Geoscience Reference
In-Depth Information
Chapter 23
Districting Problems
Jörg Kalcsics
Abstract
Districting is the problem of grouping small geographic areas, called
basic units, into larger geographic clusters, called districts, such that the latter are
balanced, contiguous, and compact. Balance describes the desire for districts of
equitable size, for example with respect to workload, sales potential, or number of
eligible voters. A district is said to be geographically compact if it is somewhat
round-shaped and undistorted. Typical examples for basic units are customers,
streets, or 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. Despite the considerable number of publications on districting problems,
there is no consensus on which criteria are eligible and important and, moreover, on
how to measure them appropriately. Thus, one aim of this chapter is to give a broad
overview of typical criteria and restrictions that can be found in various districting
applications as well as ways and means to quantify and model these criteria. In
addition, an overview of the different areas of application for districting problems
is given and the various solution approaches for districting problems that have been
used are reviewed.
Keywords
Districting criteria Political districting Sales territory design
Service districting
23.1
Introduction
Most problems discussed in this topic focus on the location of facilities: where to
locate, how many to locate, when to locate, which type to locate, etc. However,
although the driving force is the location of facilities, equally important is the second
aspect of location problems that is usually not mentioned explicitly: the allocation of
customers to facilities. Even if this task is trivial in many classical location problems
like the p-median or the p-center problem (see Chaps. 2 and
4
), only after deciding
