This study provides a detailed examination of the innovation potential of artificial intelligence (AI) in the management of pharmaceutical and medical supply chains. Particular emphasis is placed on the effective role of AI technologies in preventing stock outs. In the healthcare sector, supply chain management holds critical importance, especially during unexpected events such as pandemics and natural disasters. Stock outs can lead to disruptions in healthcare services, increased costs, and risks to patient safety. To address these challenges, the study presents AI-based forecasting models, automated inventory replenishment systems, and real-time data analysis methods. Furthermore, it discusses the implementation of demand forecasting systems developed through machine learning algorithms and safety stock optimization applications based on reinforcement learning techniques. Supported by real-world case studies, the study proposes practical solutions to common supply chain issues encountered by healthcare institutions such as hospitals and pharmaceutical enterprises. In conclusion, the integration of AI into healthcare supply chain management is highlighted as a means to significantly reduce stockout rates and to develop more resilient and sustainable systems.