Abstract Location-Routing problems involve locating a number of facilities among candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. A special case of these problems is Hamiltonian p Median Problem (HpMP). In attempting to solve this problem, numerous mathematical formulations have been proposed. Most of them have in common t...

By means of a model based on a set covering formulation, it is shown how the p-Median Problem can be solved with just a column generation approach, which is embedded in a branch-and-bound framework based on dynamic reliability branching. This method is more than competitive in terms of computational times and size of the instances which have been optimally solved. In particular, problems of siz...

This paper advocates the use of the bionomic algorithm, a recently proposed metaheuristic technique, as an effective method to solve capacitated p-median problems (CPMP). Bionomic algorithms already proved to be an effective framework for finding good solutions to combinatorial optimization problems, when good local optimization algorithms are available. The paper also presents an effective loc...

In this paper three recurrent neural network algorithms are proposed for the p-median problem according to different techniques. The competitive recurrent neural network, based on two types of decision variables (location variables and allocation variables), consists of a single layer of 2Np process units (neurons), where N is the number of demand points or customers and p is the number of faci...

Given an edge-weighted graph G = (V, E), the Hamiltonian p-median problem (HpMP) asks for determining p cycles in G whose total length is minimized such that each node is contained in exactly one cycle. As the travelling salesman problem (TSP) corresponds to the choice p = 1, the HpMP can be interpreted as a generalization of the TSP. In this paper, we study the polytope associated with the HpM...

Capacitated p-median problem (CPMP) is an important variation of facility location problem in which p capacitated medians are economically selected to serve a set of demand vertices so that the total assigned demand to each of the candidate medians must not exceed its capacity. The classical CPMP uses a network in a Euclidean plane such that distance between any two points in the network is the...

Facility-location problems have several applications in telecommunications, industrial transportation and distribution, etc. One of the most well-known facility-location problems is the p-median problem. This work addresses an application of the capacitated p-median problem to a real-world problem. We propose a genetic algorithm (GA) to solve the capacitated pmedian problem. The proposed GA use...

We further study the effect of odd cycle inequalities in the description of the polytopes associated with the p-median and uncapacitated facility location problems. We show that the obvious integer linear programming formulation together with the odd cycle inequalities completely describe these polytopes for the class of restricted Y-graphs. This extends our results for the class of Y-free grap...

The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of possible locations, in such a way that the sum of the distances between each customer and its nearest facility is maximized. The problem is NP-hard and can be formulated as an integer linear program. It was introduced in the 1990s, and a branch and cut method coupled with a tabu search has been rec...