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Network revenue management game in the railway industry: Stackelberg equilibrium, global optimality, and mechanism design

Lookup NU author(s): Dongjun Li, Dr Dewan Islam, Professor Mark RobinsonORCiD, Professor Jingxin DongORCiD, Bella Reichard



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


© 2023 The Author(s). Many countries have adopted the vertical separation governance structure in the railway freight industry over the past decades. Under this governance structure, an Infrastructure Manager (IM), which might be an independent company or a government agency, sells train itineraries to Freight Operating Companies (FOCs). After purchasing the itineraries, a FOC will have the rights to run trains on the designated paths at the designated times and thus can provide transport service to shippers. In the process, an IM needs to determine a list of prices for their train itineraries; and a FOC needs to determine which train itineraries to purchase to serve uncertain customer demands based on the IM's price list. This study considers the interaction between an IM and a FOC as a network-based Stackelberg game. Our study first formulates a bi-level optimisation model to determine the equilibrium prices that the IM would charge to maximise its own profits unilaterally without collaboration. A method involving gradient and local search has been developed to solve the bi-level model. Secondly, an inverse optimisation model is proposed to determine the prices leading to global optimality. A Fenchel cutting plane-based algorithm is developed to solve the inverse optimisation model. Thirdly, a subsidy contract is designed for the game to coordinate the players’ decisions. A two-layer gradient search method is developed to determine the optimal subsidy rate. Numerical cases based on the UK rail freight industry data are provided to validate the models and algorithms.

Publication metadata

Author(s): Li D, Islam DMZ, Robinson M, Song D-P, Dong J-X, Reimann M

Publication type: Article

Publication status: Published

Journal: European Journal of Operational Research

Year: 2024

Volume: 312

Issue: 1

Pages: 240-254

Print publication date: 01/01/2024

Online publication date: 06/07/2023

Acceptance date: 30/06/2023

Date deposited: 30/06/2023

ISSN (print): 0377-2217

ISSN (electronic): 1872-6860

Publisher: Elsevier BV


DOI: 10.1016/j.ejor.2023.06.044


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