A model for modifying the public transport service patterns to account for the imposed COVID-19 capacity

As public transport operators try to resume their services, they have to operate under reduced capacities due to COVID-19. Because demand can exceed capacity at different areas and across different times of the day, drivers have to refuse passenger boardings at specific stops to avoid overcrowding. Given the urgent need to develop decision support tools that can prevent the overcrowding of vehicles, this study introduces a dynamic integer nonlinear program to derive the optimal service patterns of individual vehicles that are ready to be dispatched. In addition to the objective of satisfying the imposed vehicle capacity due to COVID-19, the proposed service pattern model accounts for the waiting time of passengers. Our model is tested in a bus line connecting the University of Twente with its surrounding cities demonstrating the trade-off between the reduced in-vehicle crowding levels and the excessive waiting times of unserved passengers.