New variations of the maximum coverage facility location problem

Bhaswar B. Bhattacharya and Subhas C. Nandy

European Journal of Operational Research, 2013, vol. 224, issue 3, 477-485

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 L1 or L2 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(n2) time and space algorithm in the L1 and L∞ metrics. In the L2 metric, we solve the 2-MaxCov problem in the plane in O(n3logn) time and O(n2logn) 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.

Keywords: Reverse nearest neighbor; Competitive location; Computational geometry; Facility location (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221712006091
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:224:y:2013:i:3:p:477-485

DOI: 10.1016/j.ejor.2012.08.009

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().