In this study, the incremental hierarchical covering location models are presented over a multi-period planning horizon. The purpose of these models is maximizing the covering on demand locations considering the available facilities. To take into account the dynamism in modeling of the problem, the programming horizon is divided into smaller periods. The difference in the programming periods is a new capability considered in these kinds of location modeling. The available facilities in the presented models have an operation variety and the relation between them is hierarchical. Therefore the suggested model is introduced in several levels. The limitation in moving the facilities among the periods is at first concerned as the maximum number of allowed movements and afterwards this limitation and others related to the amount of available facilities are converted into budgeting limitations. Changing the target equation of the problem to the sum of costs, related to installing the facilities, had a considerable improvement on the optimum value of the target equation. A method, beyond the innovation and based on genetic algorithms is provided in order to solve the suggested model and is tested by some examples. The numeral results have demonstrated the better efficiency of the suggested model comparing to CPLEX software in relatively large samples concerning both the time of solving and the optimum of responses. Finally, the suggested models were used in locating the maintenance centers of the stations which supply compact natural gas consumed by gas-engine automobiles in Iran and analyzing the influence of the covering necessity of all the demand locations in the new programming horizon and the new limitations in covering stability on the models output.