A comprehensive integer programming formulation of the nurse rostering problem in Denmark

In this report, we present a comprehensive integer programming formulation for the nurse rostering problem (NRP). This model is the result of a collaboration between DTU Management and the Department of Data and Development Support (DU) at Region Zealand, with financial support from the Danish Ministry of Health. The work has been conducted in a close collaboration with healthcare practitioners at Danish hospitals, and the model has been iteratively built up to include all aspects that are needed to match the real-world problem that practitioners face. This report is organized as follows: Section 2 briefly introduces the problem this report considers. Section 3 presents the model, constraint by constraint, divided into subsections based on the characteristics of the constraints. Then, Section 4 describes the generation of conflict cliques, which are used to reduce the number of constraints, and at last, Section 5 presents concluding remarks. The appendices provide a summary, with a short description of the different constraints in Appendix A, an overview of the notation in Appendix B and the full model in Appendix C.