Demand side management (DSM) is an important application of the future smart grid. DSM programs allow consumers to participate in the operation of the electric grid by reducing or shifting their electricity usage during peak periods. Therefore, in this paper, we propose a two-tier cloud-based DSM to control the residential load of customers equipped with local power generation and storage facilities as auxiliary sources of energy. We consider a power system consisting of multiple regions and equipped with a number of microgrids. In each region, an edge cloud is utilized to find the optimal power consumption schedule for customer appliances in that region. We propose a two-level optimization algorithm with a linear multilevel cost function. At the edge cloud, the power consumption level of local storage and the amount of power being demanded from both local storage facilities and power grid are scheduled by using a bi-level optimization approach. The core cloud then gathers information of the total demand from consumers in different Regions and finds the optimal power consumption schedule for each microgrid in the power system. Simulation results show that the proposed model reduces consumption cost for the customers and improves the power grid in terms of peak load and peak-to-average load ratio.