Business optimization for digital manufacturing: A fine-tuned large language model approach

Digital manufacturing depends on optimization to make complex, time-critical production decisions. Yet problem formulation, an important step in optimization, still requires scarce domain expertise and strongly affects both solution validity and computational efficiency. Despite progress in modeling languages, problem formulation remains a complex undertaking, particularly for real-world digital manufacturing applications. Recent advances in large language models (LLMs) offer considerable potential for automating problem formulation in digital manufacturing contexts. However, existing studies are largely descriptive and benchmark-oriented. To our knowledge, they have not demonstrated execution-verified deployments in real-world digital manufacturing setups; instead, they have focused on synthetic or simplified cases. We introduce a systematic, cost-efficient framework that fine-tunes LLMs to automate problem formulation specifically for digital manufacturing optimization. The approach integrates modularization and prompt engineering to deliver scalable performance and quantitative validation beyond prior descriptive work. Experiments demonstrate success rates exceeding 95% in producing accurate, solver-ready formulations for both classic job-shop scheduling and real-world production scheduling, verified via execution-based evaluation on digital manufacturing case studies. On linear-programming benchmarks, the method yields approximately 30% improvement over state-of-the-art prompt-engineering baselines, while embedding analyses indicate robustness on complex combinatorial problems. Practically, the framework accelerates operator adaptation to complex planning tasks, improving production efficiency while reducing dependence on expert modelers and shortening decision cycle times. These capabilities are highly applicable to real-world digital manufacturing contexts where fast and accurate decision-making is critical. The cost-efficient design further enables adoption by small and medium-sized manufacturers with limited computational resources.