This study proposes a stochastic optimisation model for the day-ahead scheduling in power systems, which incorporates the hourly demand response (DR) for managing the variability of renewable energy sources (RES). DR considers physical and operating constraints of the hourly demand for economic and reliability responses. The proposed stochastic day-ahead scheduling algorithm considers random outages of system components and forecast errors for hourly loads and RES. The Monte Carlo simulation is applied to create stochastic security-constrained unit commitment (SCUC) scenarios for the day-ahead scheduling. A general-purpose mixed-integer linear problem software is employed to solve the stochastic SCUC problem. The numerical results demonstrate the benefits of applying DR to the proposed day-ahead scheduling with variable RES.