International audienceThis paper presents and demonstrates, by numerical simulation, a mixed-integer linear programming (MILP)-based Model Predictive Control (MPC) strategy for space-heating demand in buildings connected to a district heating system. The proposed MPC deals with space-heating demand with extended flexibility. It exploits thermal inertia, inherently present in the building and its heating system, to optimally plan space-heating load in anticipation of weather conditions and energy cost variations. MPC is based on a reliable Reduced-Order Model (ROM). Heating circuit and internal mass are carefully modelled within the ROM structure since these elements can be used for short-term heat storage and therefore play an important rol...