This case study addresses the challenge of optimizing nurse scheduling at a hospital in Mumbai. The objective of the study is to develop an efficient schedule for 52 nurses over a 30-day period, ensuring that 39 nurses work each day. To achieve this, we employed the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to generate multiple pareto optimal schedules in the solution space. 10 of these schedules were selected for detailed evaluation using three hybrid Multi-Criteria Decision-Making (MCDM) methods: AHP-TOPSIS, AHP-PROMETHEE, and AHP-VIKOR. The evaluation considered four critical factors: cost, shift distribution penalty, and overtime penalty which we had to minimize and nurse preferences which we had to maximize. A sensitivity analysis was conducted to examine the stability of the rankings by varying the cost criterion within a specified range. This analysis aimed to determine how changes in cost made an impact on the robustness of the schedule rankings. The results revealed that top schedules consistently maintained their ranks across all three MCDM methods, indicating strong stability and reliability despite fluctuations in cost. This study offers practical insights for hospital management, demonstrating how to achieve optimal and stable nurse scheduling by integrating multiple factors into the decision-making process.