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Machine learning is increasingly used in hospital operations, revenue cycle management, and quality monitoring. These administrative applications require transparency because their outputs can influence access, resource allocation, financial decisions, and accountability. This systematic review examined explainable machine learning methods applied to operational decision support, revenue cycle analytics, and quality monitoring in healthcare administration. The review focused on the type, depth, and use of transparency methods rather than predictive performance. A PRISMA 2020–compliant search strategy was applied to PubMed, Scopus, IEEE Xplore, and Web of Science for studies published between 2017 and 2022. Screening, extraction, and narrative synthesis focused on administrative domain, model type, explanation method, stakeholder use, and risk of bias. SHAP and LIME were the most frequently discussed post-hoc explanation approaches, while feature importance, partial dependence, rule-based models, and attention mechanisms appeared in smaller subsets of the literature. Operational decision support showed the strongest explainability uptake, whereas revenue cycle analytics and administrative quality monitoring remained less developed. Explainability in healthcare administration remains uneven and often superficial. The largest gap is not the availability of explanation tools, but the limited evidence that explanations improve managerial decisions, accountability, fairness, or auditability.