A simulation–optimization framework for efficient hospital bed allocation in public health systems

In this paper, we develop a model for the bed allocation problem under Indonesia’s National Health Insurance Scheme (BPJS-JKN). This scheme categorizes patients and beds into three insurance classes. A significant challenge in this scheme is that patients often face bed shortages in their designated classes causing them to be treated in higher class beds or blocked and referred to another hospital. To optimize bed allocation in each class, we develop an overflow queueing model with repacking: when a patient arrives and finds all beds in their treatment class occupied, according to the BPJS-JKN, the patient is treated in the first higher class bed and returned immediately to their original class as soon as such a bed becomes available. We prove that we can use the product form result from the overflow loss network model, enabling the calculation of performance measures of the fractions of blocked patients and overflow patients. Using these measures, we formulate an optimization model to determine the optimal number of beds allocated in each class which maximizes hospital profitability. The performance measures are estimated using Harvey-Hills method which results in an unbiased estimator and the optimization is solved using simulated annealing to fasten the exploration of the solution space, i.e., all possible bed configurations. We apply our model to a use case inspired by the Academic Hospital of Universitas Gadjah Mada in Yogyakarta, Indonesia.