Environmental Engineering Reference
In-Depth Information
W
h he
: relative degree of capability of MH equipment
e
to perform the
combination of MH operation/suboperation
C
ei
: compatibility between MH equipment
e
and part type
i
Decision Variables
Z(
ip
)
∈{
1
,
0
}
: 1 if part type
i
uses process plan
p
; 0 otherwise
Y
sj
(
ip
)
∈{
1
,
0
}
: 1 if machine
j
performs operation
s
of part type
i
under process
plan
p
; 0 otherwise
A
ijph h
∈{
1
,
0
}
: 1, if part type
i
under process plan
p
requires the combination of
MH operation/suboperation at machine
j
; 0 otherwise
X
ijph he
∈{
1
,
0
}
: 1 if the combination of MH operation/suboperation requires MH
equipment
e
at machine
j
where operation
s
of part type
i
under
process plan
p
is performed; 0 otherwise
M
j
∈{
1
,
0
}
: 1 if machine
j
is selected; 0 otherwise
D
e
∈{
1
,
0
}
: 1 if MH equipment
e
is selected; 0 otherwise
The first part of the objective function is presented as equation (1):
P(i)
S(ip)
n
m
F
1
=
d
i
OC
ipj
Y
sj
(ip)
+
SC
j
M
j
i
=
1
p
=
1
s
=
1
j
∈
J
ips
j
=
1
(1)
H
S(ip)
n
P(i)
H
+
d
i
T
ij h he
X
ijph he
.
i
=
1
p
=
1
s
=
1
j
∈
J
ips
h
=
1
h
e
∈
E
jhh
=
1
The second part of the objective function is formulated as equation (2):
H
E
H
n
P(i)
S(ip)
F
2
=
W
h he
C
ei
X
ijph he
,
(2)
e
=
1
h
=
1
h
i
=
1
p
=
1
s
=
1
j
∈
J
ips
=
1
where
t
=
1
W
et
W
it
−
C
ei
=
1
−
.
4
T
5 and refers to the five major variables used to identify the dimen-
sions of the characteristics mentioned by Ayres (1988). Integer numbers are used
to assign values to the subjective factors,
W
parameters,
W
et
,
W
h he
and
W
it
.The
rating scales range from 0 to 5 for
W
et
and
W
h he
and1to5for
W
it
(Ayres 1988).
A5for
W
et
means that the piece of equipment is best suited to handle parts with
a very high rating of product variable
t
. A 0 means, do not allow this piece of
equipment to handle parts with product variable
t
.A5for
W
h he
means that it is
excellent in performing the operation/suboperation combination. And a 0 means
that it is incapable of performing the operation/suboperation combination. A 5
for
W
it
means that the part type exhibits a very high level of the key product
variable
t
. And a 0 means that the part type exhibits a very low level of the key
product variable
t
.
Here,
T
=
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