Biomedical Engineering Reference
In-Depth Information
Table 5.2
Total Enumeration of Branch Locations Combinations
#
x
1
x
2
x
3
x
4
x
5
x
6
x
7
f (x)
1
0
0
0
0
1
1
1
36.04
2
0
0
0
1
0
1
1
39.92
3
0
0
0
1
1
0
1
40.41
4
0
0
0
1
1
1
0
46.07
5
0
0
1
0
0
1
1
35.98
6
0
0
1
0
1
0
1
36.61
7
0
0
1
0
1
1
0
55.88
8
0
0
1
1
0
0
1
36.32
9
0
0
1
1
0
1
0
43.79
10
0
0
1
1
1
0
0
44.42
11
0
1
0
0
0
1
1
35.80
12
0
1
0
0
1
0
1
39.57
13
0
1
0
0
1
1
0
47.41
14
0
1
0
1
0
0
1
39.11
15
0
1
0
1
0
1
0
41.14
16
0
1
0
1
1
0
0
44.90
17
0
1
1
0
0
0
1
36.61
18
0
1
1
0
0
1
0
46.83
19
0
1
1
0
1
0
0
48.81
20
0
1
1
1
0
0
0
41.95
21
1
0
0
0
0
1
1
34.61
22
1
0
0
0
1
0
1
33.79
23
1
0
0
0
1
1
0
36.16
24
1
0
0
1
0
0
1
41.60
25
1
0
0
1
0
1
0
39.39
26
1
0
0
1
1
0
0
35.61
27
1
0
1
0
0
0
1
31.01
28
1
0
1
0
0
1
0
35.53
29
1
0
1
0
1
0
0
36.17
30
1
0
1
1
0
0
0
32.59
31
1
1
0
0
0
0
1
33.40
32
1
1
0
0
0
1
0
32.73
33
1
1
0
0
1
0
0
36.09
34
1
1
0
1
0
0
0
33.35
35
1
1
1
0
0
0
0
33.54
The
p
-median problem is well researched in the literature. Various optimization techniques
have been developed for its solution (see Daskin, 1995; Current et al., 2002). Typically, it is
formulated as integer programming (Daskin, 1995; Current et al., 2002). We present here a
different, intuitive formulation. Suppose that
x
¼
{
x
1
,
x
2
,...,
x
7
} are seven binary variables.
A variable is assigned a value of ''1,'' if the corresponding community is selected for a branch and
''0,'' if it is not. The set
I
is defined to include all variables with a value of ''1.'' For a feasible
(acceptable) solution, the set
I
must be of cardinality 3. The service distance for community
j
is
defined as
d
j
¼
min
i
2
I
d
ij
, where
d
ij
is the distance between communities
i
and
j.
By these
definitions, the formulation is:
(
)
f
(
x
)
¼
X
20
Minimize
d
j
(5
:
1)
j
¼
1
Subject to :
X
7
x
i
¼
3
(5
:
2)
i
¼
1
x
i
2f
0
;
1
g
(5
:
3)
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