Optimizing Nurse Rostering in a Hospital Surgical Unit Using Simulated Annealing

The Nurse Rostering Problem (NRP) is a critical issue in healthcare, that ensures nurse availability for 24-hour services while adhering to various regulations. Becker's Hospital Review highlighted that scheduling issues negatively affect nurses' morale and patient care. In Indonesia, one of the hospitals that still uses manual scheduling is a regional public hospital in Bojonegoro. Manual scheduling in hospitals often results in inefficient resource allocation and errors. To address the NRP, this study applied the Simulated Annealing (SA) algorithm to create near-optimal schedules for the surgical unit. Additionally, this study analyzed the performance of the Simulated Annealing algorithm in solving the NRP, focusing on time efficiency, compliance with regulations, and all other requirements. Data collection in this study was conducted through interviews with the heads of the surgical teams. Subsequently, a mathematical model of NRP was designed as the basis for implementing the SA algorithm. Testing was conducted with parameter variations to evaluate the performance of the algorithm. The performance of the SA algorithm was evaluated through parameter variations, and the results were compared with those of the Constraint Programming (CP) algorithm. The findings indicated that the SA algorithm successfully minimized the objective function related to weekly working hours violations, achieving average weekly working hours of 41.25, 42.16, and 39.92 for the Northern Team, HCU, and Southern Team, respectively. Both SA and CP produced schedules with zero hard-constraint violations, while manual schedule contained multiple violations in shift requirements, number of days off, and total staffing. Overall, the schedules generated by SA were superior to those of manual scheduling and comparable to those obtained by the CP model in terms of time efficiency, hard constraint adherence, and objective function minimization.