Optimizing the integration of express bus services with micro-mobility: a case study

Considering a bus line, the problem of defining an express bus line consists in determining which stops of the original line will belong to the express line and the frequency of the new line. The objective of the optimization is a trade-off between the advantages of the passengers that benefit from the new service and the disadvantages of the passengers that cannot exploit the improved service. The advantages and disadvantages are measured in terms of total travel and waiting time.In this work we consider the introduction of micro-mobility, such as shared electric scooters or bikes, to mitigate the disadvantages and to increase the ridership of the express line. The contribution of the paper is twofold. On the one hand, we propose an improved mathematical model for defining an express bus line. The model is based on a longest path problem on an acyclic graph; thus, it is very efficient with respect to the other models in the literature. On the other hand, we consider the real case of two urban bus lines in the city of Milan and present the results computed on real passenger data. The results provide evidence that implementing an express line can improve total travel and waiting time. The time wasted by switching lines is in general higher than the time gained by the passengers. However, this can be compensated by the introduction of micro-mobility means of transportation.