Efficient healthcare asset management is essential for ensuring timely patient care, reducing operational delays, and improving resource utilization in modern hospitals. The increasing adoption of Industry 4.0 technologies, including Internet of Things (IoT) sensors, wireless communication, artificial intelligence, and indoor positioning systems, has created new opportunities for real-time localization and navigation of medical assets. However, the performance of localization and navigation algorithms varies significantly depending on hospital infrastructure, communication environment, and operational requirements. This study evaluates the suitability of prominent indoor localization and navigation algorithms for healthcare asset management applications. Localization algorithms such as RSSI-based localization, fingerprinting, trilateration, Kalman filter, particle filter, Bayesian localization, machine learning approaches, and deep learning approaches are critically examined. In addition, navigation algorithms including Dijkstra, A*, Bellman-Ford, Floyd-Warshall, Ant Colony Optimization, Genetic Algorithm, and dynamic path planning are reviewed for their applicability in hospital environments. The paper proposes a comparative evaluation framework based on localization accuracy, latency, navigation efficiency, computational complexity, scalability, and reliability. The findings establish the foundation for selecting appropriate algorithms for Industry 4.0-enabled healthcare asset localization, tracking, and navigation systems.