Demand-responsive Scheduling in Railway Transportation

Rural rail transportation can contribute significantly to achieving climate goals and encountering mobility challenges, especially by reactivating currently disused railway lines. Rural areas are mainly characterised by their dispersed demands. Thus, small highly automated rail vehicles could be operated on-demand and thus service-oriented. The operation of those networks is complex and the economic efficiency must be correspondingly high. Therefore, optimised resource planning is necessary. The paper focuses on the planning of a-priori known transport requests. The paper presents a formulation for the underlying Integer Programming mathematical model that optimises travel times and number of vehicles used under consideration of railway specific constraints such as headway times and deadlock prevention. The modelling goes beyond existing Dial-a-Ride approaches and adds the necessary routing constraints for rail systems as well as energy management constraints for potential refuelling or recharging. The potential for application of the approach is evaluated in a computational study. A validation scenario shows in an exemplary manner on the one hand how the constraints affect routing on a single track railway line and on the other hand how solving the model with a black-box solver such as Gurobi is handled for this scenario. On a real-world railway line, it can be shown that the Integer Programming solver is able to induce meaningful results for limited input sizes. Further potential improvements are discussed as well.