Combining clinical departments and wards in maximum-care hospitals

Sharing bed capacity across clinical departments improves bed availability via pooling effects. This means in effect that fewer beds are required to satisfy a given service level when combining departments and wards into groups. However, this increases the complexity of tending to inpatients and therefore creates what we term pooling costs. To solve the trade-off, we suggest an integer linear programming modeling and solution approach that is designed on a generalized set partitioning problem. The approach finds the cost-minimal combination of departments and wards in a maximum-care hospital that satisfies maximum walking distance thresholds for doctors and patients. In particular, costs associated with holding the required bed capacity are minimized while also considering seasonality of weekly demand as well as personnel qualification costs and management costs incurred by combining departments and allocating pooled ward capacity to these combinations. In addition, maximum walking distances between wards and central facilities for the combinations obtained are minimized. Our modeling and solution approach was co-developed and implemented at a large German maximum-care hospital comprising 22 clinical departments. As a result, the number of beds needed to maintain a unified service level of 95% can be reduced by 3.3%, while cutting costs by 2.1%. We also perform several sensitivity analyses and show general applicability by using simulated data for generalized and very large hospital settings.