An LLM-powered MILP modelling engine for workforce scheduling guided by expert knowledge

Formulating mathematical models from real-world decision problems is a core task in Operational Research, yet it typically requires considerable human expertise and effort, limiting practical application. Recent advances in large language models (LLMs) have sparked interest in automating this process from natural language descriptions. However, challenges including limited modelling expertise, dependence on large-scale training data, and hallucination affect the reliable application of LLMs in optimisation modelling. To address these challenges, we propose SMILO, an expert-knowledge-driven framework that integrates optimisation modelling expertise with LLMs to generate mixed-integer linear programming models. SMILO uses a three-stage architecture built on reusable modelling graphs and associated resources: identifying relevant modelling components, extracting instance-specific information using LLMs, and constructing models through expert-defined templates. This modular architecture separates information extraction from formula generation, enhancing modelling accuracy, transparency, and reproducibility. We demonstrate the implementation of our modelling framework using workforce scheduling problems spanning manufacturing, logistic, and service operations as illustrative cases. Experiments show that SMILO consistently generates correct models in 90% of test instances across five trials, outperforming one-step LLM baselines by at least 35%. This work offers a generalisable paradigm for integrating LLMs with expert knowledge across diverse decision-making contexts, advancing automation in optimisation modelling.