Joint optimization of train scheduling and rolling stock utilization planning: a virtual composition mode

In the context of the increasing unbalanced passenger flow in both time and space, the conventional fixed formation mode is no longer able to cater to the dynamic demands of passengers. Thus, this paper presents a mixed-integer nonlinear programming model that aims to optimize train scheduling, rolling stock utilization planning, and passenger flow control strategy by incorporating virtual formation mode, in which the virtual formation enables trains to modify their composition through coupling/uncoupling operations at stations. The model with nonlinear constraints is subsequently converted into a model with linear constraints, making it amenable to direct solution using Gurobi solver. Finally, a series of numerical experiments are conducted using actual data from the Beijing Changping metro line. The computation results show that the proposed method effectively meets passenger demands while simultaneously ensuring reasonable reductions in operational costs.