Household Electric Water Heater (HEWH) is one of the most important services in a home. It is significant to study the household electric water heater load scheduling based on demand response in real time pricing tariffs. At first, a type of first-order explicit equation is utilized to describe the thermal dynamic modes of the HEWH. Under such a background, the HEWH load scheduling is addressed using linear integer programming. Then, the energy costs of different indistinctive adjusting schemes of comfort zone are discussed. For comparison's sake, the selective adjusting schemes with synthetic weight ranking method based on multi-dimensional information are also analyzed. Simulation results indicate that adjusting the upper and lower bounds of comfort zone is useful to reduce the energy cost. Moreover, the proposed synthetic weight ranking method based on multi-dimensional information is able to obtain well economic benefit through adjusting just a small part of comfort zone. This work is supported by National Key Research and Development Program of China (No. 2017YFB0902902).