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Program. 81, 149–175 (1998) 3. : Approximation Algorithms for Access Network Design. Algorithmica 34, 197– 215 (2002) 4. : On the p-Median Polytope. Math. Program. 89, 395–411 (2001) 5. : Facets of the Knapsack Polytope. Math. Program. 8, 146–164 (1975) 6. : OR-Library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41, 1069–1072 (1990) 7. : Hub Location Problems. In: Facility Location: Applications and Theory, Z. W. ), Springer, 2002, pp. 373–407 8. : On the Significance of Solving Linear Programming Problems with Some Integer Variables.

In Table 12, we report the results for the hub location problems from the OR library. We omit the results for problems with 10 nodes as all of these problems are solved at the root node in less than one second. We also remove problems of type LL, T L with Q = 1/4 and Q = 1/5 since in these problems the capacity constraints are redundant. A branch and cut algorithm for hub location problems with single assignment 403 Table 12. 19 no. of conc 4 4 2 2 2 2 4 4 3 3 2 2 5 5 2 2 2 2 5 5 4 3 4 3 cover 151 47 0 0 0 0 64 39 18 46 0 0 379 1870 6 3 0 0 396 1473 20 15 10 7 spro 755 73 6 1 13 4 165 133 106 62 4 2 829 7757 16 8 11 4 1231 4743 18 17 115 14 step 1 0 0 0 0 0 0 0 0 0 0 0 0 19 0 0 0 0 5 32 0 1 0 0 3 3 2 26 0 2 52 15 8 0 0 0 4 4 198 102 358 336 0 0 3 16 32 0 3 2 0 0 10 15 0 0 4 3 102 69 187 99 0 0 The problems of type T T , LT are infeasible for Q = 1 and Q = 1/2 and are not considered.

A branch and cut algorithm for hub location problems with single assignment 403 Table 12. 19 no. of conc 4 4 2 2 2 2 4 4 3 3 2 2 5 5 2 2 2 2 5 5 4 3 4 3 cover 151 47 0 0 0 0 64 39 18 46 0 0 379 1870 6 3 0 0 396 1473 20 15 10 7 spro 755 73 6 1 13 4 165 133 106 62 4 2 829 7757 16 8 11 4 1231 4743 18 17 115 14 step 1 0 0 0 0 0 0 0 0 0 0 0 0 19 0 0 0 0 5 32 0 1 0 0 3 3 2 26 0 2 52 15 8 0 0 0 4 4 198 102 358 336 0 0 3 16 32 0 3 2 0 0 10 15 0 0 4 3 102 69 187 99 0 0 The problems of type T T , LT are infeasible for Q = 1 and Q = 1/2 and are not considered.

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