A Mixed Integer Linear Programming Method for Simultaneous Multi-Periodic Train Timetabling and Routing on a High-Speed Rail Network

To avoid conflicts among trains at stations and provide passengers with a periodic train timetable to improve service level, this paper mainly focuses on the problem of multi-periodic train timetabling and routing by optimizing the routes of trains at stations and their entering time and leaving time on each chosen arrival–departure track at each visited station. Based on the constructed directed graph, including unidirectional and bidirectional tracks at stations and in sections, a mixed integer linear programming model with the goal of minimizing the total travel time of trains is formulated. Then, a strategy is introduced to reduce the number of constraints for improving the solved efficiency of the model. Finally, the performance, stability and practicability of the proposed method, as well as the impact of some main factors on the model are analyzed by numerous instances on both a constructed railway network and Guang-Zhu inter-city railway; they are solved using the commercial solver WebSphere ILOG CPLEX (International Business Machines Corporation, New York, NY, USA). Experimental results show that integrating multi-periodic train timetabling and routing can be conducive to improving the quality of a train timetable. Hence, good economic and social benefits for high-speed rail can be achieved, thus, further contributing to the sustained development of both high-speed railway systems and society

Demand-Oriented Train Timetabling Integrated with Passenger Train-Booking Decisions

In recent years, with the global energy shortage and severe environmental deterioration, railway transport has begun to attract great interest as a green transportation mode. One of the vital means to realize social sustainable development is to improve railway transportation systems, in which providing a demand-oriented train timetable with a higher service level is the most viable method. A demand-oriented train timetable problem generally deals with passengers’ train-choice decisions according to the queue principle, but it is not adapted to rail systems, such as China’s, where passengers usually book tickets a few days in advance by telephone or online instead of going to stations. This paper is devoted to modeling and solving the demand-oriented train timetabling problem integrated with passengers’ train-booking decisions. Firstly, a bi-level programming model is formulated for their integrated optimization on a rail network. Its upper-level model is to optimize train arrival and departure times at each visited station with the aim of reducing passengers’ total travel cost, while its lower-level model aims to determine passengers’ train-booking behavior using the user equilibrium theory. Then, a priority-based heuristic algorithm is designed to solve this model. It has two main steps at each iteration: one is to determine the number of passengers booking each train with a given train timetable, and the other is to improve the current train timetable based on the valuable information of passenger train-booking decisions. The performance, convergence, and practicability of the proposed method were analyzed based on the Changsha–Zhuzhou–Xiangtan intercity rail in China. Experimental results show the proposed method can effectively reduce the travel cost for passengers, creating a greater passenger demand for railway travel, which is beneficial to the sustainable development of railway systems and even society