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.
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