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

arXiv: https://arxiv.org/abs/2509.18180 · HTML: https://mlsanity.com/paper/2509.18180/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 108 of its 131 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Builds on (most cited first, 30 of 108)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [LLM-Planner: Few-Shot Grounded Planning for Embodied Agents with Large Language Models](https://mlsanity.com/paper/2212.04088/) (2022)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Can Language Models Solve Graph Problems in Natural Language?](https://mlsanity.com/paper/2305.10037/) (2023)
- [PromptRobust: Towards Evaluating the Robustness of Large Language Models on Adversarial Prompts](https://mlsanity.com/paper/2306.04528/) (2023)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [Evolution through Large Models](https://mlsanity.com/paper/2206.08896/) (2022)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap](https://mlsanity.com/paper/2401.10034/) (2024)
- [Large Language Model (LLM) for Telecommunications: A Comprehensive Survey on Principles, Key Techniques, and Opportunities](https://mlsanity.com/paper/2405.10825/) (2024)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [Using Large Language Models for Hyperparameter Optimization](https://mlsanity.com/paper/2312.04528/) (2023)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://mlsanity.com/paper/2407.09887/) (2024)
- [Large Language Models for Supply Chain Optimization](https://mlsanity.com/paper/2307.03875/) (2023)
- [Multi-objective Evolution of Heuristic Using Large Language Model](https://mlsanity.com/paper/2409.16867/) (2024)
- [Algorithm Evolution Using Large Language Model](https://mlsanity.com/paper/2311.15249/) (2023)
- [Can Large Language Models be Good Path Planners? A Benchmark and Investigation on Spatial-temporal Reasoning](https://mlsanity.com/paper/2310.03249/) (2023)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [GraphArena: Evaluating and Exploring Large Language Models on Graph Computation](https://mlsanity.com/paper/2407.00379/) (2024)

## Built on by (most cited first, 6 of 6)

- [ORPilot: A Production-Oriented Agentic LLM-for-OR Tool for Optimization Modeling](https://mlsanity.com/paper/2605.02728/) (2026)
- [MM-OptBench: A Solver-Grounded Benchmark for Multimodal Optimization Modeling](https://mlsanity.com/paper/2605.12154/) (2026)
- [TriVAL: A Tri-Validation Framework for Faithful Automatic Optimization Modeling](https://mlsanity.com/paper/2605.23966/) (2026)
- [SLAI T-Rex: Full-Parameter Post-training of the DeepSeek-V4 Family on Ascend SuperPOD](https://mlsanity.com/paper/2607.20145/) (2026)
- [SOVER: Formal Certification of Optimization Reformulations via LLM-Assisted SMT Verification](https://mlsanity.com/paper/2609.00728/) (2026)
- [SAILOR: Solver-Assisted Interactive LLM-based Optimization Recovery](https://mlsanity.com/paper/2609.13945/) (2026)

## Abstract (arXiv)

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.