A General Mixed-integer Nonlinear Optimization Model for Hub Network Design

A general discrete hub network model that accounts for fixed, capacity, and operating/congestion costs on links and at hubs, with both economies and diseconomies of scale, selects hubs and links, determines their capacities, and assigns O-D flows over paths, while minimizing all system costs. Initially formulated as a mixed-integer non-linear program, the model is transformed into a mixed-integer linear program through the linearization of the capacity and congestion cost functions. The methodology is illustrated by an application to a small-scale network with hypothetical data. Extensive sensitivity analyses are carried out to assess the trade-offs between the different link and hub costs.