In this paper we address the optimal sizing and scheduling of isolated hybrid systems using an optimization framework. The hybrid system features wind and photovoltaic conversion systems, batteries and diesel backup generators to supply electricity demand. A Mixed-Integer Linear Programming formulation is used to model system behavior over a time horizon of one year, considering hourly changes in both the availability of renewable resources and energy demand. The optimal solution is achieved with respect to the minimization of the levelized cost of energy (LCOE) over a lifetime of 20 years. Results for a case study show that the most economical solution features all four postulated subsystems.