Coordinated scheduling and carbon flow tracing of discrete manufacturing processes with integrated energy-material-carbon flows model

With the rapid development of renewable energy and carbon accounting across industrial sectors, enhancing demand response capabilities and quantifying emissions have become critical for the decarbonization of production processes. However, production lines typically exhibit complex couplings among energy, material, and carbon flows, characterized by hybrid discrete-continuous dynamics. Current research still lacks a generalized model for coordinated scheduling optimization. This paper proposes a coordinated scheduling framework with unified energy and material flow (EMF) matrices modeling, and reveals the impact of EMF coupling and flexible production plans on scheduling performance. Additionally, the embodied carbon flow model in manufacturing processes is developed by defining material carbon intensity and product carbon emission flow rates. The mechanisms of carbon transmission within the EMF network are revealed to quantify product carbon footprints and allocate carbon responsibility. Then, the carbon intensity and allocation across all system nodes are quantified to provide systematic insights for industrial sustainability. Based on this framework, a coordinated rescheduling strategy is applied to an air conditioning production line, aiming to minimize both costs and carbon emissions across metal fabrication, injection molding, and components assembly processes. The energy usage results indicate a 15.9 % costs reduction and an 8.2 % carbon emissions decrease. Furthermore, the integrated flexibility of EMF is demonstrated through the convex formation of the projected feasible region. It shows that flexible production plan optimization enhances flexibility by 9.2 times, thereby enhancing peak shaving capacity for demand response by 18.38 %.