Last train timetable optimization for metro network to maximize the passenger accessibility over the end-of-service period

Purpose-This study aims to improve the passenger accessibility of passenger demands in the end-ofoperation period.Design/methodology/approach-A mixed integer nonlinear programming model for last train timetable optimization of the metro was proposed considering the constraints such as the maximum headway,the minimum headway and the latest end-of-operation time.The objective of the model is to maximize the number of reachable passengers in the end-of-operation period.A solution method based on a preset train service is proposed,which significantly reduces the variables of deciding train services in the original model and reformulates it into a mixed integer linear programming model.Findings-The results of the case study of Wuhan Metro show that the solution method can obtain highquality solutions in a shorter time;and the shorter the time interval of passenger flow data,the more obvious the advantage of solution speed;after optimization,the number of passengers reaching the destination among the passengers who need to take the last train during the end-of-operation period can be increased by 10%.Originality/value-Existing research results only consider the passengers who take the last train.Compared with previous research,considering the overall passenger demand during the end-of-operation period can make more passengers arrive at their destination.Appropriately delaying the end-of-operation time can increase the proportion of passengers who can reach the destination in the metro network,but due to the decrease in passenger demand,postponing the end-of-operation time has a bottleneck in increasing the proportion of passengers who can reach the destination.

A Distributionally Robust Optimization Method for Passenger Flow Control Strategy and Train Scheduling on an Urban Rail Transit Line

Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous 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 passen-gers 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 pro-posed approaches.

Optimization method of urban rail train operational plan based on O-D time-varying demand

Purpose–Under the constraints of given passenger service level and coupling travel demand with train departure time,this study optimizes the train operational plan in an urban rail corridor to minimize the numbers of train trips and rolling stocks considering the time-varying demand of urban rail passenger flow.Design/methodology/approach–The authors optimize the train operational plan in a special network layout,i.e.an urban rail corridor with dead-end terminal yard,by decomposing it into two sub-problems:train timetable optimization and rolling stock circulation optimization.As for train timetable optimization,the authors propose a schedule-based passenger flow assignment method,construct the corresponding timetabling optimization model and design the bi-directional coordinated sequential optimization algorithm.For the optimization of rolling stock circulation,the authors construct the corresponding optimization assignment model and adopt the Hungary algorithm for solving the model.Findings–The case study shows that the train operational plan developed by the study’s approach meets requirements on the passenger service quality and reduces the operational cost to the maximum by minimizing the numbers of train trips and rolling stocks.Originality/value–The example verifies the efficiency of the model and algorithm.