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Foundation models pre-trained on massive, multimodal data have transformed several areas of artificial intelligence. Their adaptation to healthcare operations analytics is an emerging frontier because hospital workflows generate dense streams of structured, textual, temporal, and administrative data. This systematic review examined applications of foundation models to patient flow prediction, documentation burden estimation, resource allocation, and operational risk forecasting from 2017 to 2026. The review focused on multimodal pretraining, transfer learning, downstream adaptation, validation, and implementation maturity. A PRISMA 2020-compliant search was designed for PubMed, Scopus, IEEE Xplore, and Web of Science. Records were screened by two reviewers, and eligible studies were synthesized narratively by operational domain, model architecture, data modality, and maturity level. A small but rapidly growing body of work suggests that pre-trained multimodal models may support operational prediction tasks across healthcare systems. Evidence was concentrated in patient flow and resource allocation, while documentation burden estimation and operational risk forecasting were less frequently studied. Foundation models show potential to unify operational analytics across hospital systems. The field remains immature, with limited external validation, few prospective implementation studies, and no widely adopted benchmarks for operational foundation models.