Smart homes have the potential to achieve optimal energy consumption with appropriate scheduling. The control of smart appliances can be based on optimization models, which should be realistic and efficient. However, increased realism also implies an increase in solution time. Many of the optimization models in the literature have limitations on the types of appliances considered and/or their reliability. This paper proposes a home energy management scheduling model that is more realistic and efficient. We develop a mixed integer linear optimization model that minimizes the energy cost while maintaining a given level of user comfort. Our main contribution is the variety of specific appliance models considered and their integration into a single model. We consider the use of energy in appliances and electric vehicles (EVs) and take into account renewable local generation, batteries, and demand response. Our models of a shower, a fridge, and a hybrid EV consider 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. Our results, compared with the best competitors, provide cost savings ranging from 8% to 389% over a horizon of 24 hours.