An exact method for the bus dispatching problem in rolling horizons

In this work, we adapt the rolling-horizon approach of Eberlein et al. (2001) for adjusting the dispatching times of buses at each rolling horizon. The industry practice is to adjust the dispatching time of a bus once it departs from the first stop while considering that future trips will operate as planned. In contrast, a rolling-horizon approach adjusts simultaneously the dispatching times of all trips that operate during a pre-determined time interval resulting in a coordinated effort to maintain the target headways. Due to the increased number of dispatching time decisions, this coordinated effort increases the computational burden. To reduce the computational cost, we introduce a nonlinear program and we propose a novel reformulation that limits the recursive relations of the optimization problem. Our program is proved to be convex and can be solved to global optimality under a limited computational cost. In addition, it outperforms myopic methods that adjust the dispatching time of each bus trip in isolation. The sensitivity of our method to travel time and passenger demand fluctuations is investigated on a simulation scenario of bus line 15L in Denver.