Passenger-oriented rescheduling of trains and rolling stock for handling large passenger demand: linearized models with train capacity constraint

Document Type

Journal Article

Publication Date


Subject Area

place - urban, mode - rail, mode - subway/metro, infrastructure - rolling stock, ridership - demand, operations - scheduling, operations - performance, operations - capacity, economics - operating costs, planning - methods, planning - integration


Integrated optimization, urban rail transit scheduling, rolling stock circulation plan, passenger routing, approximate and exact reformulation


This paper focuses on adjusting the offline-planned schedules for urban rail networks in the case of large passenger demand. We simultaneously reschedule train services, adjust rolling stock plans, and find the best route for passengers in the updated train schedule. The goal is to improve transport performance for passengers and to balance it with operating cost, while respecting operational constraints. A mixed-integer nonlinear programming (MINLP) model is first proposed. Approximate and exact methods are further introduced to reformulate the nonlinear term in the MINLP model, resulting in mixed-integer linear programming (MILP) models. In the models, emergency train services can be added if necessary. Short-turning and stop-pattern adaptation can speed up the circulation of rolling stock (i.e. metro vehicles). Passengers with the same characteristics are gathered into a group, and the passengers of a group may follow different routes, depending on resource availability. Experimental results on a small-scale case study demonstrate the better performance of three exact reformulation methods, i.e. they can find the first feasible solution much faster (within 180 s) and obtain solutions with much higher quality within a certain computation time, in comparison with the other proposed approximate and exact methods. Moreover, the results identify the improved performance of the operation for passengers, up to 13% improvement when properly shortening the headway time and up to 69% if operating emergency trains.


Permission to publish the abstract has been given by Taylor&Francis, copyright remains with them.