Geoscience Reference
In-Depth Information
office. In districting, this location is called the
center
of the district. One has to
be aware of the ambiguity with the notion of a center in location theory, which is
something different, see Chap.
4
. Typically, the center coincides with a basic unit,
i.e., c
k
2
J. A predetermined set of centers is denoted by J
c
.
Finally, a
districting plan
D
is defined as a set of p districts
D
Df
D
1
;:::;D
p
g
.
23.3.3
Problem Formulation
The districting problem can now informally be described as follows: Partition all
basic units J into a number of p districts that satisfy the planning criteria of balance,
compactness, and contiguity and, if required, locate a center within each district.
Unfortunately, in contrast to many other optimization problems, there does not
exist
the
mathematical model for districting problems. This is mainly due to the
considerable ambiguity on how to quantify the different planning criteria and in the
motivation and relevance of some of them.
23.4
Districting Criteria
This section presents an overview over typical criteria employed in districting
problems and various ways and means to quantify them. In the following, a measure
for a criterion applied to a single district (the whole districting plan) is termed a local
(global) measure. Moreover, if not explicitly stated otherwise, let Q
D
1.
23.4.1
Complete and Exclusive Assignment
In most cases, each basic unit is assigned to exactly one district, i.e., the districts
define a partition of the set J of basic units:
D
1
[[
D
p
D
J and D
l
\
D
k
D;
; 1
l; k
p; l
ยค
k:
The requirement of exclusive assignment is sometimes also termed
integrity
.For
political districting, these criteria are obvious. In sales territory design, unique allo-
cations result in transparent responsibilities for the sales force avoiding contentions
and allowing the establishment of long-term customer relations.
