Home energy management (HEM) is one of the crucial requirements for future smart grid environment. Usually, utility companies motivate residential consumers to participate in household demand side management (DSM) techniques. The residential consumers’ main intention is to reduce their electricity bills whereas utilities’ primary goal is to reduce their system peak load demand. The benefits of DSM can be enhanced with smart energy storage systems. In this paper, an intelligent multi-objective household DSM with battery storage systems is proposed to minimize both the objectives simultaneously. Generally, the residential DSM deals with various controllable appliances that normally have different operating time priorities according to the consumers’ preferences. Because of this, the DSM problem is modelled as a mixed integer optimization problem. In this paper, the multi-objective mixed integer linear programming technique (MOMILP) is used to solve the proposed residential DSM problem. The proposed model is tested on a system having four different residential consumers. The benefits of the battery energy storage systems are analysed by taking six different scenarios. An economic analysis of each residential consumer's battery storage system with load uncertainty modelling is also done in this paper. Simulation results of various scenarios with different objectives demonstrate the effectiveness of the proposed model.