| This research introduces the problem of locating hubs in an air transportation network when there are multiple objectives explicitly to be considered. The history, formulations and solution methods of the standard problem, which treats a single objective, are discussed. Significant extensions of hub location modeling are then developed by adding two more objectives to the formulation and treating all three simultaneously.; In the first instance the single hub problem is developed. The underlying hub problem type is straightforward and easily solvable by non-mathematical programming methods. It thus provides a check on the solutions developed, as well as facilitating interpretation of solutions to the multi-objective version. Interesting results include that the efficient set for three objectives is larger than the set of solutions for individual single objective problems.; The mufti-hub, multiple assignment problem for air transportation exists in many formulations. O'Kelly's (1998) formulation was selected, which creates a major and minor hubs, as the basis of a multiple objective extension. Solutions for two and four hubs in the system were undertaken. As discovered for the single hub model, the efficient set for 3 objectives is larger than the solution set for individual single objective problems. Stable combinations of objective functions also exist, where minor variations in the importance attached to an objective does not alter the choice of hub locations. In the multiple hub model, increasing the number of hubs, p, to be solved for did not necessarily create a superset of the hub locations for lesser p. The solver used was CPLEX with the AMPL front end on a DEC 3000 workstation. |
