Clustering clinical departments for wards to achieve a prespecified blocking probability

When the number of available beds in a hospital is limited, it can be beneficial to cluster several clinical departments such that the probability of not being able to admit a patient is acceptably small. However, not all clinical departments can be clustered for cross-infection reasons. In addition, patients from one clinical department should not be spread out over the entire hospital as this complicates the process of doing rounds and may result in alternate level of care. In this paper, we consider a situation where wards with a fixed number of beds are given. The question is how to cluster the clinical departments and to determine the assignment of these clustered departments to the available wards such that the assigned beds are sufficient to guarantee a blocking probability below a prespecified percentage. We first give an exact formulation of the problem to be able to achieve optimal solutions. However, computational experiments show that the resulting computation times for this model are too long for it to be applicable in practice. To reduce the computation time, we introduce two heuristic solution approaches. The first heuristic uses the same formulation as the exact model, however, the number of required beds is approximated by a linear function. The resulting model is again solved by an exact solver. The second heuristic uses a restricted version of the exact model within a local search approach. Hereby, the local search is used to determine the assignment of clinical departments to clusters and the exact model is used to determine the assignment of clusters to wards.