Optimizing the strategic patient mix combining queueing theory and dynamic programming

In this paper we address the decision of choosing a patient mix for a hospital that leads to the most beneficial treatment case mix. We illustrate how capacity, case mix and patient mix decisions are interrelated and how understanding this complex relationship is crucial for achieving the maximum benefit from the fee-for-service financing system. Although studies to determine the case mix that is of maximum benefit exist in the literature, the hospital actions necessary to realize this case mix have seen less attention. We model the hospital as an M/G/∞ queueing system to evaluate the impact of accepting certain patient types. Using this queueing model to generate the parameters, an optimization problem is formulated. We propose two methods for solving the optimization problem. The first is exact but requires an integer linear programming solver whereas the second is an approximation algorithm relying only on dynamic programming. The model is applied in the department of surgery at a Dutch hospital. The model determines which patient types result in the desired growth in the preferred surgical treatment areas. The case study highlights the impact of striving for a certain case mix without providing a sufficiently balanced supply of resources. In the case study we show how the desired case mix can be better achieved by investing in certain capacity