In the pursuit of sustainable energy solutions, Energy Hubs (EH) emerge as pivotal systems integrating diverse energy carriers. This paper introduces a novel short-term model for EH, incorporating Hydrogen Energy (HE) and Renewable Energy Sources (RES). Employing an advanced approach, the Information Gap Decision Theory (IGDT), we address uncertainties in electricity demand, real-time market prices, and wind farm energy production. The model optimizes EH operations, leveraging flexible Demand Response Programs (DRP) to shift demand to cost-effective off-peak hours. In contrast to conventional IGDT models, our method considers the magnitude intensity of uncertainty for each parameter, resulting in precise and tailored uncertainty management. The dynamic interplay of EH components – Combined Heat and Power (CHP) units, Diesel Generators (DG), and Hydrogen Storage Systems (HSS) – is orchestrated to maximize efficiency and cost-effectiveness. The system adapts to uncertainties, with DRP enhancing HSS performance during off-peak hours. Our main achievement lies in the robustness of uncertainty management, ensuring optimal EH performance under varying conditions. Applying the DRP in the system reduces costs by approximately 5.4%, showcasing the economic benefits of our approach. This result, coupled with enhanced reliability and adaptability, positions our model as a pioneering strategic and forward-thinking solution for industrial stakeholders navigating the complexities of energy systems.