Combining machine learning and optimization for the operational patient-bed assignment problem

Fabian Schäfer, Manuel Walther, Dominik G. Grimm, Alexander Hübner

Research output: Contribution to journalArticlepeer-review


Assigning inpatients to hospital beds impacts patient satisfaction and the workload of nurses and doctors. The assignment is subject to unknown inpatient arrivals, in particular for emergency patients. Hospitals, therefore, need to deal with uncertainty on actual bed requirements and potential shortage situations as bed capacities are limited. This paper develops a model and solution approach for solving the patient bed-assignment problem that is based on a machine learning (ML) approach to forecasting emergency patients. First, it contributes by improving the anticipation of emergency patients using ML approaches, incorporating weather data, time and dates, important local and regional events, as well as current and historical occupancy levels. Drawing on real-life data from a large case hospital, we were able to improve forecasting accuracy for emergency inpatient arrivals. We achieved up to 17% better root mean square error (RMSE) when using ML methods compared to a baseline approach relying on averages for historical arrival rates. We further show that the ML methods outperform time series forecasts. Second, we develop a new hyper-heuristic for solving real-life problem instances based on the pilot method and a specialized greedy look-ahead (GLA) heuristic. When applying the hyper-heuristic in test sets we were able to increase the objective function by up to 5.3% in comparison to the benchmark approach in [40]. A benchmark with a Genetic Algorithm shows also the superiority of the hyper-heuristic. Third, the combination of ML for emergency patient admission forecasting with advanced optimization through the hyper-heuristic allowed us to obtain an improvement of up to 3.3% on a real-life problem.

Original languageEnglish
Pages (from-to)785-806
Number of pages22
JournalHealth Care Management Science
Issue number4
StatePublished - Dec 2023


  • Emergency forecasting
  • Emergency patient admissions
  • Hospital bed management
  • Machine learning
  • Operations management
  • Operations research
  • Patient-room assignment
  • Stakeholder integration


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