# Optimal Crew Scheduling in an Intensive Care Unit: A Case Study in a University Hospital
## 4 Discussion  
This study highlights the effectiveness of a Mixed-Integer Programming (MIP) model in optimizing hospital staff scheduling by simultaneously addressing the unique requirements of nurses, junior and senior doctors, and caregivers in a Pediatric Intensive Care Unit (PICU). Unlike traditional scheduling methods that treat these personnel groups separately, this integrated approach ensures fair shift distribution, cost minimization, and compliance with operational constraints, ultimately leading to improved hospital efficiency and staff satisfaction. The findings align with previous research [1; 7], which emphasizes that mathematical models significantly enhance scheduling efficiency compared to manual methods. Manual scheduling is inefficient and error prone, leading to staff dissatisfaction. By leveraging optimization techniques, this study demonstrates how an automated approach can produce more balanced and efficient schedules in a fraction of the time. Recent advancements by [PERSON] and [PERSON] [22] further support the integration of resource allocation with scheduling, reinforcing the need for data-driven workforce management strategies that align staffing levels with patient care demands. Additionally, studies such as that by B\(\ddot{\text{o}}\)[PERSON] et al. [23] highlight the importance of adaptability in real-world healthcare environments, a key feature that could be further enhanced in future iterations of this model. One of the major contributions of this study is its holistic approach to staff scheduling, which considers the interdependencies between different healthcare roles. While previous studies have focused on nurse scheduling (NSP) [4; 7] or doctor scheduling (DSP) [16] separately, this research integrates all personnel groups within a single mathematical framework. This comprehensive approach not only promotes equity in shift allocation but also enhances the system's ability to respond to fluctuations in patient needs, a factor that is particularly crucial in critical care settings. The study by [PERSON] [13] also emphasizes the need for fairness in scheduling, further validating the importance of this study's approach. Although various optimization models for nurse or doctor scheduling have been examined in the literature, most models usually focus on a single staff group. For example, [PERSON] and [PERSON] [24], [PERSON] et al. [25], and [PERSON] et al. [26] presented a model for nurses' shift planning only, while [PERSON] et al. [27] and [PERSON] et al. [28] addressed doctors' shift-allocation processes. However, these approaches ignore cooperation and shift integration between different healthcare professionals. The most important innovation of the current  
Figure 4: Total number of shifts per year for caregivers. study is that it offers a more holistic solution by integrating all healthcare professionals into a single scheduling framework. However, when evaluating the applicability of the current model in the healthcare sector, some important challenges should be taken into account. First of all, the process of acceptance of the proposed approach by hospital managers and healthcare professionals is of critical importance. In particular, managers and employees who are accustomed to traditional manual planning methods may resist the implementation of the model. In addition, the effectiveness of the model should be aligned with hospital policies and working hours regulations. Another important factor is the necessity of a dynamic planning mechanism depending on the fluctuation of patient admission rates in hospitals. For example, unforeseen situations such as epidemic periods or seasonal patient increases can test the flexibility capacity of the model. Therefore, future studies should evaluate how the model can be adapted to unpredictable patient demands.