Integrated optimization of train schedules and cotransportation plans for a passenger-freight metro line

Abstract

Against the backdrop of developing metro-based passenger and freight cotransportation plans, this study investigates the integrated optimization problem of train schedules and flow control for a metro line shared by passenger and freight transport, in which passengers and freight share trains. Given a set of time-dependent passenger and freight demands, this problem requires determining the space--time trajectories and passenger/freight capacities for trains while also assigning the demands to these trains. By introducing the train selection variables, carriage arrangement variables and flow assignment variables, the problem of interest is formulated as an integer linear programming model for minimizing the weighted sum of the number of freight carriages, the waiting time of all passengers and the delay of all freights. The primal model has good mathematical properties, i.e., it is equivalent to a mixed-integer linear programming model, which allows the commercial solver to find the exact solution of the model more efficiently. To verify the effectiveness of the proposed method, several numerical examples with different scales are tested. The relevant results show that only by integrating the optimization of train schedules and cotransportation plans can the efficiency of the whole cotransportation system be improved to the greatest extent.