This paper proposes a computationally efficient home energy management scheduler (HEMS) to minimize the cost of electricity consumption (CoEC) within a home which consists of rooftop photovoltaics (PV), a battery energy storage systems, and controllable appliances. Differential dynamic programming (DDP) algorithm is used and the uncertainty of PV generation and household demand along with the battery degradation is incorporated. The DDP algorithm divides the original problem space into several smaller subspaces and iteratively searches for a better solution within a subspace. The effectiveness of the developed framework is investigated through numerical simulations. The proposed HEMS minimizes the CoEC by determining an appropriate schedule of all devices ensuring an acceptable level for the customer comfort. The DPP-based HEMS is faster than the exact DP, approximate DP and mixed integer non-linear programming method. It is implemented in an intra-day setting where the BESS power is adjusted based on real-time observations of uncertain variable.