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

TL;DR

This paper introduces SMILO, a modular framework that combines expert knowledge with large language models to automate the creation of optimization models, significantly improving accuracy and reliability in workforce scheduling applications.

Contribution

The paper presents a novel, expert-knowledge-driven architecture that enhances LLM-based optimization model generation, addressing limitations of existing methods and improving accuracy and reproducibility.

Findings

SMILO achieves 90% correctness in model generation across test instances.

Outperforms one-step LLM baselines by at least 35%.

Demonstrated effectiveness in manufacturing, logistics, and service operations.

Abstract

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.