With the recent development of advanced metering infrastructure, real-time pricing (RTP) scheme is anticipated to be introduced in future retail electricity market. This paper proposes an algorithm for a home energy management scheduler (HEMS) to reduce the cost of energy consumption using RTP. The proposed algorithm works in three subsequent phases namely real-time monitoring (RTM), stochastic scheduling (STS) and real-time control (RTC). In RTM phase, characteristics of available controllable appliances are monitored in real-time and stored in HEMS. In STS phase, HEMS computes an optimal policy using stochastic dynamic programming (SDP) to select a set of appliances to be controlled with an objective of the total cost of energy consumption in a house. Finally, in RTC phase, HEMS initiates the control of the selected appliances. The proposed HEMS is unique as it intrinsically considers uncertainties in RTP and power consumption pattern of various appliances. In RTM phase, appliances are categorized according to their characteristics to ease the control process, thereby minimizing the number of control commands issued by HEMS. Simulation results validate the proposed method for HEMS.