An LLM Based Framework for Automated MILP Modeling in Dynamic Multi-Robot Task Scheduling
Coordinating a team of robots in aircraft skin fabrication requires allocating and sequencing tightly coupled subtasks under spatio-temporal constraints, while the fleet must react to runtime disturbances such as robot failures and urgent task arrivals. Mixed-Integer Linear Programming (MILP) yields provably optimal coordination, but a disturbance often introduces new constraint logic rather than a mere parameter change, leaving the existing formulation structurally inadequate and requiring expert-led reformulation to accommodate the new logic. This letter proposes a Large Language Model (LLM)-based framework that automates the path from natural-language scheduling requirements to MILP formulation, executable solver code, and event-driven rescheduling, so that the optimization model can be restructured online without expert intervention. Two compact LLMs are specialized for complementary roles: a modeling LLM, empowered via knowledge augmentation, supervised fine-tuning on industrial constraint descriptions, and direct preference optimization on self-generated negatives; and a code LLM, trained via sandbox-validated knowledge distillation. On ten industrial constraint classes, the 8B modeling LLM reaches 100% constraint-level accuracy, exceeding cloud-scale general-purpose LLMs equipped with retrieval over the same knowledge base, while the 8B code LLM attains 86% under fully on-premises deployment. When a disturbance occurs, an event-triggered mechanism regenerates only the affected constraints. A case study on multi-robot scheduling for aircraft skin fabrication shows that the framework matches the schedule quality of baselines while shifting adaptation cost from offline expert labour to a bounded online inference budget.