Product classification is a crucial task in international trade, as compliance regulations are verified and taxes and duties are applied based on product categories. Manual classification of products is time-consuming and error-prone, and the sheer volume of products imported and exported renders the manual process infeasible. Consequently, e-commerce platforms and enterprises involved in international trade have turned to automatic product classification using machine learning. However, current approaches do not consider the real-world challenges associated with product classification, such as very abbreviated and incomplete product descriptions. In addition, recent advancements in generative Large Language Models (LLMs) and their reasoning capabilities are mainly untapped in product classification and e-commerce. In this research, we explore the real-life challenges of industrial classification and we propose data perturbations that allow for realistic data simulation. Furthermore, we employ LLM-based product classification to improve the robustness of the prediction in presence of incomplete data. Our research shows that LLMs with in-context learning outperform the supervised approaches in the clean-data scenario. Additionally, we illustrate that LLMs are significantly more robust than the supervised approaches when data attacks are present.