Optimal subsidy scheme design for promoting intermodal freight transport

Waterborne transport is known to have low environmental impacts compared to other modes. This paper investigates the optimal container subsidies for shippers to promote intermodal shipping involving waterways in a regional transportation network. We consider a linear subsidy scheme consisting of a fixed-rate component and a variable component proportional to the sailing distance. The optimal subsidy design problem is formulated as a bilevel program to maximize the intermodal transport split of demand and minimize the subsidy expenditure. Faster methods are developed to solve the optimization problems of two special subsidy forms, i.e., fixed-rate and distance-based schemes. A case study of the Pearl River Delta region in China suggests that an optimally designed subsidy scheme can increase the intermodal split of container transport by 16%. Many insights are unveiled from the case study regarding the performance comparison between different subsidy schemes, the optimal schemes’ environmental impacts, and their effects on individual shippers and feeder ports. For example, the subsidy is less effective for shippers originating too far from or too close to the hub port and for highly time-sensitive or time-insensitive goods. Moreover, two commonly-used objectives, maximizing the intermodal split and minimizing the CO₂ emissions, are well aligned as they yield similar solutions. These insights can assist the local governments in determining the appropriate subsidy schemes and better understanding their overall effects.