Theory and Methodology Location of hubs in a competitive environment

We o€er a formulation that locates hubs on a network in a competitive environment; that is, customer capture is sought, which happens whenever the location of a new hub results in a reduction of the current cost (time, distance) needed by the trac that goes from the speci®ed origin to the speci®ed destination. The formulation presented here reduces the number of variables and constraints as compared to existing covering models. This model is suited for both air passenger and cargo transportation. In this model, each origin±destination ̄ow can go through either one or two hubs, and each demand point can be assigned to more than a hub, depending on the di€erent destinations of its trac. Links (``spokes'') have no capacity limit. Computational experience is provided. Ó 1999 Elsevier Science B.V. All rights reserved.