  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}.
