The facility Location Problem considers a graph G=(N,A) where N is the set of nodes and A is the set of arcs. Capacities, bounds and costs may be associated with the nodes and arcs. In the practical optimization problem, the authors need to find a subset of nodes or facilities to serve a subset of demand nodes that minimize the sum of variable and fixed costs. In this paper, they focus on the Uncapacitated Location Problem in which facility capacities are disregarded. The authors present models, a survey and two algorithms. In the first one a set of p facilities are located. In the second, p is the maximum number of facilities in the solution. The authors propose a branch-and-bound algorithm based on the Lagrangean relaxation of the mixed integer model. Computational results show that the algorithms produce good solutions.
