Optimal railway freight subsidy scheme for hinterland container transportation network considering carbon tax and shippers’ choice behavior

This paper focuses on the railway freight subsidy optimization problem considering the impact of carbon tax in the port-hinterland transportation network with three modes and two ports. A bi-level model is developed to express the relationship between the government and shippers. At the upper level, the government formulate the optimal railway freight subsidy scheme serving multiple ports from a global optimization perspective, aiming to minimize total subsidy expenditure while achieving the railway volume target. In contrast, the lower-level model describes shippers’ choice behavior for ports and transportation paths by the capability-constrained nested Logit model, where the determining utility function is expressed as the opposite of generalized transportation costs consisting of freight fees, time, and carbon emissions costs. Given that the lower-level model shows convex optimization properties, the Karush-Kuhn-Tucker conditions is used to convert the bi-level model into an equivalent single-level model, solved by the active-set algorithm. Results indicate subsidies can boost railway volume, and the proposed optimal subsidy scheme is superior to individual port-centric subsidy schemes. Railway links can be classified into five categories based on subsidy amounts and utilization rates, and the fourth category with subsidy amount greater than 0 and 100 utilization rate is the main target link for the subsidy scheme, which serves port-proximate regions with strong freight demand. Moreover, subsidy-driven growth in railway volume primarily comes from demand nodes with railway stations.