This article covers a case study with homes equipped with multiple appliances for energy consumption. The central goal is to provide for aggregators’ flexibility in distribution networks by building an optimal schedule that takes advantage of load flexibility resources. This, in turn, allows for the re-scheduling of shifting/real-time home appliances to provision a request from a distribution system operator (DSO). The paper concludes with the consideration of the CBCC-RDG3, HyDE-DF, and genetic algorithms, which were used to find the best schedule that would be highly efficient and meet all the constraints associated with the problem that successfully demonstrate the effectiveness of this particular approach.