The p-cover problem
type: Item
instance of: scholarly article
title: The p-cover problem
zbMATH Open document ID: 0597.90028
DOI: 10.1016/0377-2217(86)90196-7
author: Zvi Drezner
published in: European Journal of Operational Research
publication date: 1986-01-01T00:00:00Z
review text: The p-cover problem deals with covering the most buying power with p new facilities. Each facility covers an area of a certain shape and size. When distances are rectilinear then the area covered by a facility has a shape of a diamond (a square rotated by \(45^ o)\). It is suggested to rotate the area by \(45^ o\), and thus each facility covers a square parallel to the axes. The data about the buying power is therefore given as a matrix where every entry in the matrix represents one basic square in a grid. Each facility covers a square that consists of k by k basic squares. K is determined by the size of the area of influence of the facility and the size of the basic square. The 1-cover problem is converted to selecting the k by k submatrix with the maximal sum of entries. If the area of influence is a rectangle of m by n basic squares, the problem is solved in o(mn) time. The p-cover problem for \(p>1\) is also discussed.
Mathematics Subject Classification ID: 90B05
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 05A05
zbMATH DE Number: 3963534
zbMATH Keywords: facility location
zbMATH Keywords: marketing
zbMATH Keywords: p-cover problem
zbMATH Keywords: buying power
MaRDI profile type: Publication
full work available at URL: 0377-2217(86)90196-7
OpenAlex ID: W2072766265
cites work: Note—On a Modified One-Center Model
cites work: The p-Centre Problem-Heuristic and Optimal Algorithms
cites work: On locating new facilities in a competitive environment
cites work: Heuristic procedures for the m-partial cover problem on a plane
description: scientific article; zbMATH DE number 3963534