Energy-Efficient Hybrid Flow Shop Scheduling Under Time-of-Use Pricing via Deep Reinforcement Learning

With the transformation of manufacturing toward intelligence and sustainability, it is increasingly important to reduce energy consumption in production processes while maintaining efficiency. Based on this context, this study focuses on a photovoltaic glass deep-processing flow shop, and investigates the problem of minimizing tardiness cost, and energy consumption under time-of-use electricity pricing. A multi-stage mixed-integer programming model is established, and a reinforcement learning framework integrated with graph neural networks is developed to solve the problem. Numerical experiments show that the proposed method outperforms in terms of convergence and solution quality, while also exhibiting strong generalization capability. The results provide theoretical support and decision-making references for the application of renewable energy in manufacturing, promoting the green and low-carbon transformation of the industrial sector.