Most of the publications regarding the maximal covering location problem (MCLP) address the case where the decision is to be made for one period. In this paper, we deal with a rather untouched version of MCLP which is called dynamic MCLP (DMCLP). In order to solve this problem, a simulated annealing (SA) has been presented. The proposed solution algorithm is capable of solving problems with up to 2500 demand nodes and 200 potential facilities with a fair amount of exactness. Our experiments showed that the proposed approach finds solutions with errors less than one percent.