A hierarchical hub location model for the integrated design of urban and rural logistics networks under demand uncertainty

This paper contributes to the integrated design issue of urban and rural logistics networks under demand uncertainty. A hierarchical hub location model is proposed, which minimizes the expected total system cost by optimizing the locations, number and capacities of "urban-town‒village" hierarchical logistics hubs. The interactions among the logistics hubs and among the hub‒and‒spoke connections, as well as the hub capacity constraints are explicitly considered in the presence of logistics demand uncertainty. A demand scenario‒based branch‒and‒Benders‒cut algorithm is developed to solve the proposed model. A case study of Jiangling urban‒rural region in Hubei province of China is conducted for the illustration of the model and solution algorithm. The results generated by the proposed algorithm are benchmarked against those obtained by GUROBI solver and the practical scheme being currently implemented in the region. The results showed that the proposed methodology can greatly improve the efficiency of the urban‒rural logistics system in terms of expected total system cost. It is important to explicitly model the demand uncertainty, otherwise a significant decision bias may emerge. The proposed algorithm outperforms the GUROBI solver in terms of problem size solved and computational time.