A dynamic stop-skipping model for preventing public transport overcrowding beyond the pandemic-imposed capacity levels

We consider the dynamic scheduling of skip-stop patterns in public transportation. Operators of fixed-line public transportation services seek to reduce their vehicle running times by skipping stops that will not impact significantly the waiting times of passengers. This can result in an improved trade-off between vehicle running times and passenger waiting times allowing to slightly increase the travel times of passengers in order to reduce the operational costs. Although there exist several decision support models for dynamic stop-skipping, these models do not consider the impact of skipped stops to in-vehicle crowding. That is, apart from the increased passenger waiting times, a skipped stop might result in an increased amount of passengers boarding the next trip of the line resulting in overcrowding. To rectify this, we propose a mixed-integer nonlinear model that incorporates the objective of avoiding in-vehicle overcrowding when making stop-skipping decisions. This is particularly relevant in situations where passengers are no longer able to find a seat or they have to maintain social distancing inside the vehicle because of a pandemic. Because the stop-skipping problem is NP-Hard, we introduce a number of valid inequalities that tighten its solution space and we demonstrate the performance of our model in benchmark problem instances.