Environmental Engineering Reference
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where:
i
The index of candidate locations and demand points.
j
The index of attributes of service center location problem.
S
∇
i
The final score of candidate location
i
for attributes which lower values of
them are preferred (maxi-min).
S
i
The final score of candidate location
i
for attributes which greater values of
them are preferred (maxi-max).
γ
j
The important weight of attribute
j
obtained from FAHP.
χ
ij
The value of attribute
j
for candidate location
i
.
After calculating the final scores of each candidate location, they will be ranked
based on their score values. Then candidate locations which their score of maxi-min
score (
S
∇
i
) is lower than a threshold (
α
% of the selected range
which identified by
decision maker) and also for maxi-max score (
S
i
) which is bigger than a threshold
(
β
% of the selected range
which identified by decision maker) will selected and
categorized in two set of
A
ρ
and
B
ρ
for each region of study (see Eqs.
18
and
19
).
∇
i
A
ˁ
=
i
|
S
≤ ʱ
%of the selected range
(18)
i
|
S
i
B
ˁ
=
≥ ʲ
%of the selected range
(19)
At last step of this approach, we will select locations which satisfy both selection
constraints described before. Since we are going to select at least one location for
each region to open a service center, locations will be selected from the set adher-
ing to the subscription set of
A
ρ
and
B
ρ
(see Eq.
20
):
Y
ρ
=
A
ρ
∩
B
ρ
(20)
where:
ρ
The index of region
ˁ
=
(
1,
...
,7
)
.
A
ρ
The set of candidate locations which has been selected the using minimiza-
tion selection criteria.
B
ρ
The set of candidate locations which has been selected the using maximiza-
tion selection criteria.
Y
ρ
The final selected locations for region
ρ
.
After finding the set of
Y
ρ
, the best location must be proposed, because more
than one location may satisfy the selection conditions. In classic location models
a distance function is always used to select the best location (Franco et al.
2008
).
However, in this case due to the characteristics of agricultural services other attrib-
utes in addition to distance function are adopted. These further attributes enables
to also consider the technical aspects of potential locations.
To prove the capability of the proposed sub-attributes and the developed
multi-attribute decision making process, one case study has been conducted in
a region of Iran. The studied region is Razan, a county located on the north of
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