The hierarchical hub covering facility location problems are applied to distribution systems, transportation, waste disposal, treatment services, emergency services and remote communication. The problems attempt to determine the location of service providers' facilities at different levels and specify their linking directions in order to reduce costs and to establish an appropriate condition in distribution network. By utilizing these problems, the present paper attempts to allocate "capacitated" option to each provider service and consequently establish and choose the best possible condition, so that demands centers are rationally and effectively guided by service providers' centers and their request never remains without response.To do this, the model "the capacitated single allocation hierarchical hub median location problem" is developed, created and provided. In addition, considering increasing demand, modulating choices are addressed in order to fulfill the future needs and to impose uncertainty in decision making in the results. To validate the model, we used IAD data, which the results confirm its consistency.
