In this work, an algorithm for the scheduling of household appliances to reduce the energy cost and the peak-power consumption is proposed. The system architecture of a home energy management system (HEMS) is presented to operate the appliances. The dynamics of thermal and non-thermal appliances is represented into state-space model to formulate the scheduling task into a mixed-integer-linear-programming (MILP) optimization problem. Model predictive control (MPC) strategy is used to operate the appliances in real-time. The HEMS schedules the appliances in a dynamic manner without any a priori knowledge of the load-consumption pattern. At the same time, HEMS responds to the real-time electricity market and the external environmental conditions (solar radiation, ambient temperature etc). Simulation results exhibit the benefits of proposed HEMS by showing the reduction of up to 47% in electricity cost and up to 48% in peak power consumption.