The single allocation hub location problem: a robust optimisation approach

Design of hub-and-spoke networks or the hub location problem is one of the most important problems in operational research and has many applications in different areas of transportation, logistics, and telecommunications. In this paper, a relatively new version of the single allocation hub location problem is addressed, in which quantity of the commodity flows between pairs of customer nodes are of stochastic nature. The objective here 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 with a very high probability (capacity constraints associated with the hubs are not violated). At the same time, total expected system-wide costs will be minimised. A robust optimisation approach is employed to model the problem with a standard optimisation package being used to solve it. Results obtained via numerical experiments show the capability of the presented robust model to immunise the system against violation of capacity constraints with a relatively small cost increase, known as the robustness cost.