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

Digital manufacturing relies on optimization for complex, time-critical production decisions. However, the effectiveness of optimization itself hinges on accurate problem formulation, which requires specialized domain expertise and dictates both solution validity and computational tractability. Recent advances in large language models (LLMs) offer the potential to automate the problem formulation process, yet existing studies focus predominantly on synthetic benchmarks. We present a systematic, cost-efficient framework that fine-tunes LLMs to automate problem formulation for optimization in digital manufacturing. The approach integrates modularization and prompt engineering to achieve scalable and quantitatively verifiable performance in execution-based deployments within actual manufacturing environments. Experiments demonstrate success rates exceeding 95% in generating accurate, solver-ready formulations for both classic job-shop scheduling and real-world production scheduling, as verified through execution-based evaluation. On linear programming benchmarks, the method achieves an approximately 30% improvement over state-of-the-art prompt-engineering baselines, while embedding analyses confirm robustness across complex combinatorial problems. The framework enhances production efficiency by accelerating operator adaptation to complex planning tasks, reducing dependence on expert modelers, and shortening decision cycles. The cost-efficient design of the proposed framework enables its ready adoption by small and medium-sized manufacturers, making advanced optimization accessible even with limited computational resources.