Comparison of the formulations for a hub-and-spoke network design problem under congestion

- We propose and compare two mathematical programming models for hub location problem with congestion.
- Conic quadratic reformulation our models and a strengthening method based on perspective cuts is applied.
- We apply two relaxation strategies at branch-and-cut procedure to their effect in different formulations.
- Our results are shown that outperform the existing results in literature and shown.
- Also a Simulated Annealing heuristic solution approach is provided as a supplementary document in the response letter.

In this paper, we study the hub location problem with a power-law congestion cost and propose an exact solution approach. We formulate this problem in a conic quadratic form and use a strengthening method which rests on valid inequalities of perspective cuts in mixed integer nonlinear programming. In a numerical study, we compare two well known types of mathematical modeling in the hub-location problems which are solved with different branch and cut strategies. The strength and weakness of the formulations are summarized based on an extensive numerical study over the CAB data set.