Supply chain planning coordinates demand, sourcing, inventory, capacity, logistics, and disruption response across complex supply networks. Sustainability pressures have expanded planning beyond cost and service performance to include environmental performance, resilience, social and ethical responsibility, transparency, and accountability. At the same time, organizations are exploring Generative Artificial Intelligence (GenAI) to support scenario generation, knowledge synthesis, decision explanation, and natural-language interaction with planning systems. Drawing on the Resource-Based View (RBV), this paper examines how GenAI technological resources and associated organizational capabilities can contribute to competitive advantage in sustainable supply chain planning. The study analyzes five resources: large language models, retrieval-augmented generation, GenAI-enabled optimization and decision analytics, multi-agent GenAI systems, and knowledge graphs. It also examines six capabilities, including GenAI proficiency, data governance, sustainability-aware planning, ethical oversight, human-AI collaboration, and cross-functional learning. The analysis argues that GenAI creates value when embedded within firm-specific knowledge, data, governance routines, and human expertise.