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.
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