Queue-Theoretic Priors Meet Explainable Graph Convolutional Learning: A Risk-Aware Scheduling Framework for Flexible Manufacturing Systems

For the first time, this study presents a cyber–physical framework that reconciles the long-standing conflict between transparent queue analytics and adaptive machine learning in flexible manufacturing systems. Deterministic indicators, utilization, expected queue length, waiting time, and idle probability, are fused with topological embeddings of the routing graph and ingested by a graph convolutional network that predicts station congestion with calibrated confidence intervals. Shapley additive explanations decompose every forecast into causal contributions, and these vectors, together with a percentile-based risk metric, steer a mixed-integer genetic optimizer toward schedules that lift throughput without breaching statistical congestion limits. A cloud dashboard streams forecasts, risk bands, and color-coded explanations, allowing supervisors to accept or modify suggestions; each manual correction is logged and injected into nightly retraining, closing a socio-technical feedback loop. Experiments on an 8704-cycle production census demonstrate a 38 percent reduction in average queue length and a 12 percent rise in throughput while preserving full audit traceability, enabling one-minute rescheduling on volatile shop floors. The results confirm that transparency and adaptivity can coexist when analytical priors, explainable learning, and risk-aware search are unified in a single containerized control stack.