Integrated Train Timetabling and Rolling Stock Scheduling Model Based on Time-Dependent Demand for Urban Rail Transit

1 The congestion problem of urban transportation is becoming increasingly critical for many 2 metropolises. The Urban Rail Transit (URT) system has attracted substantial attention due to its 3 safety, high speed, high capacity and sustainability. With a focus on providing a holistic 4 modelling framework for train scheduling problems, this paper proposes a novel optimization 5 methodology that integrates both train timetabling and rolling stock scheduling based on time6 dependent passenger flow demands. We particularly consider the trade-off between waiting times 7 of passengers and operation costs of the URT system. Using train paths and rolling stock 8 indicators as decision variables, this problem is formulated as a bi-level programming model. The 9 simulated-annealing (SA) based heuristic algorithm is employed to solve the proposed model and 10 generate approximate optimal solutions. Numerical examples are developed to demonstrate the 11 performance of the proposed approaches. The calculation results and comparisons indicate that, 12 even for the large-scale Beijing rail transit operations, the SA-based algorithm can efficiently 13 produce the approximate optimal scheduling strategies within acceptable computational limits, 14 demonstrating the practical value of our proposed approaches. 15 16