Geoscience Reference
In-Depth Information
Table 15.2
Total
operational costs,
completion time functions,
and the optimal flows on
links in the numerical
example
f
a
*
Link
c
a
f ðÞ
^
˄
a
(
f
a
)
3
f
1
2
+2
f
1
1
0
19.22
2
f
2
2
+ 2.5
f
2
2
0
20.02
5
f
3
2
+4
f
3
3
3
f
3
+ 1
0.00
4.5
f
4
2
+3
f
4
4
4
f
4
+ 1
0.00
f
5
2
+2
f
5
5
0
19.22
f
6
2
+.5
f
6
6
0
20.02
2.5
f
7
2
+3
f
7
7
0
19.22
3.5
f
8
2
+2
f
8
8
0
20.02
7
f
9
2
+5
f
9
9
2
f
9
+ 2
19.22
4
f
10
2
+6
f
10
10
10
f
10
+ 6
0.00
2.5
f
11
2
+4
f
11
11
7.5
f
11
+ 5
0.23
4.5
f
12
2
+5
f
12
12
1.5
f
12
+ 1.5
19.79
2
f
13
2
+4
f
13
13
2
f
13
+ 2
19.22
f
14
2
+3
f
14
14
1.5
f
14
+ 1
20.02
4
f
15
2
+5
f
15
15
3
f
15
+ 3
13.95
2.5
f
16
2
+2
f
16
16
5
f
16
+ 4
5.28
3
f
17
2
+4
f
17
17
6.5
f
17
+ 3
0.00
4
f
18
2
+4
f
18
18
7
f
18
+ 5
6.85
3
f
19
2
+3
f
19
19
4
f
19
+ 5
5.68
3.5
f
20
2
+5
f
20
3.5
f
20
+ 4
20
7.49
R
1
is assumed to have a higher demand for relief goods due to a larger population
and its potential higher vulnerability to the disasters as compared to
R
2
. The demand
for the relief item at
R
1
and at
R
2
is assumed to follow a uniform distribution on the
intervals [25,45] and [10,20], respectively.
The unit shortage and surplus penalties at the demand points are:
R
1
¼
10, 000,
R
1
¼
100,
λ
λ
R
2
¼
7, 500,
R
2
¼
150
λ
λ
:
The target times of delivery at demand points
R
1
and
R
2
are:
T
R
1
¼
72,
T
R
2
¼
70
:
Using (
15.15
), the
T
kp
's are also shown in Table
15.3
.
Recall that in selecting the penalties and the target times, the decision-maker
takes into account such data as the population, accessibility, strategic location, etc.
In addition, the decision-maker can prioritize certain paths by assigning higher
coefficients in the tardiness penalty function. In this example—unlike the illustra-
tive example—all paths are assumed to have equal tardiness penalty weights:
