Sustainable time-dependent intermodal hub-and-spoke logistic network considering hub failure: A mathematical model and a hybrid artificial bee colony algorithm

This paper addresses the design of a sustainable hub-and-spoke logistics network that integrates intermodal transportation between the hubs, hub failures, time dependency, and environmental parameters. Accordingly, we propose a novel mixed-integer linear programming (MILP) model and a hybrid artificial bee colony-based algorithm (HABCb) to minimize transportation costs and emissions in robust network configurations. The model is the first to simultaneously integrate intermodality, sustainability metrics, and hub disruption scenarios within a single framework. Computational experiments using real-life data from Turkey demonstrate that the proposed HABCb approach outperforms both genetic algorithm (GA) and artificial bee colony (ABC) algorithm. On medium-sized problem sets, it achieves average cost reductions of 7% compared to GA and 10% compared to ABC algorithm, while on large-sized problems the reductions are 10% and 15%, respectively. Furthermore, the HABCb approach provides faster convergence and higher-quality solutions for larger problem sizes. The findings highlight the practical and theoretical insights of incorporating sustainability, intermodality, and robustness into hub-and-spoke network design.