Researchers have studied the nurse rostering problem for multiple decades. Initially, the formulations were rather primitive including only a few necessary restrictions, but down the road, the formulations have become more complex. Nonetheless, a fraction of the research reaches implementation in practice, and many wards still schedule nurses manually. In this article, we introduce a flexible nurse rostering system that employs mathematical optimization to automatically schedule nurses to shifts. We have developed this system in collaboration with practitioners to fully match their needs. The system consists of a comprehensive mixed integer programming (MIP) model along with a flexible framework. In addition to common constraints from the literature, the mathematical formulation includes three new constraints that further encourage healthy work schedules for each nurse. Additionally, we have reformulated some common constraints from the literature and allow for a complex shift structure that matches the needs of real hospital wards. This flexibility results in increased adaptability for different wards with different needs and is crucial to address the complex nurse rostering problem that practitioners face. We have successfully implemented this system in two wards at two Danish hospitals. We present the MIP model along with computational results for 12 real-world rostering instances. Furthermore, we discuss the practical impact of this system and provide general feedback from the practitioners using it. Overall, the results illustrate the capabilities of the system to tackle diverse nurse rostering instances and produce outstanding results.

几十年来，研究人员一直在研究护士排班问题。最初，这些公式相当原始，只包括一些必要的限制，但后来，公式变得更加复杂。尽管如此，一小部分研究在实践中实现了，许多病房仍然手动安排护士。在本文中，我们介绍了一种灵活的护士排班系统，该系统采用数学优化来自动安排护士轮班。我们与从业者合作开发了这个系统，以完全满足他们的需求。该系统由一个综合的混合整数规划 (MIP) 模型和一个灵活的框架组成。除了文献中的常见限制外，数学公式包括三个新的约束条件，进一步鼓励每位护士制定健康的工作时间表。此外，我们从文献中重新制定了一些常见的限制条件，并允许一个复杂的轮班结构，以满足实际医院病房的需求。这种灵活性提高了对具有不同需求的不同病房的适应性，对于解决从业人员面临的复杂护士排班问题至关重要。我们已经在丹麦两家医院的两个病房成功实施了该系统。我们展示了 MIP 模型以及 12 个真实世界排班实例的计算结果。此外，我们讨论了该系统的实际影响，并提供了使用它的从业者的一般反馈。总体，