Real-Time Integrated Re-scheduling for Tramway Operations

Our work aims to develop practical solution approaches for real-time dispatch of crews and vehicles for disruption management. The practical motivation for our research arose from the operations of a public tramway system in Hong Kong. The tram system shares the road with other vehicular traffic in an urban area of the city, and thus is subject to congestion and other disruptions (unexpected traffic conditions, accidents, etc.), making it a challenge to run to schedule. Delays accumulating and propagating over the course of a day can lead to poor service and high operational cost. In this research, we investigate how the availability of historical and real-time auto-sensed location and traffic information can be utilized to improve the real-time scheduling decisions. The historical information is used to estimate the travel times for each route during different periods of the day, while the real-time information about the tram locations is utilized to update the expected completion times of the current assignments for each motorman. Updated estimated travel times and completion times of tasks are fed to a mixed-integer programming model for re-optimization of the schedule.

The dynamic and integrated vehicle and crew scheduling problem for real-time control studied in our research has the following characteristics: 1) the actual travel times may deviate from the planned times and are dependent on the time of day and 2) while the on-going route/activity assigned to a motorman cannot be revised, the future assignments can be re-optmized when unexpected events occur. We adopt a rolling horizon approach to re-optimizing the future activities of the motormen from time to time. Upon an arrival of a motorman at a tram terminus or depot, he will be given a sequence of future task assignments, consisting of the routes to run and the scheduled departure times. The motormen will follow his revised sequence of future task assignments until the next re-optimization is performed. The objective is to achieve the target route frequencies in order to provide good quality of services to passengers, and minimize the violation of staff regulations (meal-break delays and overtime). While our application is motivated by tram services, our model can also be extended for other logistics services that suffer from daily transportation disruptions and require prompt recovery of schedules, particularly for those in an urban city setting.