Combining Machine Learning and Optimization for the Operational Patient-Bed Assignment Problem

This paper develops a multi-objective decision support model for solving the patient bed assignment problem. Assigning inpatients to hospital beds impacts patient satisfaction and the workload of nurses and doctors. The assignment is subject to unknown patient arrivals and lengths of stay, 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 contributes by improving the anticipation of emergency patients using machine learning (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 an up to 17% better root mean square error when using ML methods compared to a baseline approach relying on averages for historical arrival rates. Second, we develop a new hyper-heuristic for solving real-life problem instances based on the pilot method and a specialized greedy look-ahead heuristic. When applying the hyper-heuristic in test sets we were able to increase the objective function by up to 3% in a single problem instance and up to 4% in a time series analysis compared to current approaches in literature. We achieved an improvement of up to 2.2% compared to a baseline approach from literature by combining the emergency patient admission forecasting and the hyper-heuristic on real-life situations.

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