The residential energy management system is an essential factor in the smart grid environment, which allows the implementation of demand response program among the residential consumers to manage their power usage aiming to reduce the electricity expenses. In this paper, an energy management model is proposed by considering both generation and consumption parts. Mathematical models for the grid, renewable energy resources, batteries, and electric vehicles are presented, as well as for different type of thermal and electrical appliances such as air conditioning, water heater, vacuum cleaner, and others. We have implemented an exact solution method to solve the objective constrained problem that aims to minimize the electricity cost in a smart home and find out operation modes of different loads with organizing between the considered production systems. Furthermore, a math-heuristic optimization algorithm based on mixed integer linear programming formulation is proposed to solve the problem with extended simulation time horizon. The considered mathematical model has been solved with different scenarios where results have indicated a significant reduction of the electricity cost and have illustrated the efficiency of the proposed robust optimization algorithm.