With an increasing use of distributed energy resources and intelligence in the electricity infrastructure, the possibilities for minimizing costs of household energy consumption increase. Technology is moving toward a situation in which households manage their own energy generation and consumption, possibly in cooperation with each other. As a first step, in this paper a decentralized controller based on model predictive control is proposed. For an individual household using a micro combined heat and power (μCHP) plant in combination with heat and electricity storages the controller determines what the actions are that minimize the operational costs of fulfilling residential electricity and heat requirements subject to operational constraints. Simulation studies illustrate the performance of the proposed control scheme, which is substantially more cost effective compared with a control approach that does not include predictions on the system it controls.