Minimizing total weighted tardiness in parallel machine scheduling with sequence-dependent setup times via fine-tuned large language models

초록

This study tackles a complex parallel machine scheduling problem with unrelated machines, sequence-dependent setup times and total weighted tardiness minimization. To address the scalability and expertise limitations of exact and heuristic methods, the prompt-tuned large language model (LLM) application for intelligent dispatching (PLAID) is proposed as a framework that uses fine-tuned large language models to make sequential dispatching decisions. PLAID consists of three stages: generating training data with constraint programming, supervised fine-tuning and dispatching based on learned rules. Experiments on diverse instance sizes show that PLAID achieves competitive performance relative to dispatching rules, metaheuristics and exact approaches, while remaining robust and interpretable. Fine-tuned models such as GPT-4.1-Tuned and GPT-4.1-Nano-Tuned consistently reduce total weighted tardiness, demonstrating the benefit of domain-specific adaptation. Overall, PLAID provides both scalability and transparency, positioning fine-tuned LLMs as practical, human-centric tools for complex manufacturing scheduling.

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