Geoscience Reference
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give a broad overview of typical criteria and restrictions that can be found in the
various districting applications as well as ways and means to quantify and model
these criteria. As most districting applications have a strong spatial component, it is
natural to integrate the algorithms into a Geographic Information System (GIS).
In a modern GIS, users can access and utilize the rich variety of maps, spatial
databases, and geographical objects available to appropriately mark out the problem
and display the solutions, see also Chap. 19.
The rest of the chapter is organized as follows. The next section reviews the
broad range of districting applications and identifies and motivates the different
planning restrictions. In Sect. 23.3 , basic notations are introduced. The next section
discusses the most common criteria found in districting applications and discusses
possible approaches to quantify these criteria and to incorporate them into districting
models. Finally, Sect. 23.5 presents an overview of the different solution techniques
for solving districting problems.
23.2
Applications
There are four major areas of application for districting problems: political district-
ing, sales territory design, service districting, and distribution districting, and this
section provides a comprehensive but non-exhaustive overview. But before we start,
we mention a first “application” in the context of facility location that derives from
the problem of aggregating demand points for location problems with the aim of
reducing the complexity of the problem. Simchi-Levi et al. ( 2003 ) formulate the
following guidelines (among others): aggregate demand points for 150-200 zones,
make sure each zone has an approximately equal amount of total demand, and place
aggregated points at the center of the zone. These guidelines read as a classical
districting problem.
23.2.1
Political Districting
Political districting is the problem of dividing a governmental area, such as a city or
a state, into constituencies from which political candidates are elected. Basic units
typically correspond to census tracts, which are given as polygons, and the districts
to the electoral constituencies. In general, the process of redistricting has to be
periodically undertaken to account for population shifts. The length of these periods
varies from country to country, e.g., in New Zealand every 5 years, in Canada and
the U.S. every decade (after each census). In the past, political districting has often
been flawed by manipulation aiming to favor some particular party or to discriminate
against social or ethnic minorities. Since the responsibility for approving state and
local districting plans usually falls to elected representatives, plans are likely to be
shaped implicitly, if not overly, by political considerations, e.g., to keep them in
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