Network revenue management game in the rail freight industry

Abstract

The study aims to design the optimal track access tariff to coordinate the relationship between an Infrastructure Manager (IM) and a Freight Operating Company (FOC) in a vertical separated railway system. In practice, the IM takes advantage of leader position in determining the prices to unilaterally maximise its profits without the collaboration with the FOC, which leads to a sub-optimal situation. The interaction between the IM and the FOC is modelled as a network-based Stackelberg game. First, a rigorous bilevel optimisation model is presented that determines the best prices for an IM to maximise its profits without any collaboration with the FOC. The lower level of the bilevel model contains binary integer variables representing the FOC’s choices on the itineraries, which is a challenging optimisation problem not resolved in the literature. The study proposes a uniquely designed solution method involving both gradient search and local search to successfully solve the problem. Secondly, an inverse programming model is developed to determine the IM’s prices to maximise the system profit and achieve global optimality. A Fenchel cutting plane based algorithm is developed to solve the inverse optimisation model. Thirdly, a government subsidy based pricing mechanism is designed. To identify the optimal amount of subsidy, a double-layer gradient search and local search method is developed. The proposed mechanism can lead to the global optimality and ensure that the IM and the FOC are better off than the above two scenarios. Numerical cases based on the data from the UK rail freight industry are conducted to validate the models and algorithms. The results reveal that both the optimal prices obtained via inverse optimisation and the subsidy contract outperform the non-cooperation case in the current industrial practice; and that the cooperation between the IM and the FOC in determining track access tariff is better than non-cooperation.