Robust Optimization of the Hub Location Problem for Fresh Agricultural Products With Uncertain Demand

Traditional hub location problems are usually based on deterministic circumstances. However, many uncertain factors can cause demand to vary in the long run, which increases the difficulty of strategic hub location planning. The hub location problem for fresh agricultural products is studied considering the perishability of the products and the uncertainty of customer demands. An uncertain demand variable is described by an affine function of the nominal mean and several independent uncertainty sources and is further adjusted by the deterioration rate. An uncapacitated robust hub location model for fresh agricultural products with uncertain demand is first established and solved using the Lagrangian relaxation approach. Then, a robust optimization model for the corresponding capacitated hub location problem is given. A numerical study based on the Australian Post data set (AP20) shows that the deterioration rate of fresh agricultural products, the uncertainty of demand and the degree of conservatism of decision makers all have significant impacts on the total transportation profit. Furthermore, the capacitated model yields more profit than the uncapacitated model because it allows the effects of the deterioration rate and uncertainty to be moderated through flow reallocation. The proposed models are useful for helping decision makers determine the locations and capacities of hubs for fresh agricultural products in accordance with different risk preferences.