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Abstract
The objective in terms of the facility location problem with limited distances is to minimize the sum of distance functions from the facility to its clients, but with a limit on each of these distances, from which the corresponding function becomes constant. The problem is applicable in situations where the service provided by the facility is insensitive after given threshold distances. In this paper, we propose a polynomial-time algorithm for the discrete version of the problem with capacity constraints regarding the number of served clients. These constraints are relevant for introducing quality measures in facility location decision processes as well as for justifying the facility creation.
Highlights
Location Analysis is one of the most active fields in terms of Operations Research
The algorithm was tested for different scenarios by varying instance parameters that influence its performance, such as the number of candidate points, threshold distance values, and lower and upper bounds in the number of served points
We compared our algorithm within a grid search framework with the decomposition algorithm of Fernandes et al (2011)
Summary
Location Analysis is one of the most active fields in terms of Operations Research. It deals with the decision of optimally placing facilities in order to minimize operational costs (Nickel et Puerto, 2005). Drezner et al (1991) proposed a variation of the Weber problem to model location problems in which the service provided by the facility is insensitive after a threshold distance (directly related to a maximum time limit). To illustrate their model, let us use an example provided by Drezner et al (1991) to locate a fire station. The p-median problem (cf. Galvão, 1980; Mladenović et al, 2007) is a popular example of a discrete facility location model
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