Directed Hypergraph-Enhanced PPO for Quality-Aware Single-Machine Scheduling with Sequence-Dependent Setup Times: A Computational Pilot Study

Single-machine scheduling with sequence-dependent setup times (SMSP-SDST) becomes more challenging when delivery performance and transition-related quality are considered jointly. This study proposes a directed-hypergraph-enhanced proximal policy optimization framework (DHG-PPO) for quality-aware SMSP-SDST. The scheduling problem is formulated as an episodic Markov decision process (MDP), and a directed hypergraph encodes higher-order relationships among the preceding job, candidate job, machine state, setup transition, and quality-risk state. A hypergraph encoder produces a relational state representation for a PPO actor–critic, while feasible-action masking guarantees valid job permutations. The objective jointly minimizes normalized makespan, total sequence-dependent setup time, weighted tardiness, and transition-related quality loss. A synthetic computational pilot evaluates DHG-PPO against NEH, Setup-Greedy, SPT, EDD, and Vector-PPO on held-out instances with 10, 20, 50, and 100 jobs. The learning methods use one random seed and 100 training episodes on 20-job instances; therefore, the results provide diagnostic evidence rather than definitive evidence of learning-policy superiority. NEH achieves the lowest mean composite objective at every tested problem size, whereas DHG-PPO consistently outperforms Vector-PPO. At n = 50, DHG-PPO obtains a mean composite objective of 3.549 versus 3.892 for Vector-PPO and 2.524 for NEH, corresponding to an 8.8% lower objective than Vector-PPO while remaining 40.6% above NEH. A separate 30-instance robustness stress test preserves the same ranking among the evaluated methods under 0–30% perturbations. The findings support the feasibility of directed-hypergraph state encoding and motivate a larger multi-seed study with controlled architectural ablations and stronger benchmark coverage.