Operational patient-bed assignment problem in large hospital settings including overflow and uncertainty management

Managing patient to bed allocations is an everyday task in hospitals which in recent years has moved into focus due to a general rise in occupancy levels and the resulting need to efficiently manage tight hospital bed-capacities. This holds true especially when being faced with high volatility and uncertainty regarding patient arrivals and lengths of stay. In our work with a large German hospital we identified three main stakeholders, namely patients, nurses, and doctors, whose individual objectives and constraints regarding patient-bed allocation (PBA) lead to a potential trade-off situation. We developed a decision support model that tackles the PBA problem considering this trade-off, while also being capable of handling overflow situations. In addition, we anticipate emergency patient arrivals based on historical probability distributions and account for uncertainty regarding patient arrival and discharge dates. We develop a greedy look-ahead heuristic which allows for generating solutions for large real-life operational planning situations involving high ratios of emergency patients. We demonstrate the performance of our heuristic approach by comparison with the results of a near-optimal solution achieved by Gurobi’s MIP solver. Finally, we tested our approach using data sets from the literature as well as actual clinic data from our case study hospital, for which we were able to reduce overflow by over 96% while increasing overall utilization by 5%.