Optimization models developed by operations research (OR) experts are often deployed as decision-support systems in industrial settings. However, real-world environments are dynamic, with evolving business rules and unforeseen perturbations. In such contexts, end users should ideally re-optimize models to recover feasible and implementable solutions, often without access to the original model developers. This paper introduces an agentic re-optimization framework in which a large language model (LLM) acts as an OR expert, dynamically supporting end users through natural-language interaction. The LLM translates user prompts into structured updates of the underlying optimization model, selects suitable re-optimization techniques from an optimization toolbox, and solves the resulting instance to return implementable solutions. The toolbox leverages primal information, including historical solutions, valid inequalities, solver configurations, and metaheuristics, to accelerate re-optimization while preserving solution quality. The proposed framework enables interactive and continuous adaptation of deployed optimization models, reducing dependence on OR experts, and improving the sustainability of decision-support systems. Extensive experiments on two complementary large-scale real-world case studies demonstrate the effectiveness and scalability of the proposed framework. The first considers online supply chain re-optimization, where solutions must be generated rapidly while remaining close to the deployed plan, whereas the second focuses on offline university exam scheduling, where solution quality is prioritized over runtime. Results show that the toolbox-driven architecture significantly improves computational efficiency through primal-based and solver-aware re-optimization techniques, while the structured patch-based updates improve interpretability and traceability of model modifications.