Simultaneous line planning and timetabling based on a combinational travel network for both trains and passengers: a mixed-integer linear programming approach

Abstract

This paper is devoted to designing a mixed-integer linear programming to solve the simultaneous line planning and timetabling problem. A directed graph is first constructed to represent the combinational travel network for both candidate trains and passengers. Through this graph, it is easy to simultaneously describe trains’ operation choices, passengers’ travel choices, and their restrictive relations. Based on it, a mixed-integer linear programming model with many binary and non-negative integer decision variables is built to simultaneously optimize the line plan, timetable, and passenger travel choices, which can be efficiently solved using commercial solver CPLEX for small-scale network, while a decomposition strategy is required to combine with CPLEX for large-scale network. A set of numerical experiments are carried out to analyse the impacts of flow sub-units, number of candidate trains, and weight factors. Finally, we conduct two case studies for testing the practicability of our proposed method.

KEYWORDS:

• Timetabling
• line planning
• rail network
• combinational travel network
• mixed-integer linear programming

Acknowledgements

The authors are responsible for all results and opinions expressed in this paper. In addition, we thank PRS (www.Proof-Reading-Service.com) for its linguistic assistance during the preparation of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Lianbo Deng http://orcid.org/0000-0001-6114-9093

Additional information

Funding

This research work was partially supported by the National Natural Science Foundation of China [grant number 71871226, U1934216, U1834209] and the Natural Science Foundation of Hunan Province, China [grant number 2018JJ3698].