Determine the Railway Undertakings’ profit function for TSA-OPEN

Determine the profit function F_o(x_o, x_-o) for each Railway Undertaking within the multi-objective formulation of the Time Slot Allocation in Open railway markets, which is currently unknown due to the need for confidential operator data to compute it.

Background

The paper formulates the Time Slot Allocation in Open railway markets (TSA-OPEN) as a multi-objective problem involving the conflicting interests of multiple Railway Undertakings (RUs). The natural objective functions would be the RUs’ profit functions, which depend on revenues from ticket sales, operational costs, and rolling stock investments.

However, the Infrastructure Manager (IM) lacks access to the confidential economic data needed to compute each RU’s profit function. To maintain transparency and enable decision-making, the authors replace the unknown profit objectives with a surrogate criterion that minimizes deviations between requested and allocated time slots.