Minimizing Delays of Patient Transports with Incomplete Information including Covid-19 Requirements

We investigate a challenging task in ambulatory care, namely minimizing delays in patient transport. In practice, a limited number of vehicles are available for non-emergency transport. Furthermore, the planner rarely has access to complete information when establishing a transport plan for dispatching the vehicles. If additional transport is requested on demand, the schedules have to be updated, which can lead to long waiting times. We model this 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 different models that are designed to determine fair and stable plans that are protected against uncertainties. Furthermore, we show that the model can easily be modified when transports have additional requirements, such as an affiliation to different types that can for example have a different duration or need to be separated. This is demonstrated by incorporating requirements imposed due to the Covid-19 pandemic. To show the applicability of our approach, we conduct a numerical study using historical data and compare our optimization approach to existing scheduling approaches. This reveals that and show that, in general, mathematical optimization methods can significantly decrease the delay and have considerable potential for optimized transport schedules.