Teaching LLMs to Think Mathematically: A Critical Study of Decision-Making via Optimization

This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to assess how well LLMs understand, structure, and solve optimization problems across domains. The analysis is guided by critical review questions focusing on learning approaches, dataset designs, evaluation metrics, and prompting strategies. Our systematic evidence is complemented by targeted experiments designed to evaluate the performance of state-of-the-art LLMs in automatically generating optimization models for problems in computer networks. Using a newly constructed dataset, we apply three prompting strategies: Act-as-expert, chain-of-thought, and self-consistency, and evaluate the obtained outputs based on optimality gap, token-level F1 score, and compilation accuracy. Results show promising progress in LLMs' ability to parse natural language and represent symbolic formulations, but also reveal key limitations in accuracy, scalability, and interpretability. These empirical gaps motivate several future research directions, including structured datasets, domain-specific fine-tuning, hybrid neuro-symbolic approaches, modular multi-agent architectures, and dynamic retrieval via chain-of-RAGs. This paper contributes a structured roadmap for advancing LLM capabilities in mathematical programming.