Geoscience Reference
In-Depth Information
, and the convergence
tolerance was 10
6
. In other words, the absolute values of the differences between
each pair of path flows, the path time deviations, and the Lagrange multipliers in
two consecutive iterations were less than or equal to this tolerance. We initialized
the algorithm by setting all variables equal to zero.
The computed optimal path flows, time deviations, and Lagrange multipliers are
reported in Table
15.3
and the optimal link flows in Table
15.2
.
As seen in Table
15.2
, the optimal flows on links 3 and 4, i.e., the post-disaster
procurement links, are zero. Hence, given the demand information and the cost and
time functions on the supply chain network links, the organization would be better
off by adopting the prepositioning strategy. In addition, links 10 and
11, corresponding to marine transportation of goods from the US to the affected
region have zero or very small flows. Such an outcome is due to the importance of
timely deliveries, and, thus, the organization needs to ship via air to minimize the
lateness on the demand end. Similarly, among the distribution links, the ones
representing shipments by helicopter (links 15 and 20) are assigned relatively
higher loads whereas link 17 corresponding to one of the ground distribution
links will not be utilized. Also, note that the optimal flows being almost equal on
links 1 and 2 suggests an even split of pre-positioning of the load between the two
US aid regions.
Table
15.3
points out that among the 24 paths in the supply chain network, fewer
than onethird have considerable positive flows since the others involve links that are
either costlier or more time-consuming. From the optimal values of time deviations
on paths, one can observe that significant deviations from the target times have
occurred on several paths in the network. This seems to be more of an issue in the
paths connecting the origin to demand point
R
1
, i.e., the hypothetically more
vulnerable location. Such an outcome may mandate additional investments on
critical transportation/distribution channels to
R
1
which can be done in accordance
with the optimal values of respective Lagrange multipliers. The higher the value of
the Lagrange multiplier on a path, the more improvement in time can be attained by
enhancing that path which, in turn, leads to a more efficient disaster response
system.
afg¼ :
1
1
Amherst. We set the sequence as
11
;
2
;
2
; ...
15.4.1 Variant
We then considered the following variant of the previous example. We assumed
that the organization will now procure the items locally and, hence, the time
functions associated with the direct procurement links 3 and 4 are now greatly
reduced and are given in Table
15.4
—the remainder of the input data remains as in
the previous example. The computed optimal link flow pattern for this variant is
also reported in Table
15.4
.
As can be seen from Table
15.4
, now both the storage links for pre-positioning
(links 7 and 8) and for post-disaster procurement (links 3 and 4) have positive flows.
