This paper proposes a Predictive Dispatch System (PDS) as part of a Multi-Agent system that models the Smart Home Electricity System (MASHES). The proposed PDS consists of a Decision-Making System (DMS) and a Prediction Engine (PE). The considered Smart Home Electricity System (SHES) consists of different agents, each with different tasks in the system. A Modified Stochastic Predicted Bands (MSPB) interval optimization method is used to model the uncertainty in the Home Energy Management (HEM) problem. Moreover, the proposed method to solve HEM problem is based on the Moving Window Algorithm (MWA). The performance of the proposed Home Energy Management System (HEMS) is evaluated using a JADE implementation of the MASHES.