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.

After surgery most of the surgical patients have to be admitted in a ward in the hospital. Due to financial reasons and a decreasing number of available nurses in the Netherlands over the years, it is important to reduce the bed usage as much as possible. One possible way to achieve this is to create an operating room (OR) schedule that spreads the usage of beds nicely over time, and thereby minimizes the number of required beds. An OR-schedule is given by an assignment of OR-blocks to specific days in the planning horizon and has to fulfill several resource constraints. Due to the stochastic nature of the length of stay of patients, the analytic calculation of the number of required beds for a given OR-schedule is a complex task involving the convolution of discrete distributions. In this paper, two approaches to deal with this complexity are presented. First, a heuristic approach based on local search is given that takes into account the detailed formulation of the objective. A second approach reduces the complexity by simplifying the objective function. This allows modeling and solving the resulting problem as an ILP. Both approaches are tested on data provided by Hagaziekenhuis in the Netherlands. Furthermore, several what-if scenarios are evaluated. The computational results show that the approach that uses the simplified objective function provides better solutions to the original problem for instances based on the situation in HagaZiekenhuis. By using this approach, the number of required beds for the considered instance of HagaZiekenhuis can be reduced by almost 20 %.