
Su
[
1
7
]
,
Pau
l
et
a
l
.
[
1
8
]
,
Ma
n
n
a
et
a
l
.
[
1
9
]
,
C
h
an
g
a
n
d
Ho
[
2
0
]
,
an
d
Ma
n
n
a
et
a
l
.
[
2
1
]
also
co
n
tr
ib
u
ted
b
y
in
co
r
p
o
r
atin
g
d
e
f
ec
tiv
e
p
r
o
d
u
cts
in
to
th
eir
p
r
o
d
u
ctio
n
-
a
v
ailab
ilit
y
m
o
d
el.
T
h
eir
r
esu
lts
s
h
o
w
t
h
a
t
an
i
n
v
en
t
o
r
y
m
an
a
g
em
en
t
s
tr
ateg
y
t
h
at
co
n
s
id
er
s
d
e
f
ec
tiv
e
p
r
o
d
u
cts
ca
n
h
elp
co
m
p
an
ies
o
p
tim
ize
th
e
u
s
e
o
f
th
eir
r
eso
u
r
ce
s
.
On
th
e
o
th
e
r
h
an
d
,
r
esear
ch
b
y
San
jai
an
d
Per
iy
asam
y
[
2
2
]
,
Öztü
r
k
[
2
3
]
,
an
d
Kh
ar
a
et
a
l
.
[
2
4
]
in
v
o
lv
in
g
d
e
f
ec
tiv
e
p
r
o
d
u
cts
an
d
r
ewo
r
k
p
r
o
ce
s
s
es
h
ig
h
lig
h
ts
th
e
im
p
o
r
tan
ce
o
f
ef
f
icien
cy
i
n
in
v
en
to
r
y
m
an
ag
em
e
n
t
to
av
o
id
lo
s
s
es.
Me
an
wh
ile,
s
tu
d
ies
b
y
Su
et
a
l
.
[
1
0
]
a
n
d
Kr
is
h
n
am
o
o
r
th
i
a
n
d
Pan
ay
a
p
p
an
[
1
3
]
h
a
v
e
en
r
ich
e
d
th
e
u
n
d
er
s
tan
d
i
n
g
o
f
m
o
d
els
th
at
co
n
s
id
er
d
ef
ec
tiv
e
p
r
o
d
u
cts
an
d
waste
in
th
eir
p
r
o
d
u
ctio
n
-
av
ailab
ilit
y
m
o
d
els.
T
h
ey
f
o
u
n
d
th
at
b
y
in
te
g
r
atin
g
waste
p
r
o
ce
s
s
in
g
in
to
th
e
m
o
d
el,
c
o
m
p
an
ies
ca
n
r
ed
u
ce
p
r
o
d
u
ctio
n
co
s
ts
an
d
im
p
r
o
v
e
en
v
ir
o
n
m
e
n
tal
s
u
s
tain
ab
ilit
y
.
Ho
wev
er
,
o
n
ly
s
tu
d
ies
b
y
Su
et
a
l
.
[
1
0
]
an
d
Sar
k
ar
et
a
l
.
[
2
5
]
h
a
v
e
s
u
cc
ess
f
u
lly
in
co
r
p
o
r
ated
s
to
ch
asti
c
elem
en
ts
in
d
em
an
d
m
o
d
ellin
g
,
s
h
o
win
g
it
s
im
p
o
r
tan
ce
in
d
ea
lin
g
with
u
n
ce
r
tain
ty
in
d
em
an
d
.
Al
th
o
u
g
h
v
a
r
io
u
s
m
o
d
els
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
,
a
co
m
p
r
eh
en
s
iv
e
p
r
o
d
u
ctio
n
-
a
v
ailab
il
ity
m
o
d
el
co
n
s
id
er
s
d
ef
e
ctiv
e
p
r
o
d
u
cts,
r
ewo
r
k
,
an
d
s
cr
ap
an
d
f
ac
es
s
to
ch
asti
c
ch
allen
g
es
in
d
em
an
d
.
Pre
v
io
u
s
r
esear
ch
h
as
p
r
o
v
id
ed
v
alu
a
b
le
in
s
ig
h
ts
in
to
i
n
teg
r
atin
g
th
ese
elem
e
n
t
s
in
to
th
e
m
o
d
el.
Ho
wev
e
r
,
t
h
er
e
s
till
n
ee
d
s
to
b
e
g
ap
s
in
o
u
r
u
n
d
er
s
tan
d
in
g
o
f
h
o
w
th
ese
f
ac
to
r
s
in
ter
ac
t
an
d
im
p
ac
t
o
v
er
all
in
v
e
n
to
r
y
m
an
ag
em
en
t
d
ec
is
io
n
s
.
T
h
e
lack
o
f
m
o
d
els
th
at
ca
n
ac
co
m
m
o
d
ate
all
th
ese
f
ac
to
r
s
s
im
u
ltan
eo
u
s
ly
im
p
lies
th
at
d
ec
is
io
n
-
m
ak
er
s
d
o
n
o
t
y
et
h
av
e
t
h
e
o
p
tim
al
to
o
ls
to
co
p
e
with
th
e
c
o
m
p
lex
ities
in
a
co
n
s
tan
tly
ch
an
g
in
g
p
r
o
d
u
ctio
n
an
d
d
e
m
an
d
en
v
ir
o
n
m
en
t.
T
h
er
ef
o
r
e,
th
er
e
is
a
n
ee
d
f
o
r
a
m
o
d
el
th
at
ca
n
in
teg
r
ate
all
asp
ec
ts
,
s
u
ch
as
d
ef
ec
tiv
e
p
r
o
d
u
cts,
r
ewo
r
k
,
an
d
s
cr
ap
,
an
d
d
ea
l
with
s
to
ch
asti
c
ch
allen
g
es
s
o
th
at
d
ec
is
io
n
-
m
ak
er
s
m
ak
e
m
o
r
e
in
f
o
r
m
ed
an
d
ef
f
ec
tiv
e
d
ec
is
io
n
s
in
m
an
a
g
in
g
th
eir
i
n
v
en
to
r
y
,
im
p
r
o
v
e
o
p
e
r
atio
n
al
ef
f
icien
c
y
an
d
r
esp
o
n
d
b
etter
t
o
ch
a
n
g
es
in
th
e
m
ar
k
et.
T
h
is
r
esear
ch
aim
s
to
d
e
v
elo
p
a
co
m
p
r
eh
e
n
s
iv
e
p
r
o
d
u
ctio
n
-
in
v
e
n
to
r
y
m
o
d
el
th
at
co
n
s
id
er
s
d
ef
ec
tiv
e
p
r
o
d
u
cts,
r
ewo
r
k
,
a
n
d
s
cr
ap
an
d
f
ac
es
s
to
ch
asti
c
ch
allen
g
es
in
d
em
a
n
d
.
I
n
ad
d
itio
n
,
th
is
r
esear
ch
aim
s
to
o
f
f
er
th
e
m
etah
eu
r
is
tic
p
r
o
ce
d
u
r
e
o
f
t
h
e
Aq
u
ila
alg
o
r
ith
m
as
a
m
et
h
o
d
to
f
in
d
th
e
o
p
tim
al
d
ec
is
io
n
v
ar
iab
les
[
2
6
]
.
T
h
e
Aq
u
ila
o
p
t
im
izer
,
wh
ich
is
in
s
p
ir
ed
b
y
t
h
e
h
u
n
tin
g
b
eh
a
v
io
r
o
f
th
e
Aq
u
ila
H
awk
th
at
ca
n
h
u
n
t
p
r
ey
,
h
a
s
p
r
o
v
e
n
to
b
e
ef
f
ec
tiv
e
i
n
s
o
lv
in
g
v
ar
i
o
u
s
p
r
o
b
lem
s
,
in
clu
d
i
n
g
in
d
u
s
tr
ial
en
g
in
ee
r
in
g
o
p
tim
izatio
n
p
r
o
b
lem
s
[
2
7
]
,
i
m
ag
e
class
if
icatio
n
[
2
8
]
,
a
n
d
p
o
p
u
latio
n
f
o
r
ec
ast
[
2
9
]
.
W
e
s
ee
k
to
ap
p
ly
th
is
p
r
o
ce
d
u
r
e
to
s
o
lv
e
c
o
m
p
lex
p
r
o
b
lem
s
in
p
r
o
d
u
ctio
n
-
av
ailab
ilit
y
m
o
d
els
b
ased
o
n
its
ef
f
ec
tiv
en
ess
in
v
ar
io
u
s
co
n
tex
ts
.
T
h
u
s
,
th
is
r
esear
ch
n
o
t
o
n
l
y
aim
s
t
o
f
ill
th
e
g
ap
in
u
n
d
er
s
tan
d
in
g
c
o
m
p
r
e
h
en
s
iv
e
p
r
o
d
u
ctio
n
-
av
ailab
ilit
y
m
o
d
els
b
u
t
al
s
o
to
test
an
d
v
alid
ate
th
e
p
o
ten
tial
o
f
th
e
Aq
u
ila
alg
o
r
it
h
m
as
an
ef
f
ec
tiv
e
o
p
tim
izatio
n
to
o
l.
T
h
is
r
esear
ch
co
n
tr
i
b
u
tes
s
ig
n
if
ican
tly
b
y
p
r
o
v
id
in
g
n
ew
in
s
ig
h
ts
in
to
a
co
m
p
r
eh
en
s
iv
e
p
r
o
d
u
ctio
n
-
av
ailab
ilit
y
m
o
d
el,
wh
ich
co
n
s
id
er
s
d
ef
ec
tiv
e
p
r
o
d
u
cts,
r
ew
o
r
k
,
a
n
d
s
cr
ap
a
n
d
f
ac
es
s
to
c
h
asti
c
ch
allen
g
es
in
d
em
an
d
.
Su
ch
co
n
tr
i
b
u
tio
n
s
in
clu
d
e
n
o
t
o
n
ly
th
e
d
ev
elo
p
m
en
t
o
f
a
n
ew
m
o
d
el
th
at
i
s
ex
p
ec
ted
t
o
h
el
p
co
m
p
an
ies
im
p
r
o
v
e
p
r
o
d
u
ctio
n
ef
f
icien
cy
an
d
o
p
tim
ize
in
v
en
to
r
y
lev
els
b
u
t
also
p
r
o
v
id
e
a
s
o
lid
f
o
u
n
d
atio
n
fo
r
ad
a
p
tiv
e
d
ec
is
io
n
-
m
a
k
in
g
am
id
u
n
p
r
ed
ictab
le
m
a
r
k
et
d
y
n
am
ics
in
th
is
er
a
o
f
u
n
ce
r
tain
ty
.
I
n
a
d
d
itio
n
,
t
h
is
r
esear
ch
p
r
o
p
o
s
es
a
n
ew
p
r
o
ce
d
u
r
e
f
o
r
th
e
Aq
u
ila
alg
o
r
it
h
m
to
o
p
tim
ize
th
e
p
r
o
d
u
cti
o
n
-
in
v
e
n
to
r
y
m
o
d
el
p
r
o
b
lem
.
W
ith
th
is
n
ew
p
r
o
c
ed
u
r
e,
t
h
is
r
esear
c
h
en
r
ic
h
es
th
e
o
p
tim
izatio
n
p
r
o
ce
d
u
r
es
u
s
ed
in
p
r
o
d
u
cti
o
n
-
av
ailab
ilit
y
m
o
d
el
o
p
tim
izati
o
n
,
m
ak
in
g
v
alu
a
b
le
co
n
tr
ib
u
tio
n
s
to
d
ev
elo
p
in
g
an
aly
ti
ca
l
m
eth
o
d
s
i
n
th
e
co
n
tex
t
o
f
co
m
p
lex
in
v
e
n
to
r
y
m
an
ag
em
en
t.
T
h
u
s
,
th
is
r
esear
ch
is
ex
p
ec
ted
to
p
r
o
v
i
d
e
p
r
a
ctica
l
g
u
id
an
ce
f
o
r
co
m
p
an
ies
in
m
an
ag
in
g
th
ei
r
in
v
en
t
o
r
ies
m
o
r
e
ef
f
ec
tiv
el
y
an
d
en
r
ich
th
e
ac
a
d
em
ic
l
iter
atu
r
e
with
n
ew
co
n
tr
ib
u
tio
n
s
in
th
is
f
ield
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
1
3
,
No
.
4
,
Dec
em
b
er
2
0
2
4
:
900
-
9
10
902
2.
DE
SCR
I
P
T
I
O
N
P
RO
B
L
E
M
AND
P
RO
P
O
SE
D
M
O
DE
L
2
.
1
.
Sy
s
t
e
m
cha
ra
ct
er
is
t
ics
I
n
v
en
to
r
y
s
y
s
tem
s
in
m
an
u
f
a
ctu
r
in
g
co
m
p
an
ies
h
av
e
co
m
p
lex
ch
ar
ac
ter
is
tics
an
d
in
v
o
l
v
e
v
ar
io
u
s
ty
p
es
o
f
s
ig
n
if
ican
t
co
s
ts
in
th
e
p
r
o
d
u
ctio
n
p
r
o
ce
s
s
.
So
m
e
o
f
th
e
ess
en
tial
co
s
ts
in
v
o
lv
ed
in
th
is
s
y
s
tem
in
clu
d
e
s
etu
p
co
s
t
(
K)
,
r
eg
u
l
ar
p
r
o
d
u
ctio
n
c
o
s
t
(
c)
,
s
cr
ap
p
r
o
d
u
ct
d
is
p
o
s
al
c
o
s
t
(
cs),
r
e
wo
r
k
co
s
t
(
cr
)
,
an
d
f
in
is
h
ed
p
r
o
d
u
ct
h
o
l
d
in
g
c
o
s
t
(
h
)
.
E
ac
h
co
s
t
elem
en
t
is
es
s
en
tial
in
o
p
tim
izin
g
p
r
o
d
u
ct
io
n
ef
f
icien
c
y
a
n
d
in
v
en
to
r
y
m
an
a
g
em
en
t.
Ho
w
ev
er
,
a
s
ig
n
if
ican
t
ch
allen
g
e
in
in
v
e
n
to
r
y
m
an
a
g
em
en
t
is
th
e
f
lu
ct
u
atio
n
o
r
s
to
ch
asti
city
o
f
co
n
s
u
m
e
r
d
e
m
an
d
(
D)
.
E
r
r
atic
d
em
an
d
ev
er
y
m
o
n
th
cr
ea
tes
th
e
n
ee
d
to
im
p
lem
en
t
a
s
af
ety
s
tr
ateg
y
.
T
h
e
r
ef
o
r
e
,
co
m
p
an
ie
s
m
u
s
t
id
en
tify
an
d
d
eter
m
in
e
th
e
n
u
m
b
e
r
o
f
s
af
ety
p
r
o
d
u
cts
(
S)
to
m
ain
tain
p
r
o
d
u
ct
av
ailab
ilit
y
wh
en
d
em
an
d
s
u
d
d
e
n
ly
in
c
r
ea
s
es o
r
s
ig
n
if
ica
n
t f
lu
ctu
atio
n
s
o
cc
u
r
.
I
n
ad
d
itio
n
,
co
m
p
a
n
ies
s
h
o
u
ld
also
co
n
s
id
er
p
r
o
d
u
ctio
n
asp
ec
ts
s
u
ch
as
p
r
o
d
u
ctio
n
q
u
an
tity
(
Q)
,
p
r
o
d
u
ctio
n
r
ate
(
P),
an
d
r
ewo
r
k
r
ate
(
P1
)
in
th
eir
in
v
e
n
to
r
y
s
y
s
tem
.
T
h
e
P
s
h
o
u
ld
b
e
s
et
to
m
ee
t
o
r
e
v
en
ex
ce
ed
D,
en
s
u
r
in
g
ad
e
q
u
ate
p
r
o
d
u
ct
av
ailab
ilit
y
.
C
o
m
p
an
i
es
m
u
s
t
also
co
n
s
id
er
th
e
P1
t
o
ad
d
r
ess
d
ef
ec
tiv
e
o
r
n
o
n
-
s
tan
d
ar
d
p
r
o
d
u
cts.
M
an
ag
in
g
th
is
r
ewo
r
k
r
ate
is
cr
itical
in
m
in
im
izin
g
lo
s
s
es
an
d
en
s
u
r
i
n
g
th
e
p
r
o
d
u
cts'
q
u
ality
m
ee
ts
th
e
s
et
s
tan
d
ar
d
s
.
2
.
2
.
Ass
um
ptio
ns
a
nd
no
t
a
t
io
ns
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
a
s
s
u
m
p
tio
n
s
an
d
n
o
tatio
n
s
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el.
So
m
e
o
f
th
e
k
ey
ass
u
m
p
tio
n
s
u
s
ed
as
a
f
o
u
n
d
at
io
n
in
d
esig
n
in
g
t
h
e
m
o
d
el
a
r
e
i)
o
r
d
er
i
n
g
co
s
ts
ar
e
c
o
n
s
tan
t,
m
ea
n
in
g
th
at
th
e
co
s
ts
in
v
o
lv
ed
in
th
e
o
r
d
er
in
g
p
r
o
ce
s
s
d
o
n
o
t
d
e
p
en
d
o
n
th
e
am
o
u
n
t
o
f
o
r
d
e
r
in
g
;
ii)
th
er
e
is
n
o
s
h
o
r
tag
e
o
f
r
aw
m
ater
ials
,
s
o
in
v
en
to
r
y
is
alwa
y
s
av
ailab
le
to
m
ee
t
d
em
an
d
;
iii)
s
tatin
g
th
at
s
to
r
ag
e
ca
p
ac
ity
is
u
n
lim
ited
,
th
u
s
r
em
o
v
in
g
th
e
p
h
y
s
ical
lim
itatio
n
s
ass
o
ciate
d
with
th
e
am
o
u
n
t
o
f
g
o
o
d
s
t
h
at
c
an
b
e
s
to
r
ed
;
iv
)
d
em
a
n
d
lev
els
ar
e
s
to
ch
asti
c
an
d
n
o
r
m
ally
d
is
tr
ib
u
ted
,
th
u
s
allo
wi
n
g
th
e
m
o
d
el
to
ac
c
o
u
n
t
f
o
r
d
em
an
d
v
ar
iatio
n
s
s
tatis
t
ically
;
an
d
v
)
s
tatin
g
t
h
at
r
eg
u
lar
s
to
r
ag
e
c
o
s
ts
an
d
r
ewo
r
k
co
s
ts
ar
e
ass
u
m
ed
to
b
e
e
q
u
al,
t
h
u
s
s
im
p
lify
in
g
th
e
o
v
er
al
l
co
s
t
an
aly
s
is
.
T
h
ese
f
iv
e
ass
u
m
p
tio
n
s
f
o
r
m
t
h
e
th
eo
r
etica
l
b
a
s
is
f
o
r
d
ev
elo
p
i
n
g
in
v
en
to
r
y
m
o
d
els in
th
e
co
n
tex
t o
f
p
r
o
d
u
ctio
n
a
v
ailab
ilit
y
p
r
o
b
lem
s
.
T
h
e
n
o
tatio
n
s
u
s
ed
in
th
is
r
esear
ch
ar
e
:
:
p
r
o
d
u
ctio
n
r
ate
p
er
u
n
it o
f
tim
e
1
:
r
ewo
r
k
r
ate
p
er
u
n
i
t o
f
tim
e
:
p
r
o
d
u
ctio
n
lo
t size
p
er
cy
cle
:
n
u
m
b
er
o
f
d
em
an
d
s
p
er
u
n
it o
f
tim
e
:
p
r
o
d
u
ctio
n
r
ate
o
f
d
e
f
ec
tiv
e
it
em
s
p
er
u
n
it
o
f
tim
e
1
:
p
r
o
d
u
ctio
n
r
ate
o
f
lef
to
v
er
p
r
o
d
u
cts d
u
r
in
g
r
ewo
r
k
p
e
r
u
n
it ti
m
e
2
:
p
r
o
d
u
ctio
n
r
ate
o
f
im
p
e
r
f
ec
t q
u
ality
item
s
d
u
r
in
g
r
ewo
r
k
p
er
u
n
it tim
e
0
:
to
tal
p
r
o
d
u
ctio
n
r
ate
o
f
lef
to
v
e
r
p
r
o
d
u
cts an
d
im
p
er
f
ec
t
q
u
ali
ty
item
s
p
er
u
n
it
o
f
tim
e
1
:
p
r
o
d
u
ctio
n
u
p
tim
e
in
th
e
p
r
ese
n
ce
o
f
in
v
en
to
r
y
2
:
tim
e
s
p
en
t r
ewo
r
k
in
g
3
:
tim
e
u
s
ed
wh
en
in
v
en
to
r
y
r
u
n
s
o
u
t
:
cy
cle
len
g
th
,
=
1
+
2
+
3
:
th
e
p
r
o
p
o
r
tio
n
o
f
d
ef
ec
tiv
e
ite
m
s
p
r
o
d
u
ce
d
:
th
e
p
r
o
p
o
r
tio
n
o
f
s
cr
a
p
in
d
e
f
e
ctiv
e
item
s
:
th
e
p
r
o
p
o
r
tio
n
o
f
im
p
er
f
ec
t
q
u
ality
item
s
in
d
ef
ec
tiv
e
item
s
:
th
e
p
r
o
p
o
r
tio
n
o
f
r
ep
r
o
ce
s
s
in
g
in
d
ef
ec
tiv
e
item
s
1
:
th
e
p
r
o
p
o
r
tio
n
o
f
s
cr
a
p
g
en
e
r
a
ted
d
u
r
in
g
r
ewo
r
k
1
:
th
e
p
r
o
p
o
r
tio
n
o
f
im
p
er
f
ec
t
q
u
ality
item
s
p
r
o
d
u
ce
d
d
u
r
in
g
r
e
wo
r
k
(
.
)
:
esti
m
ated
v
alu
e
:
s
etu
p
co
s
t f
o
r
ea
c
h
p
r
o
d
u
ctio
n
(
I
DR
)
:
th
e
m
ax
im
u
m
lev
el
o
f
on
-
h
an
d
in
v
en
t
o
r
y
o
f
p
e
r
f
ec
t item
s
in
u
n
its
wh
en
th
e
r
ewo
r
k
p
r
o
ce
s
s
en
d
s
:
p
r
o
d
u
ctio
n
co
s
t p
e
r
u
n
it
(
I
DR
)
1
:
th
e
m
ax
im
u
m
lev
el
o
f
o
n
-
h
a
n
d
in
v
e
n
to
r
y
o
f
p
e
r
f
ec
t
item
s
i
n
u
n
its
wh
en
th
e
r
e
g
u
lar
p
r
o
d
u
ctio
n
p
r
o
ce
s
s
s
to
p
s
:
d
is
p
o
s
al
co
s
t p
er
u
n
it
o
f
lef
to
v
er
p
r
o
d
u
ct
(
I
DR
)
ℎ
:
in
v
en
to
r
y
co
s
t p
er
u
n
it (
I
DR
)
:
r
ewo
r
k
co
s
t p
e
r
r
ewo
r
k
p
r
o
d
u
ct
(
I
DR
)
:
s
tan
d
ar
d
d
e
v
iatio
n
o
f
d
em
an
d
p
er
u
n
it
o
f
tim
e
:
s
af
ety
f
ac
to
r
:
lo
s
t
s
ale
co
s
t (
I
DR
)
(
)
:
p
r
o
b
a
b
ilit
y
d
en
s
ity
f
u
n
ctio
n
o
f
th
e
n
o
r
m
al
d
is
tr
ib
u
tio
n
(
)
:
cu
m
u
lativ
e
d
is
tr
ib
u
tio
n
f
u
n
ctio
n
o
f
th
e
n
o
r
m
al
d
is
tr
ib
u
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
Th
e
p
r
o
d
u
ctio
n
-
in
ve
n
to
r
y
mo
d
el
w
ith
imp
erfect,
r
e
w
o
r
k,
a
n
d
s
cra
p
items u
n
d
er
…
(
Da
n
a
Ma
r
s
etiya
Uta
ma
)
903
2
.
3
.
P
r
o
po
s
ed
pro
du
ct
io
n
-
in
v
ent
o
ry
m
o
del
T
h
is
s
tu
d
y
p
r
o
p
o
s
es
an
in
v
en
t
o
r
y
p
r
o
d
u
ctio
n
m
o
d
el
in
v
o
lv
i
n
g
im
p
er
f
ec
t,
r
ewo
r
k
ed
,
an
d
s
cr
ap
item
s
u
n
d
er
s
to
ch
asti
c
d
em
a
n
d
.
T
h
e
p
r
o
p
o
s
ed
m
ath
em
atica
l
m
o
d
el
aim
s
to
m
in
im
ize
th
e
to
t
al
in
v
en
to
r
y
co
s
t.
Fig
u
r
e
1
s
h
o
ws
th
e
p
r
o
p
o
s
ed
m
o
d
el'
s
av
ailab
le
in
v
en
to
r
y
a
n
d
allo
wab
le
o
r
d
er
lev
els.
T
h
e
tim
e
d
u
r
atio
n
o
f
a
cy
cle
is
th
e
s
u
m
o
f
th
e
r
eg
u
la
r
p
r
o
d
u
ctio
n
tim
e
(
1
)
,
r
ewo
r
k
ti
m
e
(
2
)
,
an
d
p
r
o
d
u
ctio
n
d
o
wn
ti
m
e
(
3
)
.
T
h
e
1
,
2
,
an
d
3
ar
e
p
r
esen
ted
in
(
1
)
-
(
3
)
,
r
esp
ec
tiv
ely
.
Me
an
w
h
ile,
b
ased
o
n
Fig
u
r
e
1
,
th
e
m
ax
im
u
m
lev
el
o
f
o
n
-
h
an
d
in
v
e
n
to
r
y
o
f
p
e
r
f
ec
t
item
s
in
u
n
its
wh
en
th
e
r
eg
u
lar
p
r
o
d
u
ctio
n
p
r
o
ce
s
s
s
to
p
s
(
1
)
a
n
d
th
e
m
ax
im
u
m
lev
el
o
f
o
n
-
h
an
d
in
v
e
n
to
r
y
o
f
p
er
f
ec
t
item
s
in
u
n
its
wh
en
t
h
e
r
ewo
r
k
p
r
o
ce
s
s
en
d
s
(
)
ca
n
b
e
f
o
r
m
u
lated
in
(
4
)
a
n
d
(
5
)
.
I
n
th
e
p
r
o
p
o
s
ed
m
o
d
el,
p
r
o
d
u
cts
ar
e
also
d
e
f
ec
tiv
e
d
u
r
i
n
g
p
r
o
d
u
ctio
n
,
s
o
th
e
in
v
e
n
to
r
y
lev
el
n
ee
d
s
to
b
e
esti
m
ated
.
An
i
llu
s
tr
atio
n
o
f
th
e
o
n
-
h
an
d
in
v
e
n
t
o
r
y
lev
el
o
f
d
ef
ec
tiv
e
item
s
is
s
h
o
wn
in
Fig
u
r
e
2
.
Def
ec
tiv
e
item
s
p
r
o
d
u
ce
d
d
u
r
i
n
g
1
ar
e
ca
lcu
lated
as in
(
6
)
.
1
=
′
=
1
−
−
(
1
)
2
=
−
1
1
−
0
−
(
2
)
3
=
(
3
)
1
=
(
−
−
)
1
(
4
)
=
1
+
(
1
−
0
−
)
2
(
5
)
=
.
1
=
(
6
)
Fig
u
r
e
1
.
I
ll
u
s
tr
atio
n
o
f
p
er
f
ec
t in
v
en
to
r
y
o
n
h
an
d
Fig
u
r
e
2
.
I
ll
u
s
tr
atio
n
o
f
i
n
v
en
t
o
r
y
lev
els o
f
a
d
ef
ec
tiv
e
item
I
n
th
is
p
r
o
p
o
s
ed
m
o
d
el,
th
e
m
ain
f
o
c
u
s
is
to
elab
o
r
ate
th
e
m
o
d
el
b
ased
o
n
th
e
illu
s
tr
ated
o
n
-
h
an
d
in
v
en
to
r
y
o
f
r
ewo
r
k
a
b
le
item
s
,
im
p
er
f
ec
t
q
u
ality
item
s
,
an
d
s
cr
ap
item
s
,
as
s
h
o
w
n
in
Fig
u
r
e
s
3
-
5
.
Fig
u
r
e
3
s
h
o
ws
th
e
illu
s
tr
ated
in
v
en
to
r
y
lev
els
o
f
r
ewo
r
k
a
b
le
item
s
,
wh
ile
Fig
u
r
e
s
4
an
d
5
d
is
p
lay
th
e
in
v
en
to
r
y
lev
els
o
f
im
p
er
f
ec
t
q
u
ali
ty
item
s
an
d
s
cr
ap
item
s
.
I
n
th
is
co
n
tex
t,
it
is
as
s
u
m
ed
th
at
th
e
p
r
o
p
o
r
tio
n
β
o
f
d
ef
ec
tiv
e
item
s
ca
n
b
e
r
eg
a
r
d
ed
as
r
ewo
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k
ab
le
item
s
,
th
e
p
r
o
p
o
r
tio
n
θ
as
s
cr
ap
item
s
,
an
d
th
e
p
r
o
p
o
r
tio
n
γ
as
im
p
er
f
ec
t
q
u
ality
item
s
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
f
o
r
t
h
e
n
u
m
b
er
o
f
r
e
wo
r
k
ab
le
item
s
,
item
s
o
f
im
p
er
f
e
ct
q
u
ality
,
an
d
s
cr
ap
item
s
p
r
o
d
u
ce
d
d
u
r
in
g
a
r
eg
u
l
ar
p
r
o
d
u
ctio
n
p
r
o
ce
s
s
ca
n
b
e
f
o
r
m
u
lated
u
s
in
g
(
7
)
-
(
9
)
.
1
=
.
1
=
1
2
=
(
7
)
2
=
.
1
=
(
8
)
4
=
.
1
=
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
1
3
,
No
.
4
,
Dec
em
b
er
2
0
2
4
:
900
-
9
10
904
Fig
u
r
e
3
.
On
-
h
an
d
in
v
e
n
to
r
y
lev
el
o
f
r
ew
o
r
k
ab
le
item
s
Fig
u
r
e
4
.
On
-
h
an
d
in
v
e
n
to
r
y
lev
el
o
f
im
p
e
r
f
ec
t q
u
ality
item
s
Fig
u
r
e
5
.
On
-
h
an
d
in
v
e
n
to
r
y
lev
el
o
f
s
cr
ap
item
s
Du
r
in
g
th
e
r
ewo
r
k
p
r
o
ce
s
s
,
th
e
s
cr
ap
a
n
d
im
p
er
f
ec
t
q
u
ality
p
r
o
d
u
ctio
n
r
ates
ar
e
cr
u
cial
p
ar
am
eter
s
to
co
n
s
id
er
.
T
h
ese
two
p
ar
am
eter
s
ar
e
r
ep
r
esen
ted
b
y
(
1
0
)
an
d
(
1
1
)
.
T
o
m
ea
s
u
r
e
t
h
e
to
ta
l
im
p
er
f
ec
t
q
u
ality
g
o
o
d
s
an
d
s
cr
a
p
g
o
o
d
s
p
r
o
d
u
ce
d
d
u
r
in
g
th
is
p
r
o
ce
s
s
,
e
qua
t
io
n
s
(
1
2
)
an
d
(
1
3
)
ar
e
u
s
ed
.
F
u
r
th
er
m
o
r
e,
in
th
is
co
n
tex
t,
it
is
ass
u
m
ed
t
h
at
0
is
th
e
s
u
m
o
f
th
e
p
r
o
d
u
ctio
n
r
ates
o
f
s
cr
ap
an
d
im
p
er
f
ec
t
q
u
ality
g
o
o
d
s
p
r
o
d
u
ce
d
d
u
r
in
g
th
e
r
ewo
r
k
p
r
o
ce
s
s
.
T
h
is
m
ea
s
u
r
em
en
t
i
s
ex
p
r
ess
ed
in
(
1
4
)
.
Fu
r
t
h
er
m
o
r
e,
th
e
i
n
v
en
to
r
y
lev
els
in
th
e
h
an
d
s
o
f
1
an
d
H
ca
n
b
e
esti
m
ated
b
ased
o
n
(
1
5
)
an
d
(
1
6
)
.
W
h
er
e,
−
−
=
(
1
−
−
)
=
1
an
d
1
−
0
−
=
1
(
1
−
1
−
1
−
1
)
=
1
2
.
Hen
ce
,
th
e
v
alu
e
o
f
T
is
ca
lcu
lated
b
ased
o
n
(
1
7
)
.
1
=
1
1
(
1
0
)
2
=
1
1
(
1
1
)
3
=
2
+
2
2
=
(
+
1
)
(
1
2
)
5
=
4
+
1
2
=
(
+
1
)
(
1
3
)
0
=
1
+
2
=
1
(
1
+
1
)
(
1
4
)
1
=
(
−
−
)
1
=
1
(
1
5
)
=
1
+
(
1
−
0
−
)
1
=
1
−
+
2
=
(
1
+
2
)
(
1
6
)
=
1
+
2
+
3
=
[
1
−
(
1
−
(
1
−
1
−
1
)
)
]
(
1
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
Th
e
p
r
o
d
u
ctio
n
-
in
ve
n
to
r
y
mo
d
el
w
ith
imp
erfect,
r
e
w
o
r
k,
a
n
d
s
cra
p
items u
n
d
er
…
(
Da
n
a
Ma
r
s
etiya
Uta
ma
)
905
Sin
ce
p
r
o
d
u
ct
d
em
an
d
is
s
t
o
ch
asti
c
with
a
n
o
r
m
al
d
is
tr
ib
u
tio
n
,
d
ec
is
io
n
-
m
a
k
er
s
m
u
s
t
in
cr
ea
s
e
in
v
en
to
r
y
lev
els b
y
in
v
o
lv
in
g
s
af
ety
s
to
ck
(
S)
.
T
h
e
S o
f
th
e
p
r
o
d
u
ct
is
m
o
d
eled
in
(
1
8
)
,
w
h
ich
is
ad
ap
ted
f
r
o
m
th
e
m
o
d
el
p
r
o
p
o
s
ed
b
y
Utam
a
et
a
l
.
[
3
0
]
.
I
n
ad
d
itio
n
,
t
h
e
e
x
p
ec
ted
d
e
m
an
d
s
h
o
r
tag
e
o
f
th
e
p
er
io
d
⁄
=
is
m
o
d
eled
in
(
1
9
)
,
wh
er
e
(
)
=
{
(
)
−
[
1
−
(
)
]
}
.
=
√
(
1
8
)
√
(
)
(
1
9
)
T
h
e
ex
p
ec
tatio
n
o
f
t
o
tal
in
v
e
n
to
r
y
c
o
s
t
in
ea
c
h
cy
cle
is
m
o
d
eled
in
(
2
0
)
.
Me
an
w
h
ile,
th
e
p
r
o
p
o
r
tio
n
o
f
d
ef
ec
tiv
e
p
r
o
d
u
cts
is
a
r
an
d
o
m
v
ar
iab
le,
s
o
th
e
p
r
o
d
u
ctio
n
cy
cle
le
n
g
t
h
T
is
also
a
r
an
d
o
m
v
ar
iab
le.
T
h
en
,
th
e
ex
p
ec
ted
c
y
cle
len
g
th
(
)
ca
n
b
e
f
o
r
m
u
lated
in
(
2
1
)
.
(
,
)
=
+
+
+
1
+
+
ℎ
(
1
(
1
)
2
+
(
1
+
)
(
2
)
2
+
(
3
)
2
+
(
1
)
2
+
1
(
2
)
2
+
√
)
+
(
√
(
)
)
=
+
+
(
+
1
)
+
+
2
(
ℎ
(
1
2
+
(
1
+
2
)
2
1
+
(
1
+
2
)
2
2
)
+
2
+
2
2
2
1
+
√
)
+
(
√
(
)
)
(
2
0
)
(
)
=
[
1
−
(
)
(
1
−
(
1
−
1
−
1
)
)
]
=
(
1
−
1
)
(
2
1
)
W
h
er
e,
1
=
(
)
(
1
−
(
1
−
1
−
1
)
)
,
2
=
1
−
(
)
−
,
3
=
(
1
−
−
)
.
B
ased
o
n
th
e
(
1
)
-
(
1
9
)
,
th
e
t
o
tal
ex
p
ec
ted
i
n
v
e
n
to
r
y
co
s
t
in
a
o
n
e
-
tim
e
h
o
r
izo
n
ca
n
b
e
m
o
d
eled
in
(
2
2
)
.
M
in
im
ize
th
e
to
tal
co
s
t
o
f
th
e
in
v
en
to
r
y
s
y
s
tem
,
ca
n
b
e
ac
h
iev
ed
b
y
s
im
u
ltan
eo
u
s
ly
d
eter
m
in
in
g
th
e
o
p
tim
al
d
ec
is
io
n
v
ar
iab
les,
n
a
m
ely
th
e
p
r
o
d
u
ctio
n
lo
t
s
ize
p
er
cy
cle
(
Q)
,
s
af
ety
f
ac
t
o
r
(
k
)
,
p
r
o
d
u
ctio
n
r
ate
(
P),
an
d
r
ewo
r
k
p
r
o
d
u
ctio
n
r
ate
(
1
)
.
T
h
e
p
r
o
d
u
ct
k
i
n
a
n
o
r
m
al
d
is
tr
ib
u
tio
n
m
u
s
t
b
e
g
r
ea
ter
th
an
0
an
d
ca
n
n
o
t
ex
ce
ed
2
.
9
9
.
Me
a
n
wh
ile,
th
e
P a
n
d
1
m
u
s
t b
e
h
ig
h
er
th
an
t
h
e
D.
(
(
,
,
,
1
)
)
=
(
(
,
)
)
(
)
=
(
1
−
1
)
+
(
+
(
)
[
(
+
1
)
+
]
)
(
1
−
1
)
+
ℎ
2
1
(
1
−
1
)
(
(
(
1
+
1
2
)
2
+
1
ℎ
)
2
(
2
)
+
2
(
1
+
1
2
2
)
(
)
2
+
(
1
+
2
+
3
)
1
2
+
√
(
1
−
1
)
)
+
(
1
−
1
)
√
(
1
−
1
)
(
)
(
2
2
)
3.
M
E
T
H
O
DS
3
.
1
.
P
r
o
po
s
ed
m
et
ho
d
A
qu
ila
o
ptim
izer
a
lg
o
rit
hm
T
o
o
p
tim
ize
th
e
p
r
o
d
u
ctio
n
-
i
n
v
en
to
r
y
m
o
d
el
p
r
o
b
lem
with
im
p
er
f
ec
t,
r
ewo
r
k
ed
,
an
d
s
cr
ap
item
s
u
n
d
er
s
to
ch
asti
c
d
em
a
n
d
,
th
i
s
s
tu
d
y
p
r
o
p
o
s
es
th
e
ad
v
an
c
ed
p
r
o
ce
d
u
r
e
o
f
Aq
u
ila
o
p
ti
m
izer
.
T
h
e
Aq
u
ila
o
p
tim
izer
is
an
alg
o
r
ith
m
in
s
p
ir
ed
b
y
th
e
h
u
n
tin
g
b
e
h
av
io
r
o
f
A
q
u
ila
H
awk
s
th
at
ca
n
h
u
n
t
p
r
e
y
[
2
8
]
.
T
h
e
Aq
u
ila
o
p
tim
izer
alg
o
r
ith
m
p
s
eu
d
o
co
d
e
is
p
r
esen
ted
in
Alg
o
r
ith
m
1
.
T
h
e
f
ir
s
t
p
h
ase
o
f
Aq
u
ila
in
h
u
n
tin
g
p
r
ey
is
to
e
x
p
an
d
th
e
s
ea
r
ch
.
W
h
er
e
th
e
Aq
u
ila
is
at
a
h
eig
h
t
to
d
eter
m
in
e
th
e
lo
ca
tio
n
o
f
its
p
r
ey
,
th
is
b
eh
a
v
io
r
is
d
escr
ib
e
d
b
y
(
2
3
)
.
1
(
+
1
)
=
(
)
×
(
1
−
)
+
(
(
)
−
(
)
∗
)
(
2
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
1
3
,
No
.
4
,
Dec
em
b
er
2
0
2
4
:
900
-
9
10
906
W
h
er
e,
1
(
+
1
)
is
th
e
r
esu
lt
f
o
r
t
in
th
e
n
ex
t
iter
atio
n
.
(
)
,
th
e
b
est
r
esu
lt
o
b
tain
ed
b
y
iter
atio
n
t
(
p
r
ey
p
o
s
itio
n
)
.
T
h
e
n
u
m
b
er
o
f
iter
a
tio
n
s
(
1
−
/
)
is
u
s
ed
to
ex
p
an
d
th
e
s
ea
r
ch
.
(
)
in
d
icate
s
th
e
a
v
er
ag
e
v
a
lu
e
o
f
iter
atio
n
t c
alcu
lated
b
ased
o
n
(
)
=
1
∑
(
)
=
1
.
R
an
d
is
a
r
an
d
o
m
v
alu
e
b
etwe
en
0
an
d
1
.
T
h
e
s
ec
o
n
d
p
h
ase
is
wh
en
th
e
p
r
ey
h
as
b
ee
n
f
o
u
n
d
at
a
h
ei
g
h
t,
a
n
d
t
h
e
Aq
u
ila
s
tar
ts
to
a
ttack
(
2
)
.
I
n
th
is
p
h
ase,
th
e
A
q
u
ila
cir
cl
es
ab
o
v
e
its
p
r
ey
an
d
p
r
e
p
ar
es
th
e
ter
r
ai
n
b
e
f
o
r
e
attac
k
in
g
af
ter
f
in
d
in
g
th
e
p
r
e
y
ar
ea
f
r
o
m
a
h
ei
g
h
t.
T
h
is
m
et
h
o
d
'
s
b
eh
av
io
r
is
co
n
to
u
r
f
ly
i
n
g
with
a
s
h
o
r
t
g
lid
in
g
attac
k
.
T
h
is
b
eh
av
io
r
is
ca
lled
n
ar
r
o
w
ex
p
lo
r
atio
n
,
m
o
d
eled
in
(
2
4
)
.
D
is
th
e
d
im
en
s
i
o
n
al
s
p
ac
e,
an
d
(
)
d
en
o
tes th
e
d
i
s
tr
ib
u
tio
n
f
u
n
ctio
n
o
f
th
e
s
tep
s
ize.
Me
an
wh
ile,
(
)
is
a
r
an
d
o
m
s
o
lu
tio
n
f
r
o
m
th
e
r
an
g
e
[
1
]
at
iter
atio
n
i.
2
(
+
1
)
=
(
)
×
(
)
+
(
)
−
(
−
)
∗
(
2
4
)
I
n
th
e
th
ir
d
p
h
ase
(
3
)
,
th
e
Aq
u
ila
ca
p
tu
r
es
p
r
ey
b
y
f
ly
in
g
l
o
w
an
d
v
er
tically
with
a
s
lo
w
attac
k
.
T
h
is
p
h
ase
is
r
ef
er
r
ed
to
as
ex
p
an
d
ed
ex
p
lo
itatio
n
.
T
h
is
b
eh
av
io
r
is
m
o
d
eled
in
(
2
5
)
.
W
h
e
r
e,
3
(
+
1
)
is
th
e
r
esu
lt
f
o
r
t
in
th
e
n
e
x
t
iter
atio
n
.
(
)
in
d
icate
s
th
e
b
est
r
esu
l
t
b
y
iter
atio
n
t
(
p
r
e
y
p
o
s
itio
n
)
.
(
)
in
d
icate
s
th
e
av
er
ag
e
v
alu
e
o
f
iter
atio
n
t.
R
an
d
is
a
r
an
d
o
m
v
alu
e
b
etwe
en
0
a
n
d
1
.
α
an
d
δ a
r
e
p
ar
am
eter
s
f
o
r
ex
p
lo
itatio
n
ad
j
u
s
tm
en
t (
0
.
1
)
.
3
(
+
1
)
=
(
(
)
×
(
)
)
×
−
+
(
(
−
)
×
+
)
×
(
2
5
)
T
h
e
f
o
u
r
th
p
h
ase
d
escr
ib
es
w
alk
in
g
an
d
ca
tch
in
g
p
r
ey
in
th
e
f
in
al
p
o
s
itio
n
.
T
h
is
p
h
ase
is
r
ef
er
r
ed
to
as
n
ar
r
o
we
d
e
x
p
lo
itatio
n
.
T
h
i
s
b
eh
av
io
r
is
m
o
d
eled
in
(
2
6
)
.
4
(
+
1
)
is
th
e
r
esu
lt
o
f
t
in
t
h
e
n
ex
t
iter
atio
n
(
3
)
.
QF
is
t
h
e
q
u
ality
f
u
n
ctio
n
f
o
r
t
h
e
b
alan
ce
s
ea
r
c
h
s
tr
ateg
y
.
(
)
,
th
e
b
est
r
esu
lt
b
y
iter
atio
n
t
(
p
r
e
y
p
o
s
itio
n
)
.
1
in
d
icate
s
th
e
v
a
r
iatio
n
o
f
Aq
u
ila
m
o
v
em
e
n
t
to
tr
ac
k
th
e
p
r
ey
.
(
)
is
th
e
q
u
ality
f
u
n
ctio
n
f
o
r
iter
atio
n
t.
T
h
e
r
an
d
v
alu
e
c
o
m
es
f
r
o
m
a
r
an
d
o
m
v
al
u
e
o
f
0
to
1
.
t
an
d
T
ar
e
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
,
r
esp
ec
tiv
ely
.
4
(
+
1
)
=
×
(
)
−
(
1
×
(
)
×
)
−
2
×
(
)
+
×
1
(
2
6
)
Alg
o
r
ith
m
1
Ps
eu
d
o
co
d
e
A
q
u
i
la
o
p
tim
izer
Initialization phase:
Initialize the population X and parameters.
While
(The end condition is not met)
do
Calculate the fitness function values.
(
)
=
Determine the best
-
obtained solution according to the fitness values.
for
(i=1,2.,N)
do
Update the mean value of the current solution
(
)
.
Update the
,
,
1
,
2
,
(
)
.
if
≤
(
2
3
)
∗
then
if
≤
0
.
5
then
⊳
Step 1: Expanded
exploration
(
1
)
Update the current solution using the Equation (23)
if
Fitness
(
1
(
+
1
)
)
<
Fitness
(
(
)
)
then
(
)
=
(
1
(
+
1
)
)
if
Fitness
(
1
(
+
1
)
)
<
Fitness
(
(
)
)
then
(
)
=
1
(
+
1
)
end if
end if
else
⊳
Step 2: Narrowed explor
ation
(
2
)
Update the current solution using the Equation (24)
if
Fitness
(
2
(
+
1
)
)
<
Fitness
(
(
)
)
then
(
)
=
(
2
(
+
1
)
)
if
Fitness
(
2
(
+
1
)
)
<
Fitness
(
(
)
)
then
(
)
=
2
(
+
1
)
end if
end if
else
if
≤
0
.
5
then
⊳
Step 3: Narrowed exploration
(
3
)
Update the current solution using the Equation (25)
if
Fitness
(
3
(
+
1
)
)
<
Fitness
(
(
)
)
then
(
)
=
(
3
(
+
1
)
)
if
Fitness
(
3
(
+
1
)
)
<
Fitness
(
(
)
)
then
(
)
=
3
(
+
1
)
end if
end if
else
⊳
Step 4: Narrowed
exploration
(
4
)
Update the current solution using the Equation (26)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
Th
e
p
r
o
d
u
ctio
n
-
in
ve
n
to
r
y
mo
d
el
w
ith
imp
erfect,
r
e
w
o
r
k,
a
n
d
s
cra
p
items u
n
d
er
…
(
Da
n
a
Ma
r
s
etiya
Uta
ma
)
907
if
Fitness
(
4
(
+
1
)
)
<
Fitness
(
(
)
)
then
(
)
=
(
4
(
+
1
)
)
if
Fitness
(
4
(
+
1
)
)
<
Fitness
(
(
)
)
then
(
)
=
4
(
+
1
)
end if
end if
end if
end if
end for
end while
Return
the best solution
(
)
3
.
2
.
Da
t
a
a
nd
ex
perim
ent
a
l
pro
ce
du
re
s
T
h
e
d
ata
f
o
r
th
is
r
esear
ch
co
m
es
f
r
o
m
a
ca
s
e
s
tu
d
y
o
f
a
m
an
u
f
ac
tu
r
in
g
in
d
u
s
tr
y
th
at
p
r
o
d
u
ce
s
p
last
ic
p
ac
k
ag
in
g
in
I
n
d
o
n
esia.
Var
io
u
s
p
ar
am
ete
r
s
r
elev
an
t
to
th
e
in
v
e
n
to
r
y
p
r
o
b
lem
,
s
u
ch
as
=1
,
6
0
7
9
k
g
,
=1
,
7
0
0
0
k
g
,
1
=5
,
0
0
0
k
g
,
=0
.
0
5
%,
=1
%,
1
=0
%,
1
=0
%,
=0
%,
=4
,
5
4
1
k
g
,
=2
7
,
5
5
7
.
3
4
R
p
/k
g
,
=3
0
,
6
4
4
.
5
7
R
p
/k
g
,
=1
1
,
0
0
0
R
p
/k
g
,
ℎ
=
I
DR
25,
=
I
DR
1
,
1
6
2
,
8
5
8
.
7
7
,
=
I
DR
4
5
,
0
0
0
.
T
h
is
r
esear
c
h
u
tili
ze
s
Aq
u
ila
o
p
tim
izer
as
an
o
p
tim
izatio
n
to
o
l
with
t
h
e
p
r
im
ar
y
o
b
jectiv
e
o
f
m
i
n
im
izin
g
to
tal
co
s
t
-
ef
f
icien
tly
.
T
h
e
d
ec
is
io
n
v
ar
i
ab
les
th
at
ar
e
th
e
f
o
cu
s
o
f
ex
p
lo
r
atio
n
in
th
is
s
tu
d
y
in
v
o
lv
e
Q,
k
,
P,
an
d
P1
.
T
ab
le
1
p
r
esen
ts
th
e
Aq
u
ila
al
g
o
r
ith
m
p
ar
am
eter
s
u
s
ed
to
o
p
tim
ize
th
e
in
v
en
to
r
y
p
r
o
b
lem
.
T
esti
n
g
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
Aq
u
ila
o
p
tim
izer
is
d
o
n
e
b
y
co
m
p
ar
in
g
it
with
th
e
h
eu
r
is
tic
alg
o
r
ith
m
an
d
Har
r
is
Haw
k
o
p
tim
izatio
n
alg
o
r
ith
m
.
I
n
a
d
d
itio
n
,
th
is
s
tu
d
y
also
ev
al
u
ates
th
e
ef
f
ec
t
o
f
d
em
an
d
f
lu
ctu
atio
n
s
(
D)
b
y
co
n
d
u
ctin
g
a
s
en
s
itiv
ity
an
al
y
s
is
o
f
ch
an
g
es
in
th
e
s
tan
d
a
r
d
d
e
v
iatio
n
(
σ
)
o
f
d
em
an
d
o
n
th
e
o
b
jectiv
e
f
u
n
ctio
n
an
d
d
ec
is
io
n
v
ar
iab
le
s
.
All
in
v
en
to
r
y
o
p
tim
izatio
n
ex
p
er
im
en
ts
wer
e
co
n
d
u
cte
d
u
s
in
g
MA
T
L
AB
R
2
0
1
8
a
p
latf
o
r
m
o
n
an
MSI
Mo
d
er
n
1
4
C
5
M
-
0
0
5
R
y
ze
n
5
5
6
2
5
U
co
m
p
u
ter
with
8
GB
R
AM
an
d
5
1
2
GB
s
to
r
a
g
e,
o
p
e
r
atin
g
u
n
d
er
W
in
d
o
ws 1
1
s
y
s
tem
.
T
ab
le
1
.
Par
am
eter
d
ata
o
f
th
e
A
q
u
ila
alg
o
r
ith
m
s
f
o
r
th
e
in
v
en
to
r
y
o
p
tim
izatio
n
p
r
o
b
lem
P
a
r
a
me
t
e
r
V
a
l
u
e
P
o
p
u
l
a
t
i
o
n
s
n
u
m
b
e
r
1
0
0
0
M
a
x
i
m
u
m
i
t
e
r
a
t
i
o
n
1
0
0
0
N
u
mb
e
r
o
f
d
e
c
i
si
o
n
v
a
r
i
a
b
l
e
4
U
p
p
e
r
b
o
u
n
d
[
1
6
0
7
9
,
2
.
9
9
,
1
8
0
0
0
,
7
0
0
0
]
Lo
w
e
r
b
o
u
n
d
[1
,
0
,
1
7
0
0
0
,
5
0
0
0
]
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
O
pti
m
iza
t
io
n wit
h
A
qu
ila
o
ptim
izer
T
h
is
s
tu
d
y
s
u
cc
ess
f
u
lly
o
p
tim
ized
th
e
p
r
o
d
u
ctio
n
-
av
ailab
ilit
y
m
o
d
el
b
y
co
n
s
id
er
in
g
im
p
e
r
f
ec
tio
n
s
,
r
ewo
r
k
ed
g
o
o
d
s
,
a
n
d
s
cr
ap
g
o
o
d
s
u
n
d
er
s
to
ch
asti
c
s
to
ck
d
em
an
d
co
n
d
itio
n
s
.
T
h
e
o
p
ti
m
izatio
n
p
r
o
ce
s
s
is
p
er
f
o
r
m
ed
u
s
in
g
t
h
e
Aq
u
ila
o
p
tim
izer
alg
o
r
ith
m
m
et
h
o
d
.
T
h
e
r
esu
lt
o
f
th
is
o
p
tim
izatio
n
s
h
o
ws
th
at
th
e
t
o
tal
co
s
t
g
en
er
ated
is
I
DR
5
3
6
,
3
0
8
,
6
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1
.
2
0
.
T
h
e
o
p
tim
al
d
ec
is
io
n
v
ar
iab
les
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en
tifie
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in
v
o
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e
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th
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o
f
5
5
4
,
k
o
f
2
.
2
4
,
P
o
f
1
8
0
0
0
,
an
d
P1
o
f
7
0
0
0
.
T
h
ese
f
in
d
in
g
s
r
ef
lect
t
h
e
ef
f
icie
n
cy
an
d
ef
f
ec
tiv
e
n
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el
in
d
ea
lin
g
with
in
v
en
to
r
y
ch
allen
g
es
with
u
n
ce
r
tain
ty
,
r
ewo
r
k
,
an
d
s
cr
ap
.
I
n
ad
d
itio
n
,
th
ese
r
esu
lts
ca
n
s
er
v
e
as
g
u
id
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f
o
r
p
r
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s
an
d
d
ec
is
io
n
-
m
ak
e
r
s
in
m
an
ag
i
n
g
i
n
v
en
to
r
y
m
o
r
e
ef
f
icien
tly
an
d
o
p
tim
izin
g
co
s
ts
s
ig
n
if
ican
tly
.
4
.2
.
Alg
o
rit
hm
co
m
pa
riso
n
A
c
o
m
p
ar
is
o
n
o
f
alg
o
r
ith
m
s
f
o
r
o
p
tim
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n
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f
p
r
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d
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cti
o
n
-
in
v
e
n
to
r
y
p
r
o
b
lem
s
ca
n
b
e
s
ee
n
in
Fig
u
r
e
6
.
T
h
e
o
p
tim
izatio
n
r
esu
lts
u
s
in
g
th
e
Aq
u
ila
o
p
ti
m
izer
alg
o
r
ith
m
a
n
d
Har
r
is
Haw
k
o
p
tim
izatio
n
r
esu
lted
in
a
n
esti
m
ated
to
tal
co
s
t
(
E
T
C
)
o
f
I
DR
5
3
6
,
3
0
8
,
6
8
1
.
2
0
.
I
n
co
m
p
a
r
is
o
n
,
th
e
h
eu
r
is
tic
p
r
o
ce
d
u
r
e
r
esu
lted
in
an
E
T
C
o
f
I
DR
5
5
5
,
2
5
6
,
0
1
2
.
1
1
.
T
h
e
al
g
o
r
ith
m
co
m
p
a
r
is
o
n
an
aly
s
is
s
h
o
w
s
th
at
th
e
Aq
u
ila
o
p
tim
izer
alg
o
r
ith
m
p
r
o
d
u
ce
s
a
s
o
lu
tio
n
eq
u
iv
alen
t
to
th
e
Har
r
is
Haw
k
o
p
tim
i
za
tio
n
alg
o
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ith
m
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d
s
u
p
e
r
io
r
to
th
e
h
e
u
r
is
tic
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r
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ce
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u
r
e.
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h
e
p
r
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o
s
ed
m
eth
o
d
,
th
e
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u
ila
o
p
tim
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alg
o
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ith
m
,
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ed
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ce
d
th
e
ex
p
ec
ted
c
o
s
t
b
y
3
.
2
2
%.
T
h
is
r
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lt
in
d
icate
s
th
at
th
e
p
r
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ce
d
u
r
e
h
as
ef
f
ec
t
iv
e
ex
p
lo
r
atio
n
ca
p
a
b
ilit
ies
[
2
8
]
.
Fu
r
th
e
r
m
o
r
e,
it
was
f
o
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n
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th
at
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esp
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ially
with
its
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to
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ce
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ts
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ig
n
if
ican
tly
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T
h
e
f
in
d
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o
f
t
h
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s
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d
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av
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m
e
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ig
n
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e
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T
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m
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aly
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izatio
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d
s
u
p
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r
is
tic
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u
r
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t
co
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ir
m
s
t
h
at
th
e
Aq
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p
tim
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alg
o
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n
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r
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m
an
ag
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m
en
t.
T
h
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allo
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Evaluation Warning : The document was created with Spire.PDF for Python.
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8
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No
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4
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2
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2
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-
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co
m
p
an
ies
to
o
b
tain
o
p
tim
al
s
o
lu
tio
n
s
in
th
eir
in
v
en
to
r
y
m
an
ag
em
en
t.
I
n
ad
d
itio
n
,
th
is
s
tu
d
y
also
p
r
o
v
id
es
in
s
ig
h
t
in
to
th
e
p
o
s
s
ib
ilit
y
o
f
im
p
r
o
v
in
g
ef
f
icien
c
y
in
i
n
v
en
to
r
y
m
an
a
g
em
en
t
i
n
th
e
f
u
tu
r
e.
W
ith
th
e
co
n
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ir
m
atio
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at
t
h
e
Aq
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ila
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tim
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ith
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s
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tio
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s
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th
is
r
esear
ch
p
r
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v
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th
e
im
p
etu
s
f
o
r
th
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f
u
r
t
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er
d
ev
elo
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m
en
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a
n
d
a
p
p
licatio
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o
f
th
e
a
lg
o
r
ith
m
i
n
a
b
r
o
ad
er
co
n
tex
t.
T
h
is
m
ea
n
s
th
at
i
n
th
e
f
u
tu
r
e,
t
h
e
Aq
u
ila
o
p
tim
izer
al
g
o
r
ith
m
will
b
e
an
i
n
v
alu
ab
le
to
o
l
f
o
r
c
o
m
p
a
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ies
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ed
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ce
th
eir
co
s
ts
an
d
im
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r
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e
t
h
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o
p
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n
al
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f
ic
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s
ig
n
if
ican
tly
.
Fig
u
r
e
6
C
o
m
p
a
r
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o
n
o
f
alg
o
r
i
th
m
s
f
o
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o
p
tim
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o
f
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r
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-
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to
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p
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s
4
.
3
.
Sens
it
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cha
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es in sta
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a
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dev
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σ)
I
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en
s
itiv
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aly
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to
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σ
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Fig
u
r
e
7
illu
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ates th
e
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σ
.
Fig
u
r
e
7
(
a)
in
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e
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t
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f
ch
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σ
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Q.
Mo
r
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Fig
u
r
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7
(
b
)
in
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e
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er
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m
o
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e
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latile
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e
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ct
d
em
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d
.
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h
e
m
ain
f
i
n
d
in
g
is
th
at
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in
cr
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s
e
i
n
th
e
σ
v
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e
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d
s
to
a
d
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r
ea
s
e
in
th
e
Q
with
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cr
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e
in
th
e
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e.
I
t
in
d
icate
s
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at
th
e
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ig
h
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e
d
e
m
an
d
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ta
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ty
,
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e
s
m
aller
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ed
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n
to
av
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d
th
e
r
is
k
o
f
lo
s
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s
ales
[
3
0
]
.
Alth
o
u
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h
th
e
P a
n
d
P1
ar
e
n
o
t a
f
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th
is
r
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lt
s
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o
ws th
at
th
ey
m
ain
tain
a
f
ix
ed
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p
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b
ab
ly
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to
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f
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s
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ted
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.
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k
r
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lts
f
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m
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f
o
r
ts
to
av
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k
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f
lo
s
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Ho
wev
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,
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e
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e,
it
also
in
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es
th
e
s
h
elf
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s
t,
in
cr
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s
in
g
th
e
e
x
p
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tatio
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o
f
E
T
C
[
3
0
]
.
T
h
er
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o
r
e
,
in
v
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to
r
y
m
an
ag
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en
t
m
u
s
t
co
n
s
id
er
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e
tr
ad
e
-
o
f
f
b
etwe
en
th
e
r
is
k
o
f
lo
s
in
g
s
ales
an
d
s
t
o
r
in
g
co
s
ts
to
o
p
tim
ize
th
e
to
tal
in
v
en
to
r
y
co
s
t.
A
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
th
e
im
p
ac
t
o
f
th
e
s
en
s
itiv
ity
o
f
σ
ch
an
g
es
o
n
s
o
m
e
in
v
en
to
r
y
m
an
ag
em
en
t
p
r
o
v
id
es
v
al
u
a
b
le
in
s
ig
h
ts
f
o
r
p
r
ac
titi
o
n
er
s
an
d
r
esear
ch
er
s
in
d
e
v
elo
p
in
g
m
o
r
e
ef
f
ec
tiv
e
s
tr
ateg
ies f
o
r
m
an
ag
in
g
d
em
a
n
d
u
n
c
er
tain
ty
an
d
im
p
r
o
v
in
g
s
u
p
p
ly
ch
ain
p
er
f
o
r
m
a
n
ce
.
T
h
is
f
in
d
in
g
s
u
g
g
ests
th
at
th
e
m
o
r
e
u
n
ce
r
tain
th
e
d
em
an
d
,
th
e
s
m
aller
th
e
p
lan
n
e
d
p
r
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d
u
ctio
n
t
o
av
o
id
th
e
r
is
k
o
f
lo
s
in
g
s
ales.
C
o
n
s
eq
u
en
tly
,
co
m
p
a
n
ies
ten
d
to
r
ed
u
ce
th
e
r
is
k
o
f
lo
s
t
s
al
es
b
y
r
ed
u
cin
g
th
e
p
lan
n
ed
p
r
o
d
u
ctio
n
q
u
an
tity
.
Ho
wev
er
,
in
cr
ea
s
in
g
th
e
k
to
av
o
id
th
e
r
is
k
o
f
lo
s
t
s
ales
d
o
es
n
o
t
co
m
e
with
o
u
t
co
n
s
eq
u
en
ce
s
.
Su
ch
ef
f
o
r
ts
in
cr
ea
s
e
s
h
elf
c
o
s
ts
d
u
e
to
m
o
r
e
e
x
ten
s
iv
e
in
v
en
to
r
ies,
i
n
cr
ea
s
in
g
th
e
E
T
C
.
T
h
er
ef
o
r
e,
m
an
a
g
em
en
t
s
h
o
u
ld
ca
r
ef
u
lly
c
o
n
s
id
er
b
ala
n
cin
g
m
an
ag
in
g
th
e
r
is
k
o
f
lo
s
t
s
ales
an
d
m
in
im
izin
g
in
v
en
to
r
y
co
s
ts
to
ac
h
iev
e
o
p
tim
al
r
esu
lts
.
Fro
m
th
ese
f
in
d
in
g
s
,
th
er
e
ar
e
o
p
p
o
r
tu
n
ities
f
o
r
f
u
r
th
e
r
r
esear
ch
th
at
f
o
cu
s
o
n
d
e
v
elo
p
in
g
in
v
en
to
r
y
m
an
a
g
em
en
t
s
tr
ateg
i
es
th
at
ar
e
m
o
r
e
ad
ap
tiv
e
an
d
r
esp
o
n
s
iv
e
to
v
ar
iab
ilit
y
in
d
e
m
an
d
.
(
a)
(
b
)
Fig
u
r
e
7
.
Sen
s
itiv
ity
an
aly
s
is
o
f
σ
ch
a
n
g
es to
(
a
)
Q
,
ETC
,
a
n
d
(
b
)
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
Th
e
p
r
o
d
u
ctio
n
-
in
ve
n
to
r
y
mo
d
el
w
ith
imp
erfect,
r
e
w
o
r
k,
a
n
d
s
cra
p
items u
n
d
er
…
(
Da
n
a
Ma
r
s
etiya
Uta
ma
)
909
5.
CO
NCLU
SI
O
N
B
ased
o
n
th
is
r
esear
ch
,
th
e
p
r
o
d
u
ctio
n
-
in
v
en
t
o
r
y
m
o
d
el
th
at
co
n
s
id
er
s
d
e
f
ec
tiv
e
item
s
,
r
ep
r
o
ce
s
s
in
g
,
an
d
lef
to
v
er
item
s
o
n
s
to
ch
as
tic
s
to
ck
d
em
an
d
s
ig
n
if
ica
n
tly
im
p
ac
ts
to
tal
c
o
s
ts
.
T
h
e
r
e
s
u
lts
s
h
o
w
th
at
th
e
Aq
u
ila
o
p
tim
izer
alg
o
r
ith
m
o
p
tim
izes
th
e
p
r
o
d
u
ct
io
n
-
in
v
en
to
r
y
p
r
o
b
lem
with
th
e
s
am
e
e
f
f
ec
tiv
en
ess
as
th
e
Har
r
is
Haw
k
o
p
tim
izatio
n
al
g
o
r
ith
m
.
Fu
r
th
er
m
o
r
e,
a
c
o
m
p
ar
is
o
n
b
etwe
en
th
e
alg
o
r
ith
m
s
s
h
o
ws
th
at
th
e
Aq
u
ila
o
p
tim
izer
alg
o
r
ith
m
n
o
t
o
n
ly
p
r
o
d
u
ce
s
s
o
l
u
tio
n
s
s
im
ilar
to
th
e
Har
r
is
Haw
k
o
p
t
im
izatio
n
alg
o
r
ith
m
b
u
t
ca
n
also
p
r
o
v
id
e
b
etter
s
o
lu
tio
n
s
th
an
h
eu
r
is
tic
p
r
o
ce
d
u
r
es.
Sen
s
itiv
ity
an
aly
s
i
s
f
o
u
n
d
in
cr
ea
s
ed
u
n
ce
r
tain
ty
in
d
e
m
an
d
in
cr
ea
s
ed
to
tal
co
s
t
an
d
s
af
ety
f
ac
to
r
s
.
Ho
wev
er
,
in
te
r
esti
n
g
ly
,
th
e
Q
d
ec
r
ea
s
ed
as
th
e
u
n
ce
r
tain
ty
in
d
e
m
an
d
in
c
r
ea
s
ed
.
I
t
p
r
o
v
id
es
v
alu
a
b
le
in
s
ig
h
ts
in
m
an
ag
in
g
in
v
en
to
r
y
b
y
co
n
s
id
er
in
g
th
e
u
n
ce
r
tain
ty
i
n
th
e
d
em
an
d
f
a
cto
r
.
T
h
u
s
,
th
is
r
esear
ch
d
ev
e
lo
p
s
a
co
m
p
lex
p
r
o
d
u
ctio
n
-
in
v
en
to
r
y
m
o
d
el
an
d
co
n
tr
ib
u
tes to
u
n
d
er
s
tan
d
in
g
h
o
w
u
n
ce
r
tain
ty
ca
n
af
f
ec
t in
v
e
n
to
r
y
m
a
n
ag
em
e
n
t d
ec
is
io
n
s
.
Alth
o
u
g
h
th
is
r
esear
ch
s
u
cc
es
s
f
u
lly
d
ev
elo
p
e
d
a
p
r
o
d
u
ctio
n
-
in
v
en
to
r
y
m
o
d
el
co
n
s
id
er
in
g
d
ef
ec
tiv
e
item
s
,
r
em
an
u
f
ac
tu
r
i
n
g
,
an
d
waste
in
th
e
co
n
tex
t
o
f
s
to
ch
asti
c
d
em
an
d
,
s
o
m
e
lim
itatio
n
s
s
till
n
ee
d
to
b
e
n
o
ted
.
First,
th
e
m
o
d
el
o
n
ly
c
o
n
s
id
er
s
f
o
u
r
m
ain
d
ec
is
io
n
v
ar
iab
les,
n
am
ely
Q,
k
,
P,
an
d
P1
.
T
h
e
p
o
s
s
ib
ilit
y
o
f
ad
d
itio
n
al
v
ar
iab
les
af
f
ec
ti
n
g
in
v
e
n
to
r
y
d
ec
is
io
n
s
co
u
ld
b
e
an
ex
citin
g
r
esear
ch
ar
ea
t
o
ex
p
lo
r
e
f
u
r
t
h
er
.
I
n
ad
d
itio
n
,
alth
o
u
g
h
t
h
e
Aq
u
ila
o
p
tim
izer
alg
o
r
ith
m
s
u
c
ce
s
s
f
u
lly
m
in
im
izes
to
tal
c
o
s
t
an
d
p
r
o
v
id
es
co
m
p
ar
ativ
e
r
esu
lts
with
th
e
Har
r
is
Haw
k
o
p
tim
izatio
n
alg
o
r
ith
m
,
f
u
r
th
er
test
s
ar
e
s
till
n
ee
d
ed
r
eg
a
r
d
in
g
t
h
e
ef
f
ec
tiv
en
ess
o
f
th
is
alg
o
r
ith
m
in
m
o
r
e
c
o
m
p
lex
p
r
o
d
u
c
tio
n
-
av
ailab
ilit
y
s
ce
n
ar
io
s
.
I
n
ad
d
itio
n
,
f
u
r
th
er
r
esear
ch
is
n
ee
d
ed
to
ev
alu
ate
t
h
e
m
o
d
el'
s
p
er
f
o
r
m
an
ce
in
p
r
ac
tical
an
d
d
y
n
am
ic
s
itu
atio
n
s
th
at
ca
n
o
cc
u
r
in
ev
er
y
d
a
y
p
r
o
d
u
ctio
n
en
v
ir
o
n
m
en
ts
.
T
h
er
ef
o
r
e,
as
a
f
u
tu
r
e
r
esear
ch
d
ir
ec
tio
n
,
it
is
n
ec
ess
ar
y
to
e
x
p
lo
r
e
f
u
r
t
h
er
th
e
d
ev
el
o
p
m
en
t
o
f
a
m
o
r
e
co
m
p
r
eh
e
n
s
iv
e
m
o
d
el
a
n
d
f
u
r
th
er
test
in
g
a
n
d
v
alid
atio
n
o
f
th
e
o
p
tim
izatio
n
m
eth
o
d
s
u
s
ed
to
i
m
p
r
o
v
e
th
e
a
p
p
licab
ilit
y
an
d
g
en
er
aliza
b
ilit
y
o
f
th
e
f
in
d
i
n
g
s
o
f
th
is
r
esear
ch
.
ACK
NO
WL
E
DG
E
M
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NT
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h
e
au
th
o
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s
wo
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ld
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to
th
an
k
th
e
Op
tim
is
atio
n
L
ab
o
r
ato
r
y
at
th
e
Dep
ar
tm
en
t
o
f
I
n
d
u
s
tr
ial
E
n
g
in
ee
r
in
g
,
Un
iv
e
r
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ity
o
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M
u
h
am
m
ad
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Ma
lan
g
f
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r
allo
win
g
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s
to
u
s
e
th
eir
f
ac
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ies.
RE
F
E
R
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NC
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S
[
1
]
S
.
M
a
h
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sh
w
a
r
i
,
A
.
K
a
u
s
a
r
,
A
.
H
a
s
a
n
,
a
n
d
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.
K
.
Ja
g
g
i
,
“
S
u
s
t
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w
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n
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g
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t
,
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n
t
.
J
.
S
y
st
.
Ass
u
r.
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.
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a
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,
v
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3.
[
2
]
D
.
M
.
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t
a
m
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.
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ma
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n
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a
u
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r
i
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si
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o
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b
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a
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mat
e
r
i
a
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a
n
d
q
u
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d
e
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r
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d
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t
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:
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2
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2
3
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5
3
.
[
3
]
D
.
M
.
U
t
a
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a
,
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S
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n
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so
,
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a
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i
a
,
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s
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mi
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o
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,
e
l
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t
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d
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u
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mp
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st
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c
d
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:
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v
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2
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[
4
]
D
.
M
.
U
t
a
m
a
,
H
.
M
.
K
h
o
l
i
k
,
a
n
d
A
.
F
.
M
u
l
y
a
,
“
I
n
t
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g
r
a
t
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d
p
r
o
c
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me
n
t
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p
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o
-
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p
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,
”
J
.
T
e
k
.
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n
d
.
,
v
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.
2
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.
[
5
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D
.
M
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ma,
S
.
K
.
D
e
w
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d
S
.
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.
D
w
i
B
u
d
i
M
a
u
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a
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a
,
“
O
p
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c
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.
[
6
]
D
.
M
.
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t
a
ma,
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.
K
.
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.
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.
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a
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,
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.
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w
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,
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,
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t
.
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.
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.
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.
,
v
o
l
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