Geoscience Reference
In-Depth Information
The new optimal time deviation on path
p
2
was:
z
p
2
¼
8
:
26,
which is higher than the value in the preceding example. The value of the
tardiness penalty function,
ʳ
R
1
zð
, has increased from 438.39 in the illustrative
example to 579.61 in its variant. Also, removal of the ground transportation link
results in a higher total operational cost in that the sole mode of transportation to the
affected region would be the costlier air transport mode.
The optimal value of Lagrange multiplier on path
p
2
was:
p
2
¼
132
ˉ
:
12,
which shows a 28 % increase.
15.2.3.3 Illustrative Example—Variant II
The second variant of the original example addresses the post-disaster procurement
strategy—as opposed to pre-positioning of the supplies. We assumed that the
organization did not store disaster items beforehand. In other words, the organiza-
tion would procure relief items only once a disaster struck. Thus, the network did
not include links
a
,
b
, and
c
—corresponding to pre-disaster procurement, shipment,
and storage of relief goods—and instead incorporated link
h
representing post-
disaster procurement, as depicted in Fig.
15.4
.
The total cost functions and the time completion functions on links
d
,
e
,
f
, and
g
remained the same as in the illustrative example. As for link
h
, we had:
c
h
fðÞ¼
5
f
h
þ
3
f
h
and
^
˄
h
fðÞ¼
3
f
h
þ
3
:
In this example, the total operational cost on the post-disaster procurement link,
h
, was higher than that on the pre-disaster procurement link
a
in the example in
Sect.
15.2.3.1
. That is because the organization is assumed to be able to procure the
relief items at a lower price under the pre-positioning strategy given the ample time
that it has for preparedness. In contrast, procuring the relief goods after a disaster
hits may leave the organization with fewer purchasing options since large quantities
of goods have to be purchased/procured quickly (and, depending on the sources,
there may even be competition for purchasing). In addition, in the network topology
of this example, the post-disaster procurement activity may also include some
transportation/shipment, further raising the total operational cost on link
h
as
compared to that on link
a
in the previous examples.
The set of paths in this problem was
P¼
{
p
3
,
p
4
} where
p
3
¼
(
h
,
d
,
f
,
g
) and
p
4
¼
(
h
,
e
,
f
,
g
). The demand distribution, the shortage and surplus penalties, as well
as the target time were identical to the previous problems. The tardiness penalty
function at the demand point was the same, except that now it was a function of the
time deviations on new paths:
