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Unpredictable hospital supply shortages can compromise patient care, interrupt clinical workflows, and force costly emergency purchasing. These shortages are often preceded by signals embedded in procurement activity, consumption patterns, vendor behavior, and inventory movement. Current hospital inventory practices frequently depend on manual review, static reorder points, and retrospective averages. These methods cannot adequately synthesize predictive data from procurement systems, clinical demand sources, supplier feeds, and inventory thresholds. This article proposes an AI-based early warning system that ingests procurement logs, real-time consumption rates, vendor delay patterns, procedure forecasts, and inventory thresholds. The system computes a dynamic shortage risk score for each monitored hospital supply item. The framework includes data ingestion pipelines, a machine learning prediction engine, a vendor risk assessor, a procedure-to-supply demand mapper, and an alert dashboard. These components convert fragmented operational data into actionable shortage risk intelligence. The system would provide actionable lead time for proactive reordering, substitution planning, vendor escalation, and redistribution across hospital locations. It could also learn from historical shortage events to support more resilient supply chain planning. A predictive, AI-augmented supply chain could transform hospital materials management from reactive replenishment to anticipatory risk mitigation. Such a system would support safer, more resilient, and more efficient hospital logistics.