Variation of Production Line Energy Consumption: Stochastic Process Models for Single and Multiple Machine Systems

The energy consumption of production lines can vary across different machines due to diverse factors such as varying processing rates, machine conditions, product characteristics, and the compatibility between products and machines. Additionally, identical products on the same type of machine may experience temporal variations in energy consumption due to real-time equipment status and operational activities. Accurately understanding these influencing factors can aid in developing more efficient energy management strategies. This study first analyzes the energy consumption of single machines processing single products, establishing a probabilistic model for the stochastic process of single-machine energy consumption over time. Mathematical tools, including convolution, are then employed to develop a stochastic process model for energy consumption across multiple machines and products within the entire plant. The overall stochastic process model is optimized, leading to the creation of a "Peak Energy Consumption Alert" and an "Energy Efficiency Alert" system to mitigate the risks of peak energy consumption and overall energy inefficiency. By utilizing the proposed optimization model for machine component energy consumption and the production scheduling module, the likelihood of exceeding contracted power capacity is significantly reduced. This approach also enhances the energy efficiency of production scheduling, thereby reducing the total energy consumption of the entire plant. Furthermore, while meeting energy planning goals, the model considers non-energy-related production indicators (e.g., completion time, order delivery dates), ultimately improving the operational efficiency of production lines.