Bus holding of electric vehicles: an exact optimization approach

In high-frequency electric bus services with more than five buses per hour, bus operators strive to increase the service regularity by minimizing the deviation between the planned and actual headways. In this pursue, bus operators apply corrective control strategies, such as bus holding(s) at control point stops. This study expands the traditional headway-based models of bus holding to
cater for the planned arrival times of electric buses at the respective charging points. To this end, this study models the bus holding problem for electric buses considering the scheduled charging times in the objective function. The resulting mathematical program is not smooth and cannot be solved to global optimality. To rectify this, this study introduces slack variables and proposes a problem reformulation into a convex, nonlinear program that can be easily solved to global optimality with exact optimization methods. The proposed bus holding logic is shown to reduce significantly the delayed arrivals at the charging points (up to 34%), while the average passenger waiting times exhibit a marginal increase when compared to the existing control methods (up to
1.08%).