Multi-agent deep reinforcement learning for low-carbon flexible job shop scheduling with variable sublots

As manufacturing shifts toward greener and more intelligent paradigms, traditional scheduling approaches are increasingly inadequate for meeting both operational efficiency and sustainability demands. The Low-Carbon Flexible Job Shop Scheduling Problem with Variable Sublots (LC-FJSP-VS) introduces significant complexity due to the need to simultaneously coordinate sublot sizing, machine selection, and carbon-aware objectives under dynamic disturbances. To address these challenges, this paper proposes a hybrid scheduling framework that integrates Multi-Agent Deep Reinforcement Learning (MADRL) with a bi-objective Mixed-Integer Linear Programming (MILP) model. A hierarchical decision-making architecture is designed, where in the operation-level agent performs real-time job dispatching, and the machine-level agent adjusts processing speeds and optimization preferences to guide sublot-level MILP scheduling. Machine failure events are stochastically simulated to emulate realistic disruptions, testing the system’s adaptability and robustness. Experimental results on extended benchmark datasets show that the proposed method significantly outperforms classical dispatching rules and advanced metaheuristics in terms of Hypervolume (HV), effectively balancing makespan and carbon emissions. This work demonstrates the feasibility and advantages of intelligent, low-carbon scheduling systems and provides a foundation for scalable and disturbance-resilient production planning.