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Optimizing geriatric care capacity from a system perspective

Beursgens, A.E. (2024) Optimizing geriatric care capacity from a system perspective.

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Abstract:Driven by the enormous costs of bed-blocking days in hospitals, this research develops mathematical models to determine the optimal capacity of the Verpleeg-, Verzorgingshuizen en Thuiszorg (VVT) organisations in the region of Enschede. Bed-blocking occurs when a patient is ready to leave the hospital, but appropriate care in the geriatric aftercare institutions is not immediately available. The optimal capacity minimizes the total costs of bed-blocking days, unused VVT beds and used VVT beds, in which the financial objectives of the hospital and the VVT are combined. The situation is modelled as an overflow system with immediate call packing. In addition to the formula for the exponential call packing system by Van Dijk and Schilstra (2022), approximations for a call packing system with general service times are studied. In addition to a stationary analysis, a time dependent analysis based on the Modified Offered Load approximation is performed as well. The performance measures obtained from the queueing analysis are the input to the optimization phase. A Mixed Integer Program is introduced which allows the time dependent behaviour of the capacity to be constrained. Moreover, possible interactions between the capacities of multiple VVT types are considered, like shared capacity. A simulation is used to evaluate the performance of the outcomes of the mathematical models. A numerical analysis is performed based on the data of the geriatric rehabilitation care division of a VVT organisation. The optimal capacity is shown to decrease when the time in overflow contributes more to a reduction in the residual length of stay in the VVT organisation. Moreover, it is influenced by the ratio between the cost of an overflow bed and the cost of an unused bed. The mathematical models and choice of financial objective function allow for a comparison between two situations: the situation in which the VVT organisations individually decide on their capacity and the situation in which the financial incentives of the hospital are taken into account as well. The results suggest that cooperation between the hospital and the VVT would be beneficial and that it would be reasonable to compensate the VVT organisations for increasing their capacity.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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