This paper presents the results of three control strategies of managed energy services with home energy management system (HEMS)-integrated devices. The HEMS controls and monitors three types of managed devices: 1) heating; 2) task-specific; and 3) energy storage devices. Three approaches are proposed for the rolling optimization by the HEMS, namely, mixed integer linear programming (MILP), continuous relaxation (CR), and fuzzy logic controller (FLC). The CR approach is identified to reduce the computational complexity of the MILP by changing the MILP into an LP solution. Three types of FLC control approaches are proposed, namely, heat-related FLC, task-related FLC, and FLC for the battery. Each control strategy is evaluated against cost optimization, computational resource, and practical implementation. The findings in this paper show that all three algorithmic control strategies successfully perform cost optimization, even with inaccurate forecasting information.