Geoscience Reference
In-Depth Information
Table 10.3
List of the set
EQ
for Example
10.3
f1;2g
f1;3g
f1;4g
f2;3g
f2;4g
f2;5g
f3;5g
f3;6g
f4;5g
f5;6g
1
2
2
3
5
6
2
3
1
2
EQ
12
2
3
4
9
2
3
1
2
EQ
13
2
3
8
9
8
9
1
6
EQ
14
1
0
0
5
6
1
2
1
6
1
6
1
2
EQ
15
8
9
8
9
5
6
EQ
16
1
1
0
1
3
2
3
2
3
1
2
EQ
23
2
3
2
3
1
2
EQ
24
Œ
4
;1
1
2
1
4
EQ
25
1
0
0
2
3
8
9
1
3
1
6
EQ
26
1
4
1
6
1
3
5
6
1
4
EQ
34
1
6
1
9
1
3
1
3
EQ
35
1
1
Œ
6
;1
1
3
5
6
1
2
EQ
36
1
0
1
2
1
3
1
3
1
9
1
3
EQ
45
1
2
Œ
3
;1 Œ
3
;1
EQ
46
0
0
0
1
0
1
2
2
3
1
9
2
3
EQ
56
Table 10.4
Solutions for some specific choices for in Example
10.3
Obj. function
Corresponding
Set of optimal solutions
Obj. value
EQ
2
46
,
EQ
3
46
,
EQ
5
34
Center
D .0;0;0;0;0;1/
5
D .0;0;0;0;
2
;
2
/
Œ
EQ
2
35
;
EQ
2
56
;Œ
EQ
3
36
;
EQ
3
14
,
Œ
EQ
5
14
;
EQ
5
13
2-Centra
5
D .0;0;0;
3
;
3
;
3
/
EQ
2
26
40
9
3-Centra
EQ
2
16
D v
3
Median
D .1;1;1;1;1;1/
18
D .
O
6
;
O
6
;
O
6
;
O
6
;
O
6
;
6
5
O
/
EQ
5
34
, 0
O
36
43
, v
3
otherwise
12
O
C 5,
5
O
C 8
17
Cent-dian
6
EQ
2
14
,
EQ
5
12
Noname
D .1;1;0;0;1;1/
13
choices for . To describe the solution set we use the notation
EQ
i
kl
to denote the
part of
EQ
kl
which lies on the edge
f
i;j
g
.
Kalcsics et al. (
2002
) gives an FDS for the single facility ordered median problem
with general node weights (the
w
-weights can be negative). Moreover, for the case
of a directed network with non-negative
w
-weights, they prove that there is always
an optimal solution in V .
10.4.2
The
p
-Facility Ordered Median Problem
In this section we deal with the multi-facility extension of the ordered median
problem.
The p-facility
ordered
median
problem
consists
of
finding
a
set
