Alternate solution approaches for competitive hub location problems

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 modeled as a non-linear 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 Kelley’s cutting plane method, the second is based on a mixed integer second order conic program reformulation, the third uses the Kelley’s cutting plane method within Lagrangian relaxation, while the fourth uses second order conic program within Lagrangian relaxation. On the basis of extensive numerical tests on well-known datasets (CAB and AP), we conclude that the Kelley’s cutting plane within Lagrangian relaxation is computationally the best. It is able to solve all the problem instances of upto 50 nodes within 1% optimality gap in less than 10 minutes of CPU time.