Abstract
Freight transportation within the hub-assisted systems enhances economies of scale for carriers by consolidating logistics operations through central hubs, thereby increasing efficiency and reducing costs. Optimally designing such transportation systems creates competitive advantages for carriers, enabling them to reduce shipping prices and, consequently, capture a larger share of the market from shippers’ demand. This research addresses the joint optimization of intermodal transportation hub network design and pricing decisions under price-dependent and uncertain demand, with the objective of maximizing carrier's profit. Since the uncertain shipping demand follows a nonlinear relation with price, the carrier not only optimizes shipping network design but also seeks optimal pricing strategies to attract shippers and increase market share. In the studied transportation network, each origin–destination (O-D) freight shipping demand is first routed from its origin to the origin hub (OH); The freight is then transported from the OH to the destination hub (DH), and finally, it is delivered from the DH to its destination. Following the problem setting and formulation, we first construct a data-driven ambiguity set using machine learning algorithms and then develop a two-stage distributionally robust optimization (DRO) model to address shipping demand uncertainty. To enhance computational efficiency, we develop a hybrid solution approach combining machine learning and decomposition (ML-Decomposition). The proposed ML-Decomposition method first partitions the problem into sub-problems focusing on hub network design, freight flow assignment, and pricing. Then, it employs second-order nonlinear regression to determine the optimal price and utilizes Benders-style cutting plane decomposition, along with valid inequalities, to jointly optimize hub network design and flow assignment. Finally, to assess the effectiveness of the proposed ML-Decomposition solution method and evaluate the robustness of DRO model, a comprehensive computational study is conducted on a diverse set of instances, demonstrating the superiority of the proposed methodology. Across these benchmarks, the proposed ML-Decomposition attains up to 19.5 % higher profit and reduces computational time by as much as 79 % compared with off-the-shelf Gurobi solver. Furthermore, the benefit of incorporating pricing decisions is analyzed to derive valuable managerial insights.
Document Type
Journal Article
Date of Publication
2-1-2026
Volume
186
Publication Title
Computers and Operations Research
Publisher
Elsevier
School
School of Business and Law
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Comments
Shekarabi, S. a. H., Mavi, R. K., Macau, F. R., Papi, A., & Teymouri, A. (2025). Machine learning-enriched distributionally robust optimization and hybrid decomposition to joint optimization of transportation hub network design and pricing. Computers & Operations Research, 186, 107291. https://doi.org/10.1016/j.cor.2025.107291