SchedGPT: Towards The First Auto-Regressive Foundation Model for List Scheduling

List scheduling underlies many combinatorial problems in manufacturing and distributed computing, yet existing learning-based schedulers are typically specialized to one problem family and one architecture. We introduce SchedGPT, an autoregressive foundation model with a graph encoder that handles diverse list-scheduling variants within a single architecture. The key insight is a unified heterogeneous graph representation over task and processor nodes, connected by precedence and eligibility relations, plus a unified priority-list encoding that specifies task ordering and per-task processor assignment and is deterministically decoded into a schedule. SchedGPT combines a relation-aware GATv2 encoder with a nanoGPT autoregressive decoder, factorizing each construction step into task sequencing and nested processor assignment via two pointer heads. Trained from scratch with a rollout-baseline policy-gradient objective, SchedGPT outperforms specialized state-of-the-art algorithms on manufacturing scheduling (JSSP and FJSP) and workflow scheduling (five variants), demonstrating that list-scheduling problems can be unified under one architecture.