Progress in operations research allowed for the widespread use of mathematical optimization in supply chain planning. Despite its numerous practical and economic benefits, human planners often doubt the solutions provided by automated optimizers, which limits their potential effectiveness. Although Explainable Artificial Intelligence (XAI) offers innovative methods to improve the transparency of various models, the tools available to explain optimization algorithms remain underdeveloped. Existing solutions tend to present explanations in numerical formats difficult to interpret. This study explores the application of Large Language Models (LLMs) to enhance the interpretability and persuasiveness of these explanations. Specifically, it investigates whether LLMs can convert numerical explanations into clear, context-aware narratives, thereby fostering greater trust among planners in the optimizer outputs. We worked on top of a supply chain planning optimizer with a LIME-inspired algorithm to generate explanations for typical supply chain scenarios. Explanations generated by LLMs were evaluated using various metrics and compared to the expectations of experienced experts in the field. Our results show that LLMs can substantially improve the clarity and persuasiveness of XAI explanations, increasing human planners’ confidence in the optimizer’s outputs. We also identify future improvements needed to fully meet the ideal standards set by expert planners.