The integration of next-generation Artificial Intelligence (GenAI) technologies into supply chain management is transforming traditional operations into intelligent, adaptive ecosystems. This paper explores how GenAI—encompassing large language models (LLMs), generative design, autonomous agents, and advanced predictive analytics—is being leveraged to enhance decision-making, improve demand forecasting, optimize logistics, and increase supply chain resilience. Through real-world case studies and technical insights, we demonstrate how GenAI enables real-time data interpretation, automates complex workflows, and augments human expertise in areas such as procurement, inventory management, and last-mile delivery. The paper also discusses the challenges of adoption, including data governance, integration with legacy systems, and ethical considerations. Ultimately, the research underscores that the strategic deployment of GenAI is not merely an innovation layer but a foundational shift toward hyper-intelligent, agile supply chains.