Large Language Models (LLMs) have emerged as powerful tools for tackling complex Operations Research (OR) problem by providing the capacity in automating optimization modeling. However, current methodologies heavily rely on prompt engineering (e.g., multi-agent cooperation) with proprietary LLMs, raising data privacy concerns that could be prohibitive in industry applications. To tackle this issue, we propose training open-source LLMs for optimization modeling. We identify four critical requirements for the training dataset of OR LLMs, design and implement OR-Instruct, a semi-automated process for creating synthetic data tailored to specific requirements. We also introduce the IndustryOR benchmark, the first industrial benchmark for testing LLMs on solving real-world OR problems. We apply the data from OR-Instruct to various open-source LLMs of 7b size (termed as ORLMs), resulting in a significantly improved capability for optimization modeling. Our best-performing ORLM achieves state-of-the-art performance on the NL4OPT, MAMO, and IndustryOR benchmarks. Our code and data are available at \url{https://github.com/Cardinal-Operations/ORLM}.

翻译：大语言模型（LLM）凭借其自动化优化建模的能力，已成为解决复杂运筹学（OR）问题的强大工具。然而，当前方法严重依赖基于闭源LLM的提示工程（例如多智能体协作），引发了数据隐私问题，这可能在工业应用中构成障碍。为解决这一问题，我们提出为优化建模训练开源LLM。我们明确了OR-LLM训练数据集的四项关键要求，设计并实现了OR-Instruct——一个为满足特定需求而创建合成数据的半自动化流程。我们还推出了IndustryOR基准测试，这是首个用于测试LLM解决现实世界OR问题的工业基准。我们将OR-Instruct生成的数据应用于多个7b规模的开源LLM（称为ORLM），显著提升了其优化建模能力。我们性能最佳的ORLM在NL4OPT、MAMO和IndustryOR基准测试中均取得了最先进的性能。我们的代码与数据公开于 \url{https://github.com/Cardinal-Operations/ORLM}。