Hospital workflow analytics has become central to improving throughput, reducing operational cost, and strengthening patient experience. Artificial intelligence offers predictive capabilities for patient flow, staffing, resource use, and delay anticipation. This systematic review examined machine learning models applied to patient flow, staff scheduling, resource utilisation, and operational delay prediction in hospital settings. The review focused on model types, operational endpoints, data sources, validation methods, and implementation maturity. A PRISMA 2020-aligned search strategy was designed for PubMed, Scopus, IEEE Xplore, and Web of Science. Screening, extraction, risk-of-bias appraisal, and narrative synthesis were structured around hospital operations rather than clinical diagnosis. The literature was dominated by retrospective, single-centre studies focused on patient flow, especially length-of-stay, admission, discharge, and bed-use prediction. Staffing, resource utilisation, and operational delay prediction were less frequently studied, and prospective deployment remained uncommon. Machine learning for hospital operations is maturing technically but remains fragmented across isolated workflow domains. Integration across patient flow, staffing, resource utilisation, and delay management requires stronger prospective evaluation.