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Large Language Models in Operations Research: Methods, Applications, and Challenges

Yang Wang, Kai Li

TL;DR

This paper surveys how large language models can transform operations research by addressing big, dynamic, multi-constraint optimization tasks. It organizes the literature into three pathways—automatic modeling, auxiliary optimization, and direct solving—and analyzes benchmarks and domain applications to map progress and gaps. The findings show that LLMs can translate natural language into mathematical or executable representations, generate heuristics, and even produce end-to-end solver outputs, though challenges remain in stability, interpretability, and industrial deployment. The work outlines directions toward robust representations, standardized workflows, cross-domain benchmarks, and lightweight deployment to enable next-generation intelligent optimization systems with improved scalability and adaptability.

Abstract

Operations research (OR) is a core methodology that supports complex system decision-making, with broad applications in transportation, supply chain management, and production scheduling. However, traditional approaches that rely on expert-driven modeling and manual parameter tuning often struggle with large-scale, dynamic, and multi-constraint problems, limiting scalability and real-time applicability. Large language models (LLMs), with capabilities in semantic understanding, structured generation, and reasoning control, offer new opportunities to overcome these challenges. They can translate natural language problem descriptions into mathematical models or executable code, generate heuristics, evolve algorithms, and directly solve optimization tasks. This shifts the paradigm from human-driven processes to intelligent human-AI collaboration. This paper systematically reviews progress in applying LLMs to OR, categorizing existing methods into three pathways: automatic modeling, auxiliary optimization, and direct solving. It also examines evaluation benchmarks and domain-specific applications, and highlights key challenges, including unstable semantic-to-structure mapping, fragmented research, limited generalization and interpretability, insufficient evaluation systems, and barriers to industrial deployment. Finally, it outlines potential research directions. Overall, LLMs demonstrate strong potential to reshape the OR paradigm by enhancing interpretability, adaptability, and scalability, paving the way for next-generation intelligent optimization systems.

Large Language Models in Operations Research: Methods, Applications, and Challenges

TL;DR

This paper surveys how large language models can transform operations research by addressing big, dynamic, multi-constraint optimization tasks. It organizes the literature into three pathways—automatic modeling, auxiliary optimization, and direct solving—and analyzes benchmarks and domain applications to map progress and gaps. The findings show that LLMs can translate natural language into mathematical or executable representations, generate heuristics, and even produce end-to-end solver outputs, though challenges remain in stability, interpretability, and industrial deployment. The work outlines directions toward robust representations, standardized workflows, cross-domain benchmarks, and lightweight deployment to enable next-generation intelligent optimization systems with improved scalability and adaptability.

Abstract

Operations research (OR) is a core methodology that supports complex system decision-making, with broad applications in transportation, supply chain management, and production scheduling. However, traditional approaches that rely on expert-driven modeling and manual parameter tuning often struggle with large-scale, dynamic, and multi-constraint problems, limiting scalability and real-time applicability. Large language models (LLMs), with capabilities in semantic understanding, structured generation, and reasoning control, offer new opportunities to overcome these challenges. They can translate natural language problem descriptions into mathematical models or executable code, generate heuristics, evolve algorithms, and directly solve optimization tasks. This shifts the paradigm from human-driven processes to intelligent human-AI collaboration. This paper systematically reviews progress in applying LLMs to OR, categorizing existing methods into three pathways: automatic modeling, auxiliary optimization, and direct solving. It also examines evaluation benchmarks and domain-specific applications, and highlights key challenges, including unstable semantic-to-structure mapping, fragmented research, limited generalization and interpretability, insufficient evaluation systems, and barriers to industrial deployment. Finally, it outlines potential research directions. Overall, LLMs demonstrate strong potential to reshape the OR paradigm by enhancing interpretability, adaptability, and scalability, paving the way for next-generation intelligent optimization systems.

Paper Structure

This paper contains 21 sections, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Introduction to Basic Principles
  3. Operations Research (OR)
  4. Foundation of Competence of LLM
  5. LLM-based Methods for Operations Research
  6. Automatic Modeling
  7. LLM-based Automatic Modeling Paradigm via prompting
  8. LLM-based Automatic Modeling Mechanism Driven by Prompt–Fine-tuning Synergy
  9. LLM-based Automatic Modeling Mechanism Guided by External Knowledge
  10. Benchmarks for Evaluating LLM-based Automatic Modeling
  11. LLM-assisted Optimization
  12. LLM-enabled Hybrid Mechanisms for Integrating Multiple Optimization Algorithms
  13. LLM-dominated Optimization Solving
  14. Benchmarks for Evaluating LLM-assisted Optimization
  15. Domain Problems
  16. ...and 6 more sections

Figures (3)

  • Figure 1: Literature classification map of LLM-driven OR research pathways and representative works.
  • Figure 2: Closed-loop framework of automatic modeling from natural language input to model execution.
  • Figure 3: Two primary approaches to LLM-assisted optimization.