Integrated optimization of capacity allocation and timetable rescheduling for metro-based passenger and freight cotransportation

Multimodal integration can effectively address the challenges of sustainable urban freight, and utilizing a metro-based passenger and freight cotransportation system during off-peak hours represents a viable interim solution before establishing an underground logistics system. Given the constraints related to passenger carriage crowding, this study explores an integrated optimization problem that involves capacity allocation and timetable rescheduling for metro-based passenger and freight cotransportation lines under a train-shared mode. The final decision-making includes determining the size of the train fleet, the train timetable, the arrangement of carriages, and the assignment of freight flow. Since demand arrival rates are considered continuous functions over time, this integrated problem is formulated as a nonlinear mixed-integer model. To address the most complex aspects of the model, a gradient-based heuristic algorithm is proposed. Finally, numerical examples using real metro lines are provided to test the applicability and effectiveness of the proposed model and algorithm, and the impact of metro-based freight on passenger experience is also analyzed.