Geoscience Reference
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of the sum of the fixed setup costs and the variable costs to serve customers
from the facilities. This problem is known as
uncapacitated
or
simple facility
location problem
(Erlenkotter
1978
). However, if efficiency is mainly viewed from
the customers' point of view, an alternative measure to be minimized can be
represented by the maximum distance between customers and their patronized
facilities. In practice this so called minmax objective, typical of the class of
center
problems (continuous or discrete), is focused on customers in the worst condition
(Hakimi
1964
; Minieka
1970
; Goldman
1971
; Elzinga and Hearn
1972
; Drezner
and Wesolosky
1980
).
Another classical concept used to measure efficiency is related to the ability of
facilities to “cover” demand. More precisely a facility is said to cover a demand
point if their mutual distance does not exceed a given “coverage radius” which
can be evaluated depending on the specific application. In this context when the
number of facilities is specified a priori, the objective consists in positioning them
in such a way that they are able to cover as much demand as possible (Maximal
Coverage Location Problem) (Church and ReVelle
1974
). When the number of
facilities represents a decision variable, the problem is to determine the minimum
number of facilities whose location ensures the coverage of the overall demand (Set
Covering Location Problem) (Hakimi
1965
; Toregas et al.
1971
).
In the case of undesirable facilities, customers wish that facilities be located as
far away from them as possible and objectives may be defined accordingly. More
specifically, instead of minisum and minmax objectives used for desirable facility
problems, maxsum and maxmin objectives are usually employed to formulate
undesirable facilities location problems (Church and Garfinkel
1978
; Dasarathy and
White
1980
; Drezner and Wesolosky
1980
). However as the adoption in the model
of such objectives (maxsum, maxmin) can lead to very poor solutions from the
efficiency point of view, constraints regarding minimum levels of efficiency should
also be included.
Another class of interesting problems is based on the so called equality measures.
Either in the case of desirable or undesirable facilities, the decision maker may
be interested in finding solutions that assure a certain “fairness” in the access
to facilities. In order to describe this objective, various expressions have been
proposed, based on the minimization of measures related to the distribution of
distances between customers and facilities. Examples of such measures include the
variance, the mean absolute deviation or the Gini coefficient. For more details, see
Marsh and Schilling (
1994
) and Eiselt and Laporte (
1995
).
However, it should be underlined that locational decision problems in practice
can involve multiple, conflicting and incommensurate evaluation criteria and, in this
sense, they are multiobjective in nature. Hence, in order to tackle FLPs formulated
using multiple conflicting objectives, appropriate multiobjective techniques are
needed, some of which have been reviewed by Current et al. (
1990
) and Farahani
et al. (
2010
).
Depending on the combinations of the elements characterizing FLPs, a wide
range of mathematical models can be defined. Due to this variety, different classi-
fication schemes have been proposed in the literature such as the ones suggested
