One-way and round-trip center location problems (original) (raw)
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The single facility location problem with minimum distance constraints
Location Science, 1997
We consider the problem of locating a single facility (server) in the plane, where the location of the facility is restricted to be outside a specified forbidden region (neighborhood) around each demand point. Two models are discussed. In the restricted l-median model, the objective is to minimize the sum of the weighted rectilinear distances from the n customers to the facility. We present an O(n log n) algorithm for this model, improving upon the O(n") complexity bound of the algorithm by Brimberg and Wesolowsky (1995). In the restricted l-center model the objective is to minimize the maximum of the weighted rectilinear distances between the customers and the serving facility. We present an O(n logn) algorithm for finding an optimal i-center. We also discuss some related models, involving the Euclidean norm.
Location-Routing Problems with Distance Constraints
Transportation Science, 2007
An important aspect of designing a distribution system is determining the locations of the facilities. For systems in which deliveries are made along multiple stop routes, the routing problem and location problem must be considered simultaneously. In this paper, a set-partitioning-based formulation of an uncapacitated location-routing model with distance constraints is presented. An alternate set of constraints is identified that significantly reduces the total number of constraints and dramatically improves the linear programming relaxation bound. A branch and price algorithm is developed to solve instances of the model. The algorithm provides optimal solutions in reasonable computation time for problems involving as many as 10 candidate facilities and 100 customers with various distance constraints.
Journal of the ACM, 1984
A general technique is described for solving certain NP-hard graph problems in time that is exponential in a parameter k defined as the maximum, over all nonseparable components C of the graph, of the number of edges that must be added to a tree to produce C; for a connected graph, k is no more than the number of edges of the graph minus the number of vertices plus one. The technique is illustrated in detail for the following facility location problem: Given a connected graph G(V, E) such that each edge has an associated positive integer length and given a positive integer r, place the minimum number of centers on points of the graph such that every point of the graph is within distance r from some center (a "point" is either a vertex or a point on some edge). An algorithm of time complexity O(I El. (6r) rkm) is given. A parallel implementation of the algorithm, with optimal speedup over the sequential version for a fairly wide range for the number of processors, is presented.
The collection depots location problem on networks
Naval Research Logistics, 2002
In this paper we investigate the collection depots location problem on a network. A facility needs to be located to serve a set of customers. Each service consists of a trip to the customer, collecting materials, dropping the materials at one of the available collection depots and returning to the facility to wait for the next call. Two objectives are considered: minimizing the weighted sum of distances and minimizing the maximum distance. The properties of the solutions to these problems are described.
The k-centrum multi-facility location problem
Discrete Applied Mathematics, 2001
The most common problems studied in network location theory are the p-center and the p-median problems. In the p-center problem the objective is to locate p service facilities to minimize the maximum of the service distances of the n customers to their respective nearest service facility, and in the p-median model the objective is to minimize the sum of these n service distances. (A customer is served only by the closest facility.) We study the p-facility k-centrum model that generalizes and uniÿes the above problems. The objective of this unifying model is to minimize the sum of the k largest service distances. The p-center and the p-median problems correspond to the cases where k = 1 and n, respectively. We present polynomial time algorithms for solving the p-facility k-centrum problem on path and tree graphs. These algorithms can be combined with the general approximation algorithms of Bartal (Proceedings of the 30th Annual ACM Symposium on Theory of Computing, 1998, pp. 161-168) and Charikar et al. (Proceedings of the 30th Annual ACM Symposium on Theory of Computing, 1998, pp. 114-123) to obtain an O(log n log log n) approximation for a p-facility k-centrum problem deÿned on a general network.
Approximation Algorithms for Single and Multi-Commodity Connected Facility Location
Lecture Notes in Computer Science, 2011
In the classical facility location problem we are given a set of facilities, with associated opening costs, and a set of clients. The goal is to open a subset of facilities, and to connect each client to the closest open facility, so that the total connection and opening cost is minimized. In some applications, however, open facilities need to be connected via an infrastructure. Furthermore, connecting two facilities among them is typically more expensive than connecting a client to a facility (for a given path length). This scenario motivated the study of the connected facility location problem (CFL). Here we are also given a parameter M ≥ 1. A feasible solution consists of a subset of open facilities and a Steiner tree connecting them. The cost of the solution is now the opening cost, plus the connection cost, plus M times the cost of the Steiner tree. In this paper we investigate the approximability of CFL and related problems. More precisely, we achieve the following results:
Single facility collection depots location problem in the plane
Computational Geometry, 2009
In this paper we consider an extension of the classical facility location problem where besides n weighted customers, a set of p collection depots are also given. In this setting the service of a customer consists of the travel of a server to the customer and return back to the center via a collection depot. We have analyzed the problem and showed that the collection depots problem using the Euclidean metric can be transformed to O (p 2 n 2) number of different classical facility location problems and this bound is tight. We then show the existence of small coresets for these problems. These coresets are then used to provide (1 +)-factor approximation algorithms which have linear running times for fixed customer weights and .
Facility Location with Tree Topology and Radial Distance Constraints
Complexity
Let Gd=V,Ed be an input disk graph with a set of facility nodes V and a set of edges Ed connecting facilities in V. In this paper, we minimize the total connection cost distances between a set of customers and a subset of facility nodes S⊆V and among facilities in S, subject to the condition that nodes in S simultaneously form a spanning tree and an independent set according to graphs G¯d and Gd, respectively, where G¯d is the complement of Gd. Four compact polynomial formulations are proposed based on classical and set covering p-Median formulations. However, the tree to be formed with S is modelled with Miller–Tucker–Zemlin (MTZ) and path orienteering constraints. Example domains where the proposed models can be applied include complex wireless and wired network communications, warehouse facility location, electrical power systems, water supply networks, and transportation networks, to name a few. The proposed models are further strengthened with clique valid inequalities which ca...
Brazilian Journal of Operations & Production Management, 2017
The objective in terms of the facility location problem with limited distances is to minimize the sum of distance functions from the facility to its clients, but with a limit on each of these distances, from which the corresponding function becomes constant. The problem is applicable in situations where the service provided by the facility is insensitive after given threshold distances. In this paper, we propose a polynomial-time algorithm for the discrete version of the problem with capacity constraints regarding the number of served clients. These constraints are relevant for introducing quality measures in facility location decision processes as well as for justifying the facility creation.