Machine Learning-Empowered Benders Decomposition for Flow Hub Location in E-Commerce

Tao Wu (), Weiwei Chen (), Jean-François Cordeau () and Raf Jans ()
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Tao Wu: School of Economics & Management, Tongji University, Shanghai 200092, China
Weiwei Chen: Department of Supply Chain Management, Rutgers University, Piscataway, New Jersey 08854
Jean-François Cordeau: Department of Logistics and Operations Management, HEC Montreal, Montreal, Quebec H3T 2A7, Canada
Raf Jans: Department of Logistics and Operations Management, HEC Montreal, Montreal, Quebec H3T 2A7, Canada

INFORMS Journal on Computing, 2026, vol. 38, issue 2, 463-489

Abstract: This paper studies a flow hub location problem (FHLP) stemming from recent trends in network design for e-commerce businesses. Specifically, e-commerce companies are flexible and agile in reoptimizing their logistics networks, including supplier (origin) and customer zone (destination) decisions. Furthermore, a large number of commodities (flows) and a relatively small sales volume for each product incentivize e-commerce retailers to lease warehouse spaces as hubs, yielding a large number of hub location candidates. As such, the proposed FHLP determines the origin and destination of each flow simultaneously with the hub location and flow routing decisions in contrast to the classical hub location problems, where the origins and destinations of all flows are predetermined. To solve this large-scale optimization problem, we propose an optimization algorithm that combines Lagrangian relaxation and Benders decomposition. Novel acceleration techniques, such as a clustering-empowered multicommodity Benders reformulation, learning-empowered elimination tests, and variable reduction techniques, are further developed to improve the performance and convergence of the algorithm. The efficiency of the proposed algorithm is evaluated via extensive computational experiments. The numerical results show that when compared with five other benchmark methods, the proposed algorithm can achieve optimal solutions faster for small-sized test instances and reduce optimality gaps for large-sized ones. For example, the proposed method achieves optimal solutions for a set of 10 test instances, with node sizes ranging from 225 to 450, within 20 minutes on average. In comparison, the automatic Benders decomposition method implemented in the commercial CPLEX solver achieves an average optimality gap of 2% within one hour.

Keywords: e-commerce; hub location; machine learning; mixed-integer linear programming; Benders decomposition (search for similar items in EconPapers)
Date: 2026
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