I
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na
l J
o
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l o
f
Adv
a
nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
5
,
No
.
1
,
Ma
r
ch
2
0
1
6
,
p
p
.
13
~
20
I
SS
N:
2252
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8814
13
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A
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©
201
6
In
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I
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8814
IJ
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Vo
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5
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1
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Ma
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201
6
:
13
–
20
14
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ciate
w
it
h
i
m
p
le
m
en
tin
g
an
o
p
tim
a
l
r
ep
len
is
h
m
e
n
t
p
o
lic
y
.
Af
ter
o
b
tain
i
n
g
t
h
e
m
o
d
el
p
r
o
p
er
ties
,
w
e
g
en
er
ate
a
n
e
x
a
m
p
le.
I
n
th
e
l
ast
s
ec
t
io
n
o
f
t
h
e
p
ap
er
,
w
e
p
r
o
v
id
e
o
u
r
co
n
cl
u
s
io
n
s
a
s
w
el
l
as
s
u
g
g
esti
o
n
s
f
o
r
f
u
r
t
h
er
r
esear
ch
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
Go
y
al
(
1
9
8
5
)
s
u
g
g
ested
a
n
E
OQ
m
o
d
el
w
it
h
a
f
i
x
ed
cr
ed
it
d
ea
d
lin
e
f
o
r
p
a
y
i
n
g
f
o
r
g
o
o
d
s
as
a
p
r
o
m
o
tio
n
th
a
t
co
u
ld
b
e
p
r
o
v
i
d
ed
b
y
th
e
s
u
p
p
lier
.
I
f
th
e
r
eta
iler
s
ell
s
t
h
e
p
r
o
d
u
ct
w
ith
in
t
h
e
li
m
it,
h
e/s
h
e
w
ill
b
e
s
p
ar
ed
th
e
i
n
ter
est
g
e
n
er
ate
d
b
y
th
e
f
u
n
d
s
t
h
at
m
u
s
t
b
e
u
s
ed
to
p
ay
f
o
r
t
h
e
g
o
o
d
s
.
T
h
at
i
s
a
t
y
p
e
o
f
c
h
a
n
ce
co
s
t.
I
f
th
e
p
ay
d
ate
p
ass
es,
h
e
/s
h
e
m
u
s
t
p
a
y
f
o
r
th
e
p
r
o
d
u
cts
an
d
th
e
in
ter
est
g
e
n
er
ated
b
y
th
e
f
u
n
d
s
th
at
h
a
v
e
alr
ea
d
y
b
ee
n
p
aid
to
t
h
e
s
u
p
p
lier
f
o
r
th
e
r
e
s
t
o
f
t
h
e
p
r
o
d
u
cts
t
h
at
ar
e
in
s
to
ck
.
Ma
n
y
r
esear
ch
er
s
h
av
e
ex
ten
d
ed
th
e
ab
o
v
e
m
o
d
el
in
d
if
f
er
en
t
w
a
y
s
.
C
h
u
n
g
(
1
9
8
9
)
in
v
esti
g
ated
t
h
e
in
ter
ac
tio
n
s
b
et
w
ee
n
cr
ed
it
tr
an
s
ac
tio
n
s
a
n
d
th
e
ti
m
e
v
alu
e
o
f
cu
r
r
en
c
y
,
a
n
d
h
e
th
e
n
e
m
p
lo
y
ed
a
d
is
co
u
n
ted
ca
s
h
f
lo
w
(
D
C
F)
m
o
d
el
to
b
u
ild
a
to
tal
v
ar
ian
t
co
s
t
f
u
n
ctio
n
f
o
r
in
v
e
n
to
r
y
.
I
n
h
is
r
e
s
ea
r
ch
,
a
n
o
p
tim
a
l r
ep
len
i
s
h
m
e
n
t p
o
lic
y
w
a
s
p
r
o
v
id
ed
.
C
h
u
n
g
(
1
9
9
8
)
r
ev
is
ed
t
h
e
m
o
d
el
b
y
Go
y
al
(
1
9
8
5
)
an
d
also
f
o
u
n
d
a
n
o
p
ti
m
al
o
r
d
er
q
u
an
tit
y
.
Hu
an
g
(
2
0
0
4
,
2
0
0
7
)
r
e
w
r
o
te
th
e
ass
u
m
p
tio
n
s
m
ad
e
b
y
Go
y
al
(
1
9
8
5
)
an
d
ar
g
u
ed
th
at
t
h
e
s
elli
n
g
p
r
ice
an
d
th
e
p
u
r
ch
a
s
e
co
s
t
f
o
r
t
h
e
p
r
o
d
u
ct
m
ig
h
t
n
o
t
b
e
eq
u
al
i
n
r
ea
l
-
w
o
r
ld
s
ce
n
ar
io
s
.
Hu
a
n
g
also
co
n
s
id
er
ed
th
e
r
ate
o
f
r
ep
len
is
h
m
en
t
to
b
e
f
in
ite
a
n
d
d
ev
elo
p
ed
h
is
r
esear
ch
in
t
w
o
p
h
ases
:
o
n
e
w
h
er
e
th
e
s
u
p
p
lier
allo
w
s
t
h
e
r
etailer
to
p
ay
f
o
r
th
e
p
r
o
d
u
cts
b
ef
o
r
e
th
e
cr
ed
it
d
ea
d
lin
e,
an
d
an
o
th
er
p
h
ase
w
h
er
e
th
e
r
etailer
also
p
r
o
v
id
es
h
is
/
h
er
cu
s
to
m
er
s
w
it
h
p
er
m
is
s
io
n
to
d
elay
p
a
y
m
e
n
ts
f
o
r
t
h
e
s
a
k
e
o
f
in
cr
ea
s
in
g
t
h
e
a
m
o
u
n
t
o
f
p
r
o
d
u
ct
th
at
is
s
o
ld
.
H
u
an
g
(
2
0
0
7
)
also
d
is
cu
s
s
ed
a
p
o
s
s
ib
ilit
y
in
w
h
ic
h
th
e
s
u
p
p
lier
o
f
f
er
s
p
ar
tial
p
er
m
is
s
io
n
f
o
r
d
ela
y
s
i
n
p
a
y
m
e
n
t
w
h
e
n
t
h
e
ac
t
u
al
o
r
d
er
q
u
a
n
tit
y
i
s
les
s
t
h
a
n
a
ce
r
tain
a
m
o
u
n
t.
He
m
i
n
i
m
ize
d
th
e
to
tal
c
o
s
t
to
en
s
u
r
e
t
h
at
th
e
in
v
e
n
to
r
y
c
y
cle
a
n
d
th
e
o
r
d
er
q
u
an
tit
y
w
er
e
o
p
tim
a
l.
L
iao
(
2
0
0
7
)
in
v
esti
g
a
ted
a
n
o
n
-
i
n
s
ta
n
ta
n
eo
u
s
i
n
v
en
to
r
y
m
o
d
el
o
f
d
eter
io
r
atio
n
f
o
r
ite
m
s
t
h
at
in
co
r
p
o
r
ated
d
elay
s
in
p
a
y
m
e
n
t.
T
s
ao
an
d
S
h
ee
n
(
2
0
0
8
)
f
o
u
n
d
a
n
o
p
ti
m
al
s
el
lin
g
p
r
ice
a
n
d
m
a
x
i
m
ized
t
h
e
p
r
o
f
it
f
o
r
d
eter
io
r
atio
n
ite
m
s
w
h
ile
i
n
cl
u
d
in
g
p
er
m
is
s
io
n
f
o
r
d
ela
y
s
i
n
p
a
y
m
e
n
t.
C
h
a
n
g
,
T
en
g
a
n
d
Go
y
al
(
2
0
0
8
)
r
ev
ie
w
ed
th
e
liter
atu
r
e
f
o
r
in
v
e
n
to
r
y
m
o
d
els
p
u
b
lis
h
ed
in
th
e
las
t
t
w
e
n
t
y
y
ea
r
s
an
d
class
i
f
ied
th
e
s
e
m
o
d
el
s
as
n
o
n
-
d
eter
io
r
atio
n
ite
m
s
,
d
eter
io
r
atio
n
ite
m
s
,
m
o
d
els
th
at
allo
w
s
h
o
r
ta
g
es,
o
r
d
er
q
u
an
tit
y
a
n
d
in
f
latio
n
.
T
h
e
y
al
s
o
s
u
g
g
ested
f
u
r
t
h
er
r
esear
ch
d
ir
ec
tio
n
s
f
o
r
ev
er
y
m
o
d
el
t
h
e
y
r
e
v
ie
w
ed
.
C
h
u
n
g
(
2
0
0
9
)
c
o
n
s
tr
u
cted
a
s
o
lu
tio
n
p
r
o
ce
d
u
r
e
f
o
r
n
o
n
-
i
n
s
ta
n
ta
n
eo
u
s
d
eter
io
r
atin
g
i
te
m
s
w
i
th
p
er
m
i
s
s
ib
le
d
ela
y
i
n
p
a
y
m
e
n
t.
Ou
y
an
g
,
T
en
g
,
Go
y
al
a
n
d
Ya
n
g
(
2
0
0
9
)
ex
ten
d
ed
th
e
w
o
r
k
b
y
Go
y
al
(
1
9
8
5
)
b
y
m
ak
in
g
a
r
u
le
t
h
at
t
h
e
p
r
o
m
o
t
io
n
ca
n
n
o
t
b
e
o
f
f
er
ed
if
t
h
e
o
r
d
er
q
u
an
tit
y
s
u
b
m
itted
b
y
t
h
e
r
etailer
is
b
elo
w
a
ce
r
tain
th
r
es
h
o
ld
.
Fu
r
t
h
er
m
o
r
e,
Ou
y
a
n
g
a
n
d
C
h
a
n
g
(
2
0
1
3
)
im
p
r
o
v
ed
th
e
ir
w
o
r
k
b
y
ta
k
in
g
t
h
e
f
ac
to
r
o
f
allo
w
i
n
g
s
h
o
r
tag
e
i
n
to
ac
co
u
n
t.
C
h
u
n
g
a
n
d
Hu
a
n
g
(
2
0
0
9
)
e
x
ten
d
ed
t
h
e
w
o
r
k
o
f
Go
y
al
(
1
9
8
5
)
b
y
u
s
i
n
g
d
u
al
v
ar
iab
les
an
d
th
e
y
ea
r
r
elev
an
t
co
s
t
to
co
n
s
tr
u
ct
an
i
n
v
e
n
to
r
y
m
o
d
el.
T
h
ey
al
s
o
p
r
o
v
ed
th
at
th
e
y
ea
r
r
elev
a
n
t
co
s
t
f
u
n
ctio
n
w
a
s
co
n
v
e
x
.
A
y
ea
r
later
,
Hu
an
d
L
iu
(
2
0
1
0
)
ad
o
p
te
d
th
e
f
in
ite
r
ep
len
is
h
m
en
t
r
ate
ass
u
m
p
tio
n
an
d
r
elax
ed
a
co
n
d
itio
n
i
n
w
h
i
ch
p
u
r
ch
a
s
e
p
r
ice
an
d
s
elli
n
g
p
r
ice
m
u
s
t
n
o
t
b
e
co
n
s
is
te
n
t
a
s
p
ar
t
o
f
th
eir
e
f
f
o
r
t
to
b
u
ild
u
p
o
n
t
h
e
w
o
r
k
o
f
C
h
u
n
g
a
n
d
Hu
a
n
g
(
2
0
0
9
)
.
Fu
r
th
er
m
o
r
e,
th
e
y
f
o
u
n
d
an
o
p
ti
m
a
l
in
v
en
to
r
y
p
o
lic
y
i
n
th
e
e
n
v
ir
o
n
m
e
n
t
th
e
y
h
ad
m
ad
e.
C
h
a
n
g
(
2
0
1
0
)
d
er
iv
ed
an
o
p
ti
m
al
r
ep
len
is
h
m
en
t p
o
lic
y
w
it
h
s
to
c
k
-
d
ep
en
d
en
t
d
em
a
n
d
.
Ma
ih
a
m
i
(
2
0
1
2
)
d
ev
elo
p
ed
a
n
o
p
ti
m
a
l
r
ep
len
i
s
h
m
e
n
t
p
o
li
c
y
f
o
r
n
o
n
-
i
n
s
tan
ta
n
eo
u
s
d
et
er
io
r
atin
g
ite
m
s
u
n
d
er
p
er
m
is
s
ib
le
d
ela
y
i
n
p
a
y
m
en
t
s
a
n
d
p
ar
tial
b
ac
k
lo
g
g
i
n
g
.
I
n
h
i
s
r
esear
c
h
,
ite
m
p
r
ice
is
also
co
n
tr
o
lled
.
Sar
k
ar
(
2
0
1
2
a,
b
)
m
o
d
eled
E
OQ
u
n
d
er
tr
ad
e
cr
ed
it
f
i
n
an
ci
n
g
w
it
h
t
i
m
e
-
d
ep
en
d
en
t
d
eter
io
r
atio
n
r
ate
an
d
s
to
ck
d
ep
en
d
e
n
t
d
e
m
an
d
,
r
e
s
p
ec
tiv
el
y
.
Mo
u
s
s
aw
i
-
Haid
ar
a
n
d
J
ab
er
(
2
0
1
3
)
in
co
r
p
er
ated
ca
s
h
m
an
a
g
e
m
e
n
t
i
n
to
r
etailer
’
s
lo
t
s
izi
n
g
in
v
e
n
to
r
y
p
r
o
b
le
m
u
n
d
er
d
elay
in
p
a
y
m
en
ts
to
f
i
n
d
t
h
e
o
p
ti
m
al
s
o
l
u
tio
n
f
o
r
m
o
r
e
ef
f
ec
ti
v
e
o
p
er
atio
n
al
an
d
f
i
n
a
n
cial
d
ec
is
io
n
m
a
k
i
n
g
.
Ya
n
g
an
d
C
h
a
n
g
(
2
0
1
3
)
an
d
B
h
u
n
ia,
J
ag
g
i,
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
AA
S
I
SS
N:
2252
-
8814
A
n
Op
tima
l
R
ep
len
is
h
men
t
P
o
licy
fo
r
th
e
E
P
Q
Mo
d
el
w
ith
P
ermis
s
ib
le
Dela
y
in
P
a
yme
n
t
… (
S
h
ih
-
Min
g
Ou
)
15
Sh
ar
m
a
an
d
Sh
ar
m
a
(
2
0
1
4
)
d
e
v
elo
p
ed
a
t
w
o
-
w
ar
e
h
o
u
s
e
i
n
v
e
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to
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m
o
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A
3
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Sin
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k
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Evaluation Warning : The document was created with Spire.PDF for Python.
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IJ
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Evaluation Warning : The document was created with Spire.PDF for Python.
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.
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,
Ma
r
ch
201
6
:
13
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20
18
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e
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al
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ep
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s
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t ti
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e
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ter
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n
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o
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e
r
d
e
r
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ativ
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d
T
T
V
C
d
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o
te
as th
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e
m
e
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h
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n
g
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mm
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n
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r
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n
g
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T
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r
o
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m
A
3
.
3
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s
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at
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g
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a
n
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n
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itio
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lt.
4.
NUM
E
RICAL
E
XAM
P
L
E
T
o
o
b
tain
s
u
f
f
icie
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t
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g
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lier
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o
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elay
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it
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er
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u
ild
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eir
in
v
en
to
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y
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o
d
el.
F
u
r
th
er
m
o
r
e,
an
o
p
ti
m
al
r
ep
len
i
s
h
m
e
n
t
p
o
lic
y
th
at
d
r
a
m
atica
ll
y
r
ed
u
ce
s
to
tal
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s
t
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n
al
s
o
b
e
o
b
tain
ed
.
Data
w
er
e
co
llecte
d
f
r
o
m
s
o
m
e
co
m
p
a
n
ies
lo
ca
t
ed
in
T
ai
w
a
n
a
n
d
p
r
o
ce
s
s
ed
w
it
h
th
e
m
o
d
el.
T
o
m
i
m
ic
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ea
lit
y
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th
e
p
ar
a
m
e
t
er
s
u
s
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in
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h
e
p
r
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p
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s
ed
m
o
d
el
ar
e
ass
ig
n
ed
as
f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
AA
S
I
SS
N:
2252
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8814
A
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Op
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ermis
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a
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S
h
ih
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)
19
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p
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s
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lt,
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er
s
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s
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in
Fig
u
r
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r
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r
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n
ad
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itio
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th
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d
ela
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a
y
m
e
n
t
s
o
f
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er
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lier
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ld
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lt
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a
n
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tiv
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cts
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r
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ased
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u
r
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er
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r
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h
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w
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n
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NCLU
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aim
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t
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p
ap
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t
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r
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ates
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s
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h
e
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el
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h
m
e
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t
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d
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s
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p
le
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ased
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u
m
e
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ical
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al
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is
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h
e
s
u
f
f
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t
co
n
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itio
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ex
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ce
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n
d
u
n
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s
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m
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s
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p
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t
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u
m
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a
m
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le
h
as
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ee
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g
i
v
en
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ill
u
s
tr
ate
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h
eo
r
etica
l
r
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lts
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s
h
o
w
n
i
n
Fig
u
r
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o
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r
ch
ase
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cts
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u
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er
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r
e,
a
w
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n
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n
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ac
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e
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d
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ca
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as
s
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t
t
h
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m
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es
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n
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er
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m
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etit
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m
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ta
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.
A
cc
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h
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w
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as
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t
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Fo
r
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a
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tak
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ti
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g
.
RE
F
E
R
E
NC
E
S
[1
]
Bh
u
n
ia,
A
.
K.,
Ja
g
g
i,
C.
K.,
S
h
a
r
m
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Tw
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De
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Item
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De
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rti
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Ba
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Ap
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.
[2
]
Ch
a
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g
,
C.
T
.
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e
n
g
,
J.
T
.
&
G
o
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.
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M
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r
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ra
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Cre
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s:
A
Re
v
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.
Asia
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c
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o
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Res
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[3
]
Ch
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Op
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Re
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P
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De
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De
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Pr
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[4
]
Ch
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H
.
In
v
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Co
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8814
IJ
AA
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Vo
l.
5
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No
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1
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Ma
r
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201
6
:
13
–
20
20
[5
]
Ch
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J.
A
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De
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e
r
Co
n
d
i
ti
o
n
s
o
f
P
e
r
m
issib
le
De
la
y
in
P
a
y
m
e
n
ts.
Co
mp
u
ter
s a
n
d
Op
e
ra
ti
o
n
s R
e
se
a
rc
h
,
1
9
9
8
,
2
5
,
4
9
–
5
2
.
[6
]
Ch
u
n
g
,
K.
J.
&
Hu
a
n
g
,
C.
K.
An
o
rd
e
ri
n
g
P
o
li
c
y
w
it
h
A
ll
o
wa
b
le
S
h
o
rtag
e
a
n
d
P
e
rm
iss
ib
le
De
la
y
in
P
a
y
m
e
n
ts.
Ap
p
li
e
d
M
a
t
h
e
ma
ti
c
a
l
M
o
d
e
ll
i
n
g
,
2
0
0
9
,
3
3
,
2
5
1
8
-
2
5
2
5
.
[7
]
Ch
u
n
g
,
K.
J
.
A
Co
m
p
lete
P
r
o
o
f
o
n
th
e
S
o
l
u
ti
o
n
P
ro
c
e
d
u
re
f
o
r
No
n
-
i
n
sta
n
tan
e
o
u
s
De
terio
ra
ti
n
g
w
it
h
P
e
rm
issib
le
De
la
y
in
P
a
y
m
e
n
t.
Co
mp
u
ter
s
&
In
d
u
stria
l
En
g
in
e
e
rin
g
,
2
0
0
9
,
5
6
,
2
6
7
-
2
7
3
.
[8
]
G
o
y
a
l,
S
.
K.
Eco
n
o
m
ic
Ord
e
r
Qu
a
n
ti
ty
u
n
d
e
r
Co
n
d
it
i
o
n
s
o
f
P
e
rm
i
ss
ib
le
De
la
y
in
P
a
y
m
e
n
ts.
J
o
u
rn
a
l
o
f
Op
e
ra
ti
o
n
a
l
Res
e
a
rc
h
S
o
c
iety
,
1
9
8
5
,
3
6
,
3
3
5
-
3
3
8
.
[9
]
Hu
,
F
.
&
L
iu
,
D.
Op
ti
m
a
l
Re
p
len
ish
m
e
n
t
P
o
li
c
y
f
o
r
th
e
EP
Q
M
o
d
e
l
w
it
h
P
e
rm
issib
le
De
la
y
in
P
a
y
m
e
n
ts
a
n
d
A
ll
o
w
a
b
le S
h
o
rtag
e
s.
Ap
p
li
e
d
M
a
th
e
ma
ti
c
a
l
M
o
d
e
ll
i
n
g
,
2
0
1
0
,
3
4
,
3
1
0
8
-
3
1
1
7
.
[1
0
]
Hu
a
n
g
,
Y.
F
.
Op
ti
m
a
l
Re
tailer’s
Re
p
len
ish
m
e
n
t
P
o
l
icy
f
o
r
th
e
E
P
Q
M
o
d
e
l
u
n
d
e
r
th
e
S
u
p
p
li
e
rs
T
ra
d
e
Cre
d
it
P
o
l
icy
.
Pro
d
u
c
t
io
n
Pl
a
n
n
in
g
&
Co
n
tro
l
,
2
0
0
4
,
1
5
,
2
7
-
3
3
.
[1
1
]
Hu
a
n
g
,
Y.
F
.
O
p
ti
m
a
l
Re
tailer’s
Re
p
len
is
h
m
e
n
t
De
c
isio
n
s
in
t
h
e
E
P
Q
M
o
d
e
l
u
n
d
e
r
T
w
o
L
e
v
e
ls
o
f
T
ra
d
e
Cre
d
it
P
o
li
c
y
.
Eu
ro
p
e
a
n
J
o
u
rn
a
l
o
f
Op
e
ra
ti
o
n
a
l
Res
e
a
rc
h
,
2
0
0
7
,
1
7
6
,
1
5
7
7
-
1
5
9
1
.
[1
2
]
L
i,
J
.
,
F
e
n
g
,
H.
&
Zen
g
,
Y.
In
v
e
n
to
ry
Ga
m
e
s
w
it
h
P
e
rm
issib
le De
l
a
y
in
P
a
y
m
e
n
ts.
Eu
ro
p
e
a
n
J
o
u
rn
a
l
o
f
Op
e
ra
ti
o
n
a
l
Res
e
a
rc
h
,
2
0
1
4
,
2
3
4
,
6
9
4
-
7
0
0
.
[1
3
]
L
iao
,
J.
J.
On
A
n
E
P
Q
M
o
d
e
l
f
o
r
De
terio
ra
ti
n
g
Item
s
u
n
d
e
r
P
e
rm
issib
le
De
la
y
in
P
a
y
m
e
n
ts.
Ap
p
li
e
d
M
a
th
e
ma
t
ica
l
M
o
d
e
ll
in
g
,
2
0
0
7
,
3
1
,
3
9
3
–
4
0
3
.
[1
4
]
M
e
c
a
,
A
.
,
T
i
m
m
e
r,
J.,
G
a
rc
í
a
-
Ju
r
a
d
o
,
I
.
&
B
o
rm
,
P
.
I
n
v
e
n
to
ry
g
a
m
e
s.
Eu
ro
p
e
a
n
J
o
u
rn
a
l
o
f
Op
e
ra
ti
o
n
a
l
Res
e
a
rc
h
,
2
0
0
4
,
1
5
6
,
1
2
7
-
1
3
9
.
[1
5
]
M
a
ih
a
m
i,
R.
&
A
b
a
d
i
,
I.
N.
K.
Jo
in
t
Co
n
tro
l
o
f
In
v
e
n
to
ry
a
n
d
it
s
P
ricin
g
f
o
r
No
n
-
in
sta
n
ta
n
e
o
u
s
ly
De
terio
ra
ti
n
g
it
e
m
s
u
n
d
e
r
p
e
rm
issib
le
De
la
y
i
n
P
a
y
m
e
n
ts
a
n
d
P
a
rial
Ba
c
k
lo
g
g
in
g
.
Ap
p
li
e
d
M
a
th
e
m
a
ti
c
a
l
M
o
d
e
ll
in
g
,
2
0
1
2
,
5
5
,
1
7
2
2
-
1
7
3
3
.
[1
6
]
M
o
u
s
sa
w
i
-
Ha
id
a
r,
L
.
&
Ja
b
e
r,
M
.
Y.
A
Jo
in
t
M
o
d
e
l
f
o
r
Ca
sh
a
n
d
In
v
e
n
to
ry
M
a
n
a
g
e
m
e
n
t
f
o
r
a
Re
tai
ler
u
n
d
e
r
De
lay
in
P
a
y
m
e
n
ts.
Co
mp
u
ter
s
&
In
d
u
st
ria
l
E
n
g
i
n
e
e
rin
g
,
2
0
1
3
,
6
6
,
7
5
8
-
7
6
7
.
[1
7
]
Ou
y
a
n
g
,
L
.
Y.,
T
e
n
g
,
J.
T
.
,
G
o
y
a
l
,
S
.
K.
&
Ya
n
g
,
C.
T
.
A
n
Eco
n
o
m
ic
Ord
e
r
Qu
a
n
ti
ty
M
o
d
e
l
f
o
r
D
e
terio
ra
ti
n
g
Item
s
w
it
h
P
a
rti
a
ll
y
P
e
rm
issib
le De
la
y
i
n
P
a
y
m
e
n
ts
L
in
k
e
d
to
Ord
e
r
Qu
a
n
ti
ty
.
Eu
ro
p
e
a
n
J
o
u
rn
a
l
o
f
Op
e
ra
ti
o
n
a
l
Res
e
a
rc
h
,
2
0
0
9
,
1
9
4
,
4
1
8
-
4
3
1
.
[1
8
]
Ou
y
a
n
g
,
L
.
Y.
&
Ch
a
n
g
,
C.
T
.
Op
ti
m
a
l
P
ro
d
u
c
ti
o
n
L
o
t
w
it
h
Im
p
e
rf
e
c
t
P
r
o
d
u
c
ti
o
n
P
r
o
c
e
ss
u
n
d
e
r
P
e
r
m
issib
le
De
la
y
in
P
a
y
m
e
n
ts
a
n
d
Co
m
p
lete
Ba
c
k
l
o
g
g
in
g
.
In
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
Pro
d
u
c
t
io
n
Eco
n
o
mic
s
,
2
0
1
3
,
1
4
4
,
6
1
0
-
6
1
7
.
[1
9
]
S
a
rk
a
r
,
B.
A
n
EOQ
M
o
d
e
l
w
it
h
De
la
y
in
P
a
y
m
e
n
ts
a
n
d
T
i
m
e
V
a
ry
in
g
D
e
terio
ra
ti
o
n
Ra
te.
M
a
th
e
ma
t
ica
l
a
n
d
Co
mp
u
ter
M
o
d
e
ll
in
g
,
2
0
1
2
a
,
5
5
,
3
6
7
-
3
7
7
.
[2
0
]
S
a
rk
a
r,
B.
A
n
EOQ
M
o
d
e
l
w
it
h
d
e
la
y
in
P
a
y
m
e
n
ts
a
n
d
S
to
c
k
De
p
e
n
d
e
n
t
De
m
a
n
d
in
th
e
P
re
se
n
c
e
o
f
I
m
p
e
r
f
e
c
t
P
r
o
d
u
c
ti
o
n
.
Ap
p
li
e
d
M
a
t
h
e
ma
ti
c
s
a
n
d
Co
m
p
u
t
a
ti
o
n
,
2
0
1
2
b
,
2
1
8
,
8
2
9
5
-
8
3
0
8
.
[2
1
]
T
sa
o
,
Y.
C.
&
S
h
e
e
n
,
G
.
J.
Dy
n
a
m
ic
P
ricin
g
,
P
r
o
m
o
ti
o
n
a
n
d
Re
p
l
e
n
ish
m
e
n
t
P
o
li
c
ies
f
o
r
A
De
terio
ra
ti
n
g
Item
u
n
d
e
r
P
e
rm
issib
le De
la
y
in
P
a
y
m
e
n
ts.
Co
mp
u
ter
s
a
n
d
Op
e
ra
ti
o
n
s
Res
e
a
rc
h
,
2
0
0
8
,
3
5
,
3
5
6
2
-
3
5
8
0
.
[2
2
]
Wi
lso
n
,
R.
H.
A
S
c
ien
ti
f
ic Ro
u
ti
n
e
f
o
r
S
to
c
k
Co
n
tr
o
l.
H
a
rv
a
rd
Bu
s
in
e
ss
Rev
iews
,
1
9
3
4
,
1
3
,
1
1
6
-
1
1
8
.
[2
3
]
Ya
n
g
,
H.
L
.
&
Ch
a
n
g
,
C.
T
.
A
Tw
o
-
w
a
re
h
o
u
se
P
a
rti
a
l
Ba
c
k
lo
g
g
in
g
In
v
e
n
to
ry
M
o
d
e
l
f
o
r
De
terio
r
a
ti
n
g
Item
s
w
it
h
P
e
rm
issib
le De
la
y
in
P
a
y
m
e
n
t
u
n
d
e
r
In
f
latio
n
.
Ap
p
li
e
d
M
a
th
e
ma
ti
c
a
l
M
o
d
e
ll
in
g
,
2
0
1
3
,
3
7
,
2
7
1
7
-
2
7
2
6
.
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