Adaptive distributionally robust hub location and routing problem with a third-party logistics strategy

In this paper, we study an essential and more realistic variant of the hub location-routing problem in which third-party logistics (3PL) are incorporated into a self-built distribution hub network. A two-stage mixed-integer programming model is developed to address the proposed hub location-routing problem with mixed logistical strategies. In the strategic stage, the hub location and allocation decisions are made before the realization of uncertain demands to minimize the total construction and transportation costs. In the operational stage, the managers make vehicle routing decisions with and without the 3PL strategy, and route planning is considered for multiple owned and 3PL vehicles on the basis of simultaneous pickup and delivery. We investigate the effects of uncertain factors on the network design of this framework, as the node demands are often unobservable or difficult to obtain accurately in practice. To address the inherent uncertainty of the problem, we propose an adaptive distributionally robust model by limiting uncertain demands to a specified ambiguity set. Moreover, we reformulate the proposed model into tractable robust counterpart forms under the ambiguity set with information about the support, mean and upper bounds on the dispersion. We design a genetic algorithm with local search to solve the reformulated model on a large scale. Finally, we conduct a case study for a leading retail enterprise in the Beijing–Tianjin–Hebei region to demonstrate the effectiveness and applicability of our model.