<p>Healthcare systems face complex challenges in optimizing resource allocation, minimizing patient delays, and managing costs under uncertainty. This study addresses how hospitals can efficiently balance conflicting objectives in resource-constrained and uncertain environments. To solve this, we develop a multi-objective mathematical model that targets three key goals: (i) minimizing medical supply costs, (ii) reducing ICU bed congestion and patient transfer delays, and (iii) minimizing patient appointment wait times while maximizing doctor efficiency. To capture uncertainty in hospital operations, the model integrates a new Fermatean fuzzy score function under the Fermatean fuzzy programming approach to convert fuzzy parameters into a crisp form. The deterministic version of the model is then solved using a neutrosophic goal programming approach, allowing for the simultaneous optimization of conflicting objectives. The IBM CPLEX solver ensures scalability and computational efficiency. The model is validated using real-world data from AIIMS Delhi, and the results demonstrate significant improvements in procurement cost control, ICU utilization, and patient flow management. The study contributes to healthcare decision science by presenting a scalable, uncertainty-aware optimization framework that integrates advanced fuzzy and neutrosophic logic. This framework can support hospital administrators in making data-driven, adaptive decisions to improve operational efficiency and service quality.</p>