The energy-aware scheduling problem is a multi-objective optimization problem where the main goal is to achieve energy savings without affecting productivity in a manufacturing system. In this work, we present an approach for energy-aware flow shop scheduling problem and energy-aware job shop scheduling problem considering the process speed as the main energy-related decision variable. This approach allows one to set the appropriate process speed for every considered operation in the corresponding machine. When the speed is high, the processing time is short but the energy demand increases, and vice versa. Therefore, two objectives are worked together: a production objective, paired with an energy efficiency objective. A generic elitist multi-objective genetic algorithm was implemented to solve both problems. Results from a simple comparative design of experiments and a nonparametric test show that it is possible to smooth the energy demand profile and obtain reductions that average 19.8% in energy consumption. This helps to reduce peak loads and drops on applied energy sources demand, stabilizing the conversion units operational efficiency across the entire operational time with a minimum effect on the production maximum completion time (makespan).