A Bi-Objective Column Generation Approach for Real-World Rolling Stock Circulation Planning Problems

To make the planning in rail transport more efficient, this work deals with a real-world Rolling Stock Circulation Problem. In this study, sequences of trips and empty runs are formed for each traction unit to cover all scheduled trips. Practical restrictions for station-wise balanced planning are integrated into a Set Covering Problem formulation which is solved with a column generation approach. The decision makers give two objectives, the number of traction units and empty run kilometers. They have different priorities at different planning stages, and it is hard for the decision makers to quantify the cost of one traction unit or one empty run kilometer. A bi-objective column generation approach is built by integrating the epsilon constraint method, which is recognized as a classical method to handle multi-objective optimization problems. To evaluate the relation between both criteria, the algorithm is tested using real-world use cases. The generated circulation plans are presented in solution fronts, illustrating the targets' mutual influence. The identified trade-off between fewer traction units or fewer empty run kilometers can serve as decision support for planners in railway systems.