Optimization of production scheduling and energy cost considering carbon trading strategies

China's manufacturing sector is progressively implementing carbon market quota management while manufacturing enterprises are endeavoring to develop multi-source energy supply systems to mitigate carbon emissions. However, coordinating the supply of multiple energy sources to achieve carbon reduction remains an urgent challenge for the industry. This study proposes a two-stage optimization model for production and energy use scheduling under a multi-source energy supply framework. In the first stage, a production scheduling model is formulated to minimize the maximum completion time, prioritizing product delivery schedules. In the second stage, an energy use planning model is developed to minimize total energy costs, incorporating carbon trading strategies, time-of-use tariffs, photovoltaic energy usage, and carbon quota constraints. The proposed model is validated through a case study of a manufacturing enterprise in Southwest China. Results indicate that the proposed method can increase the proportion of clean energy use in production activities by 21.82 %, reduce carbon emissions by 12.67 %, and decrease total costs by 0.87 %.