This paper details a proposed demand response (DR) application to optimize the operation of appliances in an indeterminate environment in a home energy management system. An indeterminate environment results from forecasted errors of electricity prices and system loads, so a probabilistic analysis of the system performance is of significant interest. Herein, a chance constrained optimization-based model is formulated to accommodate these uncertainties. The resulting DR application can be easily embedded in resource limited electric devices. To reduce the computational cost, both improved particle swarm optimization (PSO) and a two-point estimate method are presented to solve the chance constrained problem. The improved PSO is used to provide the optimum solution, while the probabilistic assessment of uncertainties is estimated using a two-point estimate method. Numerical comparisons were made to justify the effectiveness of the method. The simulated results obtained using the models indicate that the proposed method can significantly reduce the computational burden while maintaining a high level of accuracy.