Geoscience Reference
In-Depth Information
Tam ir
1990
). We shall see that aggregation results developed for one model often
also apply to the other.
These examples of models illustrate two equivalent approaches for representing
n
DPs with an aggregation of
q
ADPs. Either we have a partition of the DP index set
J
into
q
sets
J
1
, :::,
J
q
with one ADP per set, or for each
v
j
there is a replacing ADP
v
j
, with each
v
j
in the set of
q
distinct ADPs. In either case, three aggregation
decisions (Francis et al.
1999
) must be made: (1) the number of ADPs, (2) the
location of ADPs, (3) the replacement rule: for each
v
j
,whatis
v
j
? The (reasonable)
replacement rule often used is to replace each DP by a closest ADP. Further, for
the aggregation to be computationally useful we require the number of ADPs,
q
,to
be less (usually much less) than the number of DPs,
n
; also it is reasonable to have
p
q
. The authors note that versions of these three aggregation decisions occur in
location modeling. Hence results in location theory help in doing DP aggregation,
so DP aggregation is a sort of “second-order” location problem to solve prior to
solving the original or “first-order” problem.
These three examples may suggest that as more ADPs are used the aggregation
error decreases—ideally, if we could use
q
D
n
ADPs, we don't have an aggregation
error at all. In fact there are classes of location models where the law of diminishing
returns applies: aggregation error decreases at a decreasing rate as
q
increases
(Francis et al.
2004a
). Thus a very small value of
q
may cause a very high
aggregation error, while a large value of
q
might give little less error than an
appreciably smaller value of
q
.
18.3
Case Study
This section is based on the work by Dekle et al. (
2005
), where supplemental
information may be found. We refer to the authors of this study as the “team”.
FEMA is an acronym for Federal Emergency Management Agency, a national
U.S. agency that deals with disasters such as fires, floods, hurricanes, tornadoes, and
terrorist attacks. This work stems from a FEMA request to all counties in Florida to
identify possible locations for disaster recovery centers (DRCs). FEMA describes a
DRC as “a facility established in or nearby the community affected by the disaster,
where people can meet face-to-face with representatives from Federal, State, local
and volunteer agencies to obtain assistance.” For the county this study deals with,
Alachua County, FEMA required the identification of at least three DRCs, which
could be called upon at very short notice for use in a local disaster. Alachua County
had a population of about 219,000 at the time of the study. The east-west and
north-south dimensions of the county are about 32 and 30 miles (51.5, 48.3 km)
respectively; the land area is about 874 square miles (2,266 km
2
).
FEMA provided seven DRC requirements/evaluation criteria. The County
accepted all of these requirements, but added four more, including that the proposed
DRC locations should be buildings allowing reasonable travel distances to them by
potential users. This criterion was the most challenging to satisfy, and led to the
