Geoscience Reference
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about allocations can we evaluate a given facility configuration and, thus, try to find
the optimal one. Hence, the allocations have a fundamental impact on the location
of facilities and different rules of allocation will result in different evaluations of the
same facility configuration. The aim of districting problems is now the other way
around: we first find allocations—or, more generally, determine which customers
should be served together—and then, if necessary, we find locations for the facilities
serving the customers.
In general, districting is the problem of grouping small geographic areas, called
basic units, into larger geographic clusters, called districts, in a way that the latter
are acceptable according to relevant planning criteria. Typical examples for basic
units are customers, streets, or zip code areas. Depending on the practical context,
districting is also called territory design, territory alignment, zone design, or sector
design. Three important criteria are balance, contiguity, and compactness. Balance
describes the desire for districts of equitable size with respect to some performance
measure for the districts. Depending on the context, this criterion can either be
economically motivated, for example, equal sales potentials, workload, or number
of customers, or have a demographic background, for example, the same number of
inhabitants or eligible voters. A district is called contiguous if it is possible to travel
between the basic units of the district without having to leave the district. Finally,
a district is said to be geographically compact if it is somewhat round-shaped,
undistorted, and without holes. Contiguous and compact districts usually reduce the
travel time of the person responsible for servicing the district. Unfortunately, a rigid
and concise mathematical definition of contiguity and compactness is often difficult
and strongly depends on the available data. In addition, for each district often the
location of a “facility” is either given or should be sought. This facility can be a
branch office, a depot, or the home address of a sales person. Figure
23.1
shows an
example of a districting plan for streets and for zip code areas.
Districting problems are motivated by quite different applications ranging from
political districting over the design of districts for schools, social facilities, waste
collection, or winter services, to sales and service territory design. Looking at
the literature, it is striking that only few authors consider the districting problem
independently from a practical background. Therefore, the aim of this chapter is to
Fig. 23.1
An example of a districting plan for streets and for zip-code areas
