Managing the patient portfolio using mathematical programming: decision support guidelines using a real-world use case at a university hospital

Many hospitals in Germany are facing escalating economic pressures. After several years of stagnation, the number of inpatient hospital treatments dropped by in 2020 compared to the previous year. This negative tendency can also be seen in operating theaters (OTs). Strategic management of the case mix in hospital OTs now necessitates a solid data foundation. The case mix and the case mix index have become central economic indicators in contemporary hospital operations. In this work, we develop a mathematical model for case mix optimization at Augsburg University Hospital in Germany, which is based on an extensive data analysis with descriptive methods. The optimization model is subject to rigorous testing and evaluation through an extensive series of scenario analyses. The primary objective is to calculate a revenue-maximizing patient mix while respecting the available scarce personnel resources in the OT and intensive care unit. This research marks a pioneering effort in delineating the practical integration of case mix planning into a hospital’s routine operations using mathematical optimization. The analyses reveal a strong correlation between an upsurge in revenue and an increased number of cases. Furthermore, the results demonstrate that strategic planning of the patient mix has the potential to enhance revenue with existing resources. Even though the optimal patient mix may not be directly implementable in practice, the findings yield valuable insights for managerial decision-making. A critical examination of these results also fosters a nuanced discourse on the utilization of optimization models as decision support tools within hospital management.