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Once again, we see that the difficulty of the problem depends a lot on the demand and capacity level of the problem. For two problems, the program stopped before finding a feasible solution. In fact, a feasible solution can be found by assigning each node to itself. In most cases, such a solution has a very big cost compared to the one of the optimal solution (the number of hubs installed is not more than five for the problems solved), which will probably not improve the performance of the algorithm.

The other changes did not improve the results. We also solved the other problems applying the first strategy. The results did not change significantly. Based on this result and some preliminary tests, we decided to use Algorithm 3 during the preprocessing and to separate the cover inequalities on linear knapsacks for the remaining test instances as they have bigger sizes than the problems we solved up to now. We also adapted the separation of projection inequalities so that we only consider the commodities with nonzero traffic demands.

On the Significance of Solving Linear Programming Problems with Some Integer Variables. The Rand Corporation, document, 1958, p. 1486 9. : Valid Inequalities, Facets and Computational Results for the Capacitated Concentrator Location Problem. Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027-6699, 1992 10. : Solution Algorithms for the Capacitated Single Allocation Hub Location Problem. Ann. Oper. Res. 86, 141–159 (1999) 11. : Telecommunication and Location.

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A branch and cut algorithm for hub location problems with single assignment by Labbe M.

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