Smart homes have the potential to achieve optimal energy consumption with appropriate scheduling. It is expected that 35% of households in North America and 20% in Europe will be smart homes by 2020. The control of smart appliances can be based on optimization models, which are desirable to be realist and efficient. However, from the optimization perspective, sometimes increasing realism implies a decrease in efficiency. One should make a trade-off between realism and complexity. Many of the optimization models in the literature have limitations on the types of appliances considered and/or their reliability. This paper proposes an Home Energy Management scheduling model that is accurate and efficient from the optimization perspective. Our model is an extensive appliance integrated mixed integer linear optimization model that minimizes the energy cost while keeping a given level of user comfort. Our main contribution is not only the variety of specific and accurate appliances models considered, but also their integration into a single optimization model. We consider the use of energy in appliances and electric vehicles (EV) and take into account renewable local generation, batteries, and demand-response. We propose models of a shower, a fridge and a hybrid EV that considers both the electricity consumption and the conventional fuel cost. We present computational results to validate the model and indicate how it overcomes the limitations of other models in the literature. For the instances considered in Brazil, our model gives results that, compared to the closest models in the literature, provide a cost savings in the range of 8% and 389% over a horizon of 24 hours.