Improving the Service Level of Bus Transportation Systems: Evaluation and Optimization of Bus Schedules’ Robustness

Abstract

This study proposes an optimization model to improve the robustness of an existing bus schedule. Robustness represents the ability of schedules to absorb deviations from the timetable and to prevent their propagation through the daily operations. The model developed proposes an optimal assignment of arrival times and distribution of slacks among Time Control Points of a bus line, in order to minimize delays and anticipations from schedule. This required the use of data collected through GPS devices installed in buses, informing the location of buses during their daily operation. The robustness of bus schedules was evaluated through the quantification of delays and anticipations of real observations of bus shifts by comparison with the timetable. The performance measures used to evaluate robustness are the average delay (or anticipation) of buses by comparison with the timetable, and the probability that a passenger that arrives on time according to the timetable will miss the bus or have to wait more than a specified threshold at a Time Control Point. We also compared the improvement of the schedule proposed by the optimization model with the original schedule. The results obtained in a real-world case study, corresponding to a bus line operating in Porto, showed that the model could return an improved schedule for all performance measures considered when compared with the original schedule.