Graph-based deep reinforcement learning for hybrid flow shop scheduling with human resource constraints

The hybrid flow shop scheduling problem (HFSP) has been extensively studied due to its wide applications in modern manufacturing systems. However, existing research primarily focuses on machine-centric scheduling while neglecting the critical role of human resources, whose varying skill levels impact processing efficiency and whose availability constraints complicate scheduling decisions. Therefore, this paper investigates the HFSP with human resource constraints (HFSP-HRC), which requires the joint optimization of job sequencing, machine allocation, and worker assignment to obtain efficient scheduling solutions. We propose a deep reinforcement learning (DRL) method integrated with a meta-path-based heterogeneous graph neural network (MP-HGNN) to solve this problem. It innovatively captures complex interdependencies among operations, machines, and workers through machine-centric and worker-centric meta-paths, overcoming limitations of existing methods that fail to model heterogeneous resource competition relationships. The integration enables high-order semantic feature fusion for enhanced scheduling robustness. Combined with the proximal policy optimization (PPO) algorithm, the framework realizes end-to-end learning from raw scheduling states to optimal decisions. Experiments across four different problem scales demonstrate that the proposed method significantly outperforms baseline heuristic rules and DRL method in makespan, with particularly outstanding performance on large-scale instances.