LP-based Approximation Algorithms for Capacitated Facility Location

TL;DR: In this article, the authors considered the capacitated facility location problem with hard capacities and proposed an approximation algorithm to minimize the sum of the facility opening costs and the client assignment costs.

Abstract: There has been a great deal of recent work on approximation algorithms for facility location problems [9]. We consider the capacitated facility location problem with hard capacities. We are given a set of facilities, \({\mathcal F}\), and a set of clients \({\mathcal D}\) in a common metric space. Each facility i has a facility opening costf i and capacityu i that specifies the maximum number of clients that may be assigned to this facility. We want to open some facilities from the set \({\mathcal F}\) and assign each client to an open facility so that at most u i clients are assigned to any open facility i. The cost of assigning client j to facility i is given by their distance c ij , and our goal is to minimize the sum of the facility opening costs and the client assignment costs.