Robust Hub Location Problem with Flow-Based Set-Up Cost

Abstract

Hub location problems are network design problems on the level of strategic decision-making processes. During strategic planning, input data, such as flows and set-up costs, are not always known in advance. Hence, decisions have to be made in an uncertain environment. In this paper, two sources of uncertainty are considered: the flows from origins to destinations and the set-up costs of hubs. A robust optimization formulation is proposed for both single and multiple allocation cases, in which the flow between each pair of nodes is assumed to be uncertain and correlated. In addition, the set-up cost of a hub is related to the total flow through the hub. Nonlinear integer program models are presented for both single and multiple allocation cases, and they are solved using CPLEX. Computational tests using the Civil Aeronautics Board and Australian Post datasets are provided. The numerical results suggest that the robust optimization strategy locates more hubs than in the deterministic case with a relatively small cost increase, and the total cost of the robust solution calculated for the multiple allocation case is marginally lower than that for the single allocation case. The robust optimization strategy is proven to be effective for protecting the solution against the worst case for different uncertain parameters.