The metric capacitated facility location is a well-studied problem for which, while constant factor approximations are known, no efficient relaxation with constant integrality gap is known. The question whether there is such a relaxation is among the most important open problems of approximation algorithms [14]. In this paper we show that, if one is restricted to linear programs that use the na...

Metric uncapacitated facility location is a well-studied problem for which linear programming methods have been used with great success in deriving approximation algorithms. Capacitated facility location (Cfl) is a generalization for which there are local-search-based constant-factor approximations, while there is no known compact relaxation with constant integrality gap. This paper produces, t...

In a surprising result, Korupolu, Plaxton, and Rajaraman [13] showed that a simple local search heuristic for the capacitated facility location problem (CFLP) in which the service costs obey the triangle inequality produces a solution in polynomial time which is within a factor of 8+ ǫ of the value of an optimal solution. By simplifying their analysis, we are able to show that the same heuristi...

We consider a generalization of the Connected Facility Location problem (ConFL), suitable to model real world network extension scenarios such as fiber-tothe-curb. In addition to choosing a set of facilities and connecting them by a Steiner tree as in ConFL, we aim to maximize the resulting profit by potentially supplying only a subset of all customers. Furthermore, capacity constraints on pote...

The Capacitated Connected Facility Location Problem (CConFL) is an NPhard combinatorial optimization problem which arises in the design of last mile communication networks (fiber-to-the-curb scenarios) [1]. Formally, we are given an undirected, weighted graph G = (V,E), with edge costs ce ≥ 0, ∀e ∈ E. The node set V = {r}∪F ∪T is the disjoint union of the root node r, potential facility locatio...

The Capacitated Facility Location Problem (CFLP) consists of locating a set of facilities with capacity constraints to satisfy the demands of a set of clients at the minimum cost. In this paper we propose a simple and effective heuristic for largescale instances of CFLP. The heuristic is based on a Lagrangean relaxation which is used to select a subset of “promising” variables forming the core ...

Recently studies in area of supply chain network (SCN) have focused on the disruption issues in distribution systems. Also this paper extends the previous literature by providing a new biobjective model for cost minimization of designing a three echelon SCN across normal and failure scenarios with considering multi capacity option for manufacturers and distribution centers. Moreover, in order t...

In this paper we initiate the study of the heterogeneous capacitated k-center problem: given a metric space X = (F ∪C, d), and a collection of capacities. The goal is to open each capacity at a unique facility location in F , and also to assign clients to facilities so that the number of clients assigned to any facility is at most the capacity installed; the objective is then to minimize the ma...

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network.

Consider a graph G = (V,E). At the vertices of G there are consumers of some product and the possible places of its production. For each vertex i in V the demand volume b(i), the cost f(i) for opening a facility and the restriction a(i) on the facility’s capacity are given. For each edge e in E, there are given the cost of the transportation of the product unit ce and the maximum quantity qe of...