The construction of smart homes under the infrastructure of smart grids (or micro grids) is currently one of the most important topics in the field of smart energy systems. Demand-side management confers many benefits on both users and utility companies. This paper proposes a novel scheduling procedure for power consumption in homes equipped with energy storage devices. The proposed optimal power scheduling method can reduce electricity bills and improve peak-to-average ratio (PAR) while taking into account the comfort of residents. Real-time pricing combined with an inclining block rate (IBR) tariff is used to prevent high power consumption at times of low cost, and to simultaneously improve the PAR index. Because erroneous determination of the state of the charge of storage systems can have deleterious effects on PAR, a revised formulation is therefore applied to attain the best solution of the problem. Home devices and batteries are modelled in a practical and efficient manner. The proposed multi-objective optimization problem is solved with non-dominated sorting genetic algorithm (NSGA-II) using MATLAB software. Then fuzzy decision is applied to obtain the most preferred solution.