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=
1
n
i
=1
n
j
=1
(
b
ij
−
μ)
2
σ
n
2
•
(3.16)
3.7.1
Quadratic Assignment Problem Example
As example for the QAP is given as the faculty location problem given in Fig 3.16.
The objective is to allocate location to faculties. There is a specific distance be-
tween the faculties, and there is a specified flow between the different faculties, as
shown by the thickness of the lines. An arbitrary schedule can be
{
2
,
1
,
4
,
3
}
,asgivenin
Fig 3.16. Two distinct matrices are required: one
distance
and one
flow
matrix as given
in
Tables 3.36 and 3.37.
Applying the QAP formula, the function becomes:
⎧
⎨
⎫
⎬
D
(1
,
2)
•
F
(1
,
2)+
D
(1
,
3)
•
F
(2
,
4)+
Sequence
=
⎩
D
(2
,
3)
•
F
(1
,
4)+
⎭
D
(3
,
4)
•
F
(3
,
4)
Loc 1,
Fac 2
Loc 2,
Fac 1
Loc 4,
Fac 3
Loc 3,
Fac 4
Flow
Fig. 3.16.
Faculty location diagram for 2, 1, 4, 3
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