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Household Demand Side Management (DSM) systems play a key role in improving the efficiency of the entire electrical system. An efficient management of the energy resources can indeed allow spreading domestic energy loads in a smart way in order to reduce the peak power of the overall demand. To achieve this goal, home appliances and energy storage systems have to be controlled through the definition of energy plans for future periods (offline) and the real time control of energy resources (online). In this paper, we propose an optimization model and a set of heuristics for the online demand side management, to properly react in real time to events which were unexpected in a previous offline stage of the home management system, such as wrong weather forecasts or user's misbehaviours. The final goal is to reschedule the energy consumption and production coherently with the energy plan defined in the offline phase, taking into account the real production of renewable energy sources and the capacity of storage devices. Along with the heuristics, we show the numerical results obtained by applying them on realistic instances of the problem.