We investigate a challenging task in ambulatory care, the minimizing of delays of patient transports. In practice, a limited number of vehicles is available for non-rescue transports. Furthermore, the dispatcher rarely has access to complete information when establishing a transport plan for dispatching the vehicles. If additional transport is requested on demand then schedules need to be updated, which can lead to long delays. We model the scheduling of patient transports as a vehicle routing problem with general time windows and solve it as a mixed-integer linear problem that is modified whenever additional transport information becomes available. We propose a modeling approach that is designed to determine fair and stable plans. Furthermore, we show that the model can easily be modified when transports need to satisfy additional requirements, e.g., during pandemics, exemplarily the Covid-19 pandemic. To show the applicability and efficiency of our modeling approach, we conduct a numerical study using historical data from the region of Middle Franconia. The results reveal and show that, by applying mathematical optimization - or, to be more precise by solving mixed-integer linear problem formulations - one can significantly decrease delays and have considerable potential for optimized patient transports.
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