A parallelized Lagrangean relaxation approach for the discrete ordered median problem

We study a flexible discrete location model which has as particular cases the p ‐median problem, the p ‐center problem and the k‐centrum problem, among many others, called the discrete ordered median problem. A previous formulation is adapted and a Lagrangean relaxation is carried out on this formulation in order to produce lower and upper bounds on the optimal value of the problem. The relaxed problem can be split into several subproblems whose resolution is simultaneously tackled by means of a parallelized algorithm. The results are compared to other methods proposed in the literature for this problem.