Design of Robust Hub-and-Spoke Logistics Network with Stochastic Demands for Logistics Service Providers

Logistics service providers (LSPs) are playing an increasing role in the management of supply chains. LSPs offer a wide range of logistics services، e. g.، warehousing and transportation services and hence play an important role in supporting production and service systems. We consider an LSP who is responsible for managing the distribution of goods from multiple origins to multiple destinations for its clients. It is assumed that the commodity flow between each origin and destination is of stochastic nature with a symmetric and bounded probability distribution. The objective is to determine the number، location، and capacity of the hubs and also to allocate the customers to these hubs in such a way that transferring all the commodities in the network is ensured without capacity constraints associated with the hubs are not violated. At the same time، total expected system-wide costs will be minimized. The problem is modeled using one of the most recent robust optimization approaches and a standard optimization package being used to solve it. Results obtained via numerical experiments show the capability of the presented robust model to immunize the system against violation of capacity constraints with a relatively small cost increase، known as the robustness cost.