Loading optimization of mixed-type containers for double-stack trains in multi-hub logistics

Abstract

Electrified double-stack container trains (DSTs) play a crucial role in modern logistics by offering increased capacity per trip, reduced rail car usage, lower transportation costs, and fewer emissions. However, optimizing container loading for DSTs is challenging due to constraints such as height limits, center of gravity balance, and other operational requirements. This paper introduces a mixed-integer programming (MIP) model aimed at maximizing transportation efficiency in multi-hub logistics networks, which include intermodal terminals and freight stations. The model supports mixed loading of containers of varying lengths (20/40/48 feet), heights (standard/high cube), load statuses (empty/loaded), and types (regular/foldable), originating from and destined for different locations. Additionally, it incorporates the combination of double-stack container well cars with other rail car types, increasing flexibility in rail car organization and accelerating DST departure times. To solve the complex loading problem, a hybrid genetic algorithm combined with simulated annealing (hybrid GA-SA) is developed. The hybrid GA-SA demonstrates strong performance in numerical case studies across different scales, significantly reducing the number of rail cars needed for large-scale logistics operations while achieving optimal loading configurations. Sensitivity analysis highlights key factors influencing overall transportation benefits. This study offers practical insights for enhancing the operational efficiency and profitability of DSTs and improving container hub throughput within modern logistics networks.