Geoscience Reference
In-Depth Information
8
<
1046
x
p
3
þ
1038
x
p
4
p
3
p
4
þ
18
:
5
ˉ
þ
9
:
5
ˉ
¼
10088
1038
x
p
3
þ
1052
x
p
4
p
3
p
4
¼
10086
þ
9
:
5
ˉ
þ
11
:
5
ˉ
7
z
p
3
ˉ
p
3
¼
0
16
z
p
4
ˉ
p
4
¼
0
:
18
:
5
x
p
3
9
:
5
x
p
4
þ z
p
3
¼
57
9
:
5
x
p
3
11
:
5
x
p
4
þ z
p
4
¼
61
:
Solution of the above yields:
x
p
3
¼
0
33 and
x
p
4
¼
6
:
:
26
:
which yields the following optimal link flows:
f
h
¼ f
f
¼ f
g
¼ x
p
3
þ x
p
4
¼
6
59,
f
d
¼ x
p
3
¼
0
33, and
f
e
¼ x
p
4
¼
6
:
:
:
26
:
Note that, under a post-disaster procurement strategy, the optimal flow on the
ground transportation link is significantly lower than that in the pre-disaster pro-
curement strategy. This is due to the fact that the duration of the procurement
activity is now being incorporated, and the organization wants to avoid excessive
delays caused by assigning large quantities to the ground transportation path. In
addition, the optimal flow on the air transportation link has experienced a 17 %
decrease which is a consequent of increased operational costs.
The value of the projected demand is:
v
R
1
¼ x
p
3
þ x
p
4
¼
6
:
59,
which is 23 % lower than that for the example in Sect.
15.2.3.1
. Furthermore, the
projected demand is now closer to the lower bound of the demand uniform
distribution. Therefore, in the case that pre-positioning of supplies is not available,
the decision-maker must be careful in assessing the shortage penalties. A sensitivity
analysis on the shortage penalty value and the impact on the solution is presented in
Sect.
15.2.3.4
.
The optimal time deviations on paths
p
3
and
p
4
are:
z
p
3
¼
8
54 and
z
p
4
¼
14
:
:
09,
which are higher than their respective values in the first example. The incurred
tardiness penalty value,
zð
, is equal to 1, 844.16, i.e., a 321 % increase from
ʳ
R
1
that in the first example.
Finally, the optimal Lagrange multipliers on paths
p
3
and
p
4
are:
p
3
¼
59
p
4
¼
225
ˉ
:
77 and
ˉ
:
49
:
15.2.3.4 Sensitivity Analysis for Variant II
In the illustrative example in Sect.
15.2.3.1
and its variants in Sects.
15.2.3.2
and
15.2.3.3
, we investigated the impact of the shortage penalty on the optimal solution.
