Environmental Engineering Reference
In-Depth Information
optimal solution should have the shortest distance from the positive ideal solution
and the farthest from the negative ideal solution (Oztaysi
2014
). In current
research, the maximum value of each attribute is considered as positive ideal solu-
tion and the minimum value as negative ideal solution. This values is mentioned
for positive attributes where higher value of them are preferred for the location of
ASC, e.g. population of candidate location, while for negative attributes is vice
versa. To determine these values, the decision matrix is formed and normalized by
using the linear method. Then the positive ideal solution (
A
+
) and negative ideal
solution (
A
−
) is determined as described in Roy (
2004
).
After calculating the ideal solutions, the distances of each alternative to the
A
+
and
A
−
calculated as
R
+
and
R
−
, respectively (see Eqs.
10
and
11
) (Oztaysi
2014
):
m
+
j
+
j
)
2
R
(
v
ij
−
v
i
=
1, 2,
...
,
J
=
(10)
j
=
1
m
−
j
−
j
)
2
R
(
v
ij
−
v
i
=
1, 2,
...
,
J
=
(11)
j
=
1
where;
v
j
is the negative ideal for the criteria
j
.
Using these calculated values closeness index (C.I.) for each alternative is com-
puted using Eq.
12
(Roy
2004
):
+
j
is the positive ideal and
v
−
(
R
−
)
C
.
I
.
=
R
+
(12)
+ (
R
−
)
The closeness index can get values between 0 and 1 and the alternative which has
the highest
C
.
I
. is selected as the best alternative (Oztaysi
2014
).
2.6 DEA Technique
DEA first introduced by Charnes, Cooper, and Rhodes (CCR) (Charnes et al.
1978
). The original CCR model was applicable only to technologies characterized
by constant returns to scale (CRS) globally. Banker et al. (
1984
) divide the over-
all efficiency into technical and scale efficiencies. Technical efficiency is defined
as the Decision Making Unit (DMU's) ability to achieve maximum output from
given inputs. Using standard notations, the efficiency can be written as Eq.
13
(Charnes et al.
1978
):
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