On the capacitated concentrator location problem: a reformulation by discretization

In this paper, we present and discuss a discretized model for the two versions of the capacitated concentrator location problem: a simple version (SCCLP) and a version with modular capacities (MCCLP). We show that the linear programming relaxation of the discretized model is at least as good as the linear programming relaxation of conventional models for the two variations of the problem under study. A technique for deriving valid inequalities from the equations of the discretized model is also given. We will show that this technique provides inequalities that significantly enhance the linear programming bound of the discretized model. Our computational results show the advantage of the new models for obtaining the optimal integer solution for the two versions of the problem.