Demand-Driven Hub Network Design Under Uncertainty for Less-Than-Truckload Carriers

We consider a planning problem for freight transportation carriers that seek to profitably match supply with demand while recognizing uncertainty in shipment volumes. On the supply side, the problem determines transportation network design decisions regarding hub locations and the number of vehicles to be dispatched within the network in each period of the planning horizon. On the demand side, the problem incorporates the carrier’s ability to expand its service coverage by selectively accepting additional customer demands beyond its existing contractual base. Furthermore, although some of these additional customers seek a long-term commitment from the carrier, others are transactional and only require the transportation of a single set of shipments. We refer to this problem as the demand-driven hub network design under uncertainty problem and formulate it as a two-stage stochastic program. Further, we develop an enhanced Benders decomposition–based solution method for solving instances of this model. The solution methodology is inspired by partial Benders decomposition, leveraging a problem reformulation that embeds subsets of subproblem variables and constraints into the master problem while also incorporating valid inequalities to strengthen the formulation. We illustrate with an extensive computational study that the proposed method outperforms adaptations of benchmarks proposed for similar problems. We validate the benefits of solving the proposed model, which integrates decisions that have not yet been jointly modeled, with an analysis based on sample average approximation. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2022-03523].