Driven by the advancement of smart electrical grid technologies, automated home energy management systems are being increasingly and extensively studied, developed, and widely accepted. A system like this is indispensable for and symbolic of a smart home. Mixed integer linear programming (MILP) together with dynamic electricity tariff and smart home appliances is a common way to developing energy management systems capable of automatically scheduling appliance operation and greatly saving monetary cost. This study transformed an existing plain MILP model to a goal programming model with priority to better address the conflict among each single appliance cost saving objective and user time preference objective. Constraints regarding the delays between pairs of closely related appliances are either extended or newly introduced. Numerical experiments on five appliances under different situations justify the validness of the proposed framework. Besides, the influences of key parameters on model performance are also investigated.