We consider the queueing maximal covering location-allocation problem (QM-CLAP) with an M/M/1 queueing system. We propose a new solution procedure based on decomposition of the problem into smaller sub-problems. We solve the resulting sub-problems both with a branch and bound algorithm and with the meta-heuristic GRASP. We also solve the entire model with GRASP. Computational results for these approaches are compared with the solutions obtained by CPLEX. Results show that using the new procedure in which sub-problems were solved with Branch and bound is better.