This research investigates the production scheduling problems under maximum power consumption constraints. Probabilistic models are developed to model dispatching-dependent and stochastic machine energy consumption. A multi-objective scheduling algorithm called the energy-aware scheduling optimization method is proposed in this study to enhance both production and energy efficiency. The explicit consideration of the probabilistic energy consumption constraint and the following factors makes this work distinct from other existing studies in the literature: 1) dispatching-dependent energy consumption of machines, 2) stochastic energy consumption of machines, 3) parallel machines with different production rates and energy consumption pattern, and 4) maximum power consumption constraints. The proposed three-stage algorithm can quickly generate near-optimal solutions and outperforms other algorithms in terms of energy efficiency, makespan, and computation time. While minimizing the total energy consumption in the first and second stages, the proposed algorithm generates a detailed production schedule under the probabilistic constraint of peak energy consumption in the third stage. Numerical results show the superiority of the scheduling solution with regard to quality and computational time in real problems instances from manufacturing industry. While the scheduling solution is optimal in total energy consumption, the makespan is within 0.6 % of the optimal on average.