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of aggregation”. We have also presented an application of the covering location
model to a real public sector location problem in the state of Florida, and have
demonstrated error bound analysis for this problem.
Difficulties in computing actual errors lead to the concept of an error bound, and
this error bound can be used as a surrogate for the maximum absolute error. In fact,
error bounds can be computed for many other location models since many of these
models share properties with (PMM), (PCM), or (CLM). In addition, error bound
analysis can be extended to more general costing functions g if f ( S ) D g ( D ( S , V ))
and the costing function g is s ub a dditive and n on d ecreasing (SAND) (see Francis
et al. 2000 , 2009 ).
Based on our work on demand point aggregation for location modeling, we offer
the following observations:
1. the work of Hillsman and Rhoda is widely recognized and influential; in
particular, self-canceling error is a helpful concept for models with additive
2. there is little average-case analysis of aggregation error;
3. much more research on aggregation for the median problem has been done than
for center, covering and other models;
4. progress is definitely being made in understanding aggregation error;
5. aggregation error bounds can be useful, particularly for center and covering
6. aggregation error measures used vary greatly, and there is no agreement on how
to measure error; hence it is pointless to ask which aggregation algorithm is best,
since “best” is not defined.
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