Effective traffic incident management is essential for ensuring safety, minimizing congestion, and reducing response times in emergency situations. Traditional highway incident management relies heavily on radio room operators, who must make rapid, informed decisions in high-stakes environments. This paper proposes an innovative solution to support and enhance these decisions by integrating Large Language Models (LLMs) into a decision-support system for traffic incident management. We introduce two approaches: (1) an LLM + Optimization hybrid that leverages both the flexibility of natural language interaction and the robustness of optimization techniques, and (2) a Full LLM approach that autonomously generates decisions using only LLM capabilities. We tested our solutions using historical event data from Autostrade per l'Italia. Experimental results indicate that while both approaches show promise, the LLM + Optimization solution demonstrates superior reliability, making it particularly suited to critical applications where consistency and accuracy are paramount. This research highlights the potential for LLMs to transform highway incident management by enabling accessible, data-driven decision-making support.