Multiple allocation hub location with service level constraints for two shipment classes

In this paper, we study a hub network design problem arising in the context of a third-party logistics (3PL) service provider, which acts as an intermediary between shippers and carriers. A 3PL service provider usually caters to different classes of shipments that require different levels of service, e.g. two-day delivery, next-day delivery etc. We, therefore, study the problem under stochastic demand from two classes of shipments, with one class receiving priority over the other in service at the hubs to maintain the different service levels required by them. To this end, we present two models for designing a capacitated hub network with a service level constraint, defined using the distribution of time spent at hubs, for each shipment class. The models seek to design the hub network at the minimum total cost, which includes the total fixed cost of equipping open hubs with sufficient processing capacity and the variable transportation costs. The network of hubs, given their locations, is thus modeled as spatially distributed priority queues. The resulting model is challenging to solve, for which we propose a cutting plane-based exact solution method.