Vehicle scheduling problem with loss in bus ridership

•Formulation of the vehicle scheduling problem with loss in ridership.•Develop a column generation to solve very large instances of the problem.•Solution method was positively evaluated in random instances.•Tests in a real-life instance demonstrate the efficiency and efficacy of the approach. This paper presents an optimization approach for the bus scheduling problem in transit systems, considering the loss in ridership. This research work is motivated by the considerable loss in the demand for bus transportation in Brazil in the last few decades. The main objective of the optimization approach is to allow transit operators to adjust the fleet given the loss of passengers. The approach combines services trips within a small time interval in the timetabling, being the peak demand of the grouped trips adjusted to the heterogeneous fleet, defining a lower cost assignment for a fallen demand of passengers. The grouping strategy was formulated as an integer linear programming model. Due to the complexity of the formulation, a column generation-based algorithm has been designed. We carried out several experiments with the developed approach, using real-world data from a transportation company in southern Brazil and large randomly generated instances, considering different demand profiles and acceptable grouping trip intervals. The results of model allowed savings in the vehicle scheduling, while keeping good service levels for passengers. The model proved to support decision making in the planning of public transport, considering different operational scenarios.