New variations of the maximum coverage facility location problem

Abstract

Consider a competitive facility location scenario where, given a set U of n users and a set F of m facilities in the plane, the objective is to place a new facility in an appropriate place such that the number of users served by the new facility is maximized. Here users and facilities are considered as points in the plane, and each user takes service from its nearest facility, where the distance between a pair of points is measured in either L 1 or L 2 or L ∞ metric. This problem is also known as the maximum coverage (MaxCov) problem. In this paper, we will consider the k-MaxCov problem, where the objective is to place k (⩾1) new facilities such that the total number of users served by these k new facilities is maximized. We begin by proposing an O(nlogn) time algorithm for the k-MaxCov problem, when the existing facilities are all located on a single straight line and the new facilities are also restricted to lie on the same line. We then study the 2-MaxCov problem in the plane, and propose an O(n 2) time and space algorithm in the L 1 and L ∞ metrics. In the L 2 metric, we solve the 2-MaxCov problem in the plane in O(n 3 logn) time and O(n 2 logn) space. Finally, we consider the 2-Farthest-MaxCov problem, where a user is served by its farthest facility, and propose an algorithm that runs in O(nlogn) time, in all the three metrics.

On the complexity of the upgrading version of the maximal covering location problem

“…Similar results have been obtained for various location problems, including covering problems [10,24,25,33], center problems [44], median problems [1,35], or other facility location problems [27,29,34,38], as well as flow/shortest path problems [17,26,42].…”

Joint Distribution Center Location Problem for Restaurant Industry Based on Improved K-Means Algorithm With Penalty

“…To limit the influence of far-away receivers on the location of DC, the coverage radius was used as a criterion in the location selection model [37]. Bhattacharya and Nandy [38] raised that the coverage radius of facility could maximize the number of users it served. Miyagawa [39] calculated the maximum joint distribution distances between two facilities to analyze their location reliability.…”

A reconfiguration of fire station and fleet locations for the Santiago Fire Department

“…Murray and Wei (2013) propose an approach for eliminating error in the solution of the location set covering problem with respect to the spatial representation of the area under analysis. Bhattacharya and Nandy (2013) develop a O(nlogn) time algorithm for the maximum coverage problem for k facilities in one dimension. For two-dimensional case they study when k = 2 and propose a O(n 2 ) time and space algorithm in the L 1 and L ∞ metrics.…”