Mitigating revenue loss and congestion surcharge by rail freight subsidy optimization in a multimodal multicommodity freight transportation market

Abstract

This study discusses a bilevel optimization problem for allocating rail freight subsidies in a multimodal multicommodity freight transportation market so as to simultaneously mitigate the revenue loss of the rail carrier and the congestion cost of cargo shippers choosing rail freight services. The lower-level part poses a freight transportation network equilibrium model that explicitly considers transportation capacity and bottleneck congestion. The upper-level part sets line-specific subsidies under a subsidy budget, minimizing a weighted sum of the total revenue loss and total congestion surcharge. Revenue loss reflects the potential loss of the rail carrier due to unused capacity, while congestion surcharge quantifies individual shippers’ waiting delay for the limited transportation capacity of rail lines. The solution procedure relies on a tabu search metaheuristic, in which the lower-level equilibrium problem is solved by the iterative balancing algorithm in the Lagrangian relaxation framework. The proposed optimization model and solution method are applied to the China-Europe freight transportation market. The results show that the optimized subsidy scheme significantly outperforms the current subsidy scheme by reducing both the total revenue loss and total congestion surcharge in all months of the year of 2019. Specifically, the optimized subsidy scheme reduces the total revenue loss by 27.3% and the total congestion surcharge by 64.2%. The weighting coefficient can effectively adjust the relative importance of the carrier and shippers in the freight subsidy design: minimizing only the total revenue loss reduces it by up to 16.3% but increases the total congestion surcharge by up to 540%; minimizing only the total congestion surcharge reduces it by up to 44.2% but increases the total revenue loss by up to 30.1%.

Keywords

China Railway Express, freight subsidy optimization, network equilibrium, revenue loss, congestion surcharge, tabu search

Article History

Received 2 August 2025; Accepted 29 October 2025

Recommended citation: Wang, R., Xie, C., Zou, B., & Fu, X. (2026). Mitigating revenue loss and congestion surcharge by rail freight subsidy optimization in a multimodal multicommodity freight transportation market. [Paper presentation]. 105th Annual Meeting of the Transportation Research Board, Washington, D.C., U.S.
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