Hub-and-spoke network and line plan optimisation with formation-based discount for rail-road freight

Seaport-affiliated operators face challenges in routing containerised freight through China's rail-based overland network. This study integrates formation-based incremental unit (IU) discounts into joint service network design and rail-sea intermodal train (RSIT) line planning. Heterogeneous shipments are assigned to existing railway container transport (ERCT) services, new RSITs, and direct trucking. The problem is formulated as a mixed-integer linear programme and solved using an adaptive genetic algorithm with problem-specific decoding rules. Results show that IU discounts promote a concentrated hub-and-spoke network, improving ERCT utilisation and RSIT formation size. Network configurations remain stable across a range of discount levels, revealing a discontinuous response to discount magnitude. Most adjustments occur at the initial discount levels, while subsequent increments yield progressively smaller changes. These findings demonstrate the practical value of formation-based discounts for railway enterprises and provide a reference for operators in service network design under such discount schemes.