Tabea Brandt: Combinatorial Analysis of Patient-to-Room Assignment in Hospitals
Hospitals are under tremendous cost pressure and must achieve a balance between economic efficiency and a treatment that focuses on the patient. To improve clinical operations and patient safety, methods from economics, mathematical optimization and IT-driven management systems are imported into the operational management of hospitals. The goal is to maintain the high quality in medical care while lowering the costs. A major challenge in this optimization process is the changing demand arising from emergencies or patients without appointments, which are difficult to forecast, and thus are, in general, not integrated into the planning process. In this part of the project we will focus on the integration of such uncertainties into the operational planning and utilization of hospital beds.
In the next subsection we will give a rough overview of existing scientific work. Finally, we will describe our approach to these problems in detail.
In 2012, Hulshof et al.  published a detailed bibliography and taxonomic classification on methods from operations research applied to problems in health care. Uncertainties are part of most decision problems in planning and controlling in health care. Mainly methods from queuing theory, Markov processes, and stochastic programming are used to include them into the optimization process, e.g., [1, 2, 3, 23, 40]. Besides dealing with uncertainties, Hulshof et al.  identify the challenge for researchers to develop integral models of different hierarchical planning levels and services in health care.
The location of beds and the assignment of patients to these beds in a hospital is studied in operations research at the strategical, tactical and operational level. To support strategic planning queuing techniques, simulation and models from mathematical programming are already used. Traditionally, these planning decisions are based on target occupancy levels. However, Green  points out that, due to high fluctuations, different measurements such as patient waiting time  or patient refusal rate  need to be integrated into the optimization process. In , Ma and Demeulemeester combine the allocation of beds with the appointment of elective patients. In order to integrate emergencies, they reserve a fixed capacity. The Patient-to-Bed Assignment Problem on an operational level has been formalized in 2010 by Demeester et al. . They use a combination of a patient-bed-suitability rating, the number of inpatient transfers and the number of mixed-gender-occupied rooms as the objective function and propose a hybrid tabu search algorithm for this problem. Later, the problem is reformulated to patient-to-room assignment, as it is generally assumed that all beds, located in the same room, are equal. Also more practical variants and other exact and heuristic approaches for patient-to-room assignment have been published, e.g., [7,8,50].
Contrary to all previously published work, we do not regard a weighted combination of the patient-bed-suitability rating, the number of inpatient transfers and the number mixed-gender-occupied rooms as the objective function. Choosing appropriate weights is very challenging and, also, no procedure has yet been proposed to check afterward if good weights have been chosen. Also, using a weighted combination prevents us from gaining better insights into how the different objectives influence each other. For this reason we keep the three different aspects separated and treat them as independent objective functions.
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