In this work, two novel mixed-integer linear programming models for energy efficient scheduling of flexible job-shops with simultaneous consideration of machine switching off-on strategy are developed. While the first model is based on the unit-specific event-based approach, the other one uses the sequence-based approach. The computational results demonstrate that the proposed models, especially the unit-specific event-based model, are more robust and efficient than the existing models. To solve industrial-scale problems efficiently, a hybrid algorithm is developed through the combination of the existing eGEP algorithm and mathematical programming approach. The hybrid algorithm leads to up to 15 % more energy savings in comparison to the eGEP algorithm.