Public transport vehicle scheduling featuring multiple vehicle types

• New methodology is proposed for the multiple vehicle types vehicle scheduling problem (MVT-VSP).
• The methodology is based on a minimum-cost network flow model utilizing sets of Pareto-optimal timetables.
• Four separate methods are suggested, all of which are solved optimally.
• It is shown that allowing vehicle types substitutions is highly beneficial.
• Using sets of Pareto efficient timetables, as input, can reduce the scheduling cost by more than 15%.

Vehicle scheduling is a crucial step of the public transport planning process because it results in the number of vehicles required, thus it is directly related to fixed cost and labor cost. It is desirable, therefore, to minimize the number of vehicles used and operational cost. This paper proposes a new methodology for the multiple vehicle types vehicle scheduling problem (MVT-VSP). The methodology is based on a minimum-cost network flow model utilizing sets of Pareto-optimal timetables for individual bus lines. Given a fixed fleet size the suggested methodology also allows a selection of the optimal timetable. The method developed enables to stipulate the use of a particular vehicle type for a trip or to allow for a substitution either by a larger vehicle or a combination of smaller vehicles with the same or higher total capacity. Moreover, a variation of the method portrayed makes it possible to construct sub-optimal timetables given a reduction of the vehicle-scheduling cost. It is demonstrated that a substitution of vehicles is beneficial and can lead to significant cost reductions in the range of more than 27%. The suggested methodology is applied to a real-life case study in Auckland, New Zealand, and the results show improvements of greater than 15% in terms of the cost of fleet compared with vehicle schedules that are provided by standard models.