Abstract In the context of increasing decentralization of the energy supply system, the concepts of microgrids are well suited to realise a reduction of CO2-emissions and create opportunities for new business models. For this the operation of the microgrid has a significant impact. In real systems, however, the consideration of uncertainties in generation and consumption data is essential for the operating strategy. Therefore, in this paper we propose an optimization model based on mixed-integer linear programming for the hybrid microgrid of a residential building district and include stochastic optimization in a computationally efficient way. For this, a two-stage approach is used. In a first step, we do a day-ahead optimization to determine a schedule for the combined heat and power plant and the power exchanged with the grid. In a second step, based on the results of the day-ahead optimization and the observed values for the uncertain parameters the intraday optimization is carried out. Using a numerical example, we demonstrate the advantages of this stochastic optimization over conventional optimization based on point forecasts. The data used originates from a real project district in Darmstadt, Germany.