The novel mixed passengers and freights transportation mode has brought both opportunities and challenges to the operation and management of high-speed railway in China. This paper proposes an integer linear programming model for the collaborative optimization problem of train schedules and freight allocation on a shared freight and passenger high-speed railway system to minimize the train dwell time, the number of detained freight, and operating costs, where the arrival and departure times of trains, the formation of trains, and the freight allocation are the decision variables. Then, extensive numerical experiments based on the operational data of the Beijing-Shanghai high-speed railway line are conducted to verify the effectiveness of the model, and the CPLEX optimization solver is used to solve the problem. The results show that the proposed method can improve the train capacity by flexibly deciding the train schedule and increasing the train composition while minimizing the impact on the quality of passenger service. Compared to the optimization method with fixed train timetables, the integrated optimization method can significantly improve the freight transportation capacity while only a slight increase in stopping time, providing theoretical support for the relevant operational departments to make mixed transportation plans.

Regular coronavirus disease 2019 (COVID-19) epidemic prevention and control have raised new requirements that necessitate operation-strategy innovation in urban rail transit. To alleviate increasingly serious congestion and further reduce the risk of cross-infection, a novel two-stage distributionally robust optimization (DRO) model is explicitly constructed, in which the probability distribution of stochastic scenarios is only partially known in advance. In the proposed model, the mean-conditional value-at-risk (CVaR) criterion is employed to obtain a tradeoff between the expected number of waiting passengers and the risk of congestion on an urban rail transit line. The relationship between the proposed DRO model and the traditional two-stage stochastic programming (SP) model is also depicted. Furthermore, to overcome the obstacle of model solvability resulting from imprecise probability distributions, a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form. A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming (MILP) solver is developed to improve the computational efficiency of large-scale instances. Finally, a series of numerical examples with real-world operation data are executed to validate the proposed approaches.

Considering the continuous arrival characteristics of outside arrival passenger flow and the impulsive feature of transferring passengers, this paper investigates the metro train timetabling and passenger flow control strategy under the influence of transferring passengers. This paper formulates an integer nonlinear collaborative optimization model for the metro train timetabling and passenger flow control strategy, which aims to minimize the number of detained passengers. The proposed model is reformulated into an integer linear programming model by introducing the 0-1 decision variables. A case study of a real-world urban rail transit line is performed to verify the effectiveness of the proposed approach, which is solved by the CPLEX software. The results reveal that, the proposed approach has good optimization quality and computational efficiency. Compared to the plan only optimize timetables, the obtained plan reduced the number of detained passengers by 17.69% and the service level was significantly improved. This study provides theoretical support for the high-quality operation of the urban rail transit system.