Continuous and discrete demand hub location problems

Hub and spoke designs have been adopted by many air carriers and motor carriers in recent years. This paper compares rectilinear distance transportation costs for hub networks with two types of demand to investigate how well an idealized model predicts the cost for real-world demand. The idealized model approximates the transportation cost for a hub network serving a continuous uniform distribution of demand in a square service region with equal origin-destination flows. The cost for the approximation formula is compared to the optimal cost for discrete demand hub location problems. The ability of the approximation formula to predict the optimal transportation cost is measured, and the quality of the prediction is related to characteristics of the discrete demand.