In this paper, we propose a robust approach for scheduling of smart appliances and electrical energy storages (EESs) in active apartments with the aim of reducing both the electricity bill and the CO₂ emissions. The proposed robust formulation takes the user behavior uncertainty into account so that the optimal appliances schedule is less sensitive to unpredictable changes in user preferences. The user behavior uncertainty is modeled as uncertainty in the cost function coefficients. In order to reduce the level of conservativeness of the robust solution, we introduce a parameter allowing to achieve a trade-off between the price of robustness and the protection against uncertainty. Mathematically, the robust scheduling problem is posed as a multi-objective Mixed Integer Linear Programming (MILP), which is solved by using standard algorithms. The numerical results show effectiveness of the proposed approach to increase both the electricity bill and CO₂ emissions savings, in the presence of user behavior uncertainties. Mathematical insights into the robust formulation are illustrated and the sensitivity of the optimum cost in the presence of uncertainties is investigated. Although home appliances and EESs are considered in this work, we point out that the proposed scheduling framework is generally applicable to many use cases, e.g., charging and discharging of electrical vehicles in an effective way. In addition, it is applicable to various scenarios considering different uncertainty sources, different storage technologies and generic programmable electrical loads, as well as different optimization criteria.