Vehicle scheduling based on variable trip times with expected on-time performance

The vehicle scheduling problem (VSP) is concerned with determining the most efficient allocation of vehicles to carry out all the trips in a given timetable. The duration of each trip (called trip time) is normally assumed to be fixed. However, in practice, the trip times vary due to the variability of traffic, driving conditions, and passengers’ behavior. It is therefore difficult to adhere to the compiled schedule. This paper proposes a new VSP model based on variable trip times. Instead of being a fixed value, the duration of a trip falls into a time range that can be easily set based on the schedulers’ experience or the data collected by automatic vehicle location systems. Within this range, an expected trip time is provided according to the schedulers’ expectation of on-time performance. This new model can reduce schedulers’ pressure on setting fixed scheduled trip times. Moreover, computational results generated using CPLEX show that this model can increase the on-time performance of resulting schedules without increasing the fleet size.