High energy demand in corporate and/or public buildings is nowadays one of the main reasons of excessive energy consumption. At the same time, electric vehicles (EVs) have become very popular worldwide being a considerable alternative power source when parked. In this work we propose a scheduling mechanism which optimizes the control of the charging-discharging schedule of an altered but finite number of EVs arriving at a university building for a typical load-day in February aiming at the minimization of the energy demand and the electricity cost of the building. In the aforementioned framework, a parallel operation of a small sized gas turbine generator (GGT) is considered. To this end, a mixed integer linear programing (MILP) model containing binary and continuous variables has been developed to optimize the control process and minimize energy cost. Results showed that the use of the EVs as an alternative energy source can significantly contribute to the reduction of the building's energy demand leading to important cost decrease. The exploitation of the energy produced by the GGT further contributed to the minimization of the total energy consumption of the building and the total electricity cost.