This work proposes a discrete-time Mixed Integer Linear Programming (MILP) formulation based on a combined rolling horizon and stochastic programming approach for the simultaneous management of energy supply and demand in microgrids, considering flexible demand profiles, which allows delays in the nominal energy demands by applying penalty costs. This mathematical formulation uses a scenario-based stochastic programming approach, which considers different scenarios associated to internal variations in the duration of the energy consumptions, to contemplate all possible scenarios related to the energy demand. However, the high complexity related the estimate the weather forecast with a high degree of precision makes unaffordable the consideration of all possible external scenarios, thereby updating input data is needed to ensure the adequate quality in the obtained results. Hence, the proactive MILP stochastic programming formulation is introduced into a rolling horizon approach.