An interval number optimization method is proposed in this paper to tackle the household load scheduling problem with uncertain hot water demand and ambient temperature. The household loads considered include residential thermostatically controlled loads such as electric water heater and air conditioner, and interruptible loads such as clothes washer and pool pump. The uncertain-but-bounded parameters are modelled as interval numbers, based on which the uncertain load scheduling problem is formulated and transformed. A binary particle swarm optimization combined with integer linear programming is introduced to solve the transformed problem. Two schemes, named cost scheme and trade-off scheme, are contrastively discussed to study the economic impacts of different tolerance degrees for constraint violation. Simulation results demonstrate that the proposed method is flexible to different consumer demands and robust to the uncertainties. (C) 2016 Elsevier B.V. All rights reserved.