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In-Depth Information
observed that the Maximal Covering Location Problem is also prone to MAUP and
employed GIS functions to formulate new models that are more robust and are less
affected by changes in the scale or units of data. Finally, Kim and Murray (
2008
)
developed a similar model for a specific version of the coverage problem (Backup
Coverage Location Problem) which eliminates MAUP in comparison to the original
formulation. All these new models are based on the functionality of GIS which
provides tools for accurately calculating the portions of the demand areas that are
covered by different configurations of the facilities.
19.4.4
Uncertainty and Error Propagation
Uncertainty and error are inherent in many location problems. Demand for a product
or service is rarely determined with accuracy and is usually estimated on the basis of
historical data. Other parameters, such as transportation costs or distances between
facilities are also characterized by uncertainty. The coordinates of the potential
facilities themselves or the distribution of the customers may also be recorded
incorrectly or inaccurately. A variety of approaches has been proposed in the
location science literature to deal with this uncertainty. Most of these approaches
are based on the formulation of stochastic models, the performance of sensitivity
analysis or the definition of scenario-based problem formulations. A detailed review
of such approaches can be found in Snyder (
2006
).
As far as GIS is concerned, it can be safely said that no map or digital
representation of spatial and attribute data is error free. According to Murray and
Grubesic (
2012
), the uncertainty associated with the use of GIS is multifaceted
and is related to several aspects including the accuracy, precision, spatial scale
and geographic abstraction of the information stored in the GIS. Moreover, this
uncertainty and error propagate through the application of GIS functions thus
amplifying their effect. Since the early stages of GIS development, it became evident
that this uncertainty and error can influence the quality of the analysis and the
reliability of the results (Heuvelink
1998
). Hence, a broad range of literature has
focused on data imperfections and ways to deal with them in GIS. Error propagation
has been studied for certain GIS functions such as overlay (see Veregin
1995
). Other
methods to cater for uncertainty and error include the use of Monte Carlo simulation
or multiple analyses conducted on perturbed data in order to obtain more reliable
results. A detailed review can be found in Li et al. (
2012
). It must be noted that
although these methods seem to be well known in the GIS community, relatively
few applications are encountered in location science problems. This may be due to
the fact that a deeper understanding of GIS is required by location analysts in order
to fully exploit the capabilities of GIS for dealing with uncertainty and error (see
Murray
2010
).
A notable example where GIS is used to study uncertainty and error in loca-
tion science is given by Murray (
2003
) who considered the planar multi-facility
location-allocation problem and used an Avenue script within ArcView to perturb
