Alternate solution approaches for competitive hub location problems

Abstract

In this paper, we study the hub location problem of an entrant airline that tries to maximize its share in a market with already existing competing players. The problem is modelled as a nonlinear integer program, which is intractable for off-the-shelf commercial solvers, like CPLEX and Gurobi, etc. Hence, we propose four alternate approaches to solve the problem. The first among them uses the Kelly’s cutting plane method, the second is based on a mixed integer second order conic program reformulation, the third uses the Kelly’s cutting plane method within Lagrangian relaxation, while the fourth uses second order conic program within Lagrangian relaxation. The main contribution of this paper lies in the fourth approach, which along with refinements is the most efficient. Many of the problem instances that were not solvable using standard techniques, like the Kelly’s cutting plane method, have been solved in less than 2 hours of CPU time within 1% optimality gap.