Research Article
Facility Location with Tree Topology and Radial Distance Constraints
Table 8
Numerical results for
and
for the instances in Table
1.
| # | | | | CPU (s) | | | | Ub | CPU (s) | (%) | | Ub | CPU (s) | (%) |
| Instances using radial coverage of 0.2 km | 1 | 500 | 50 | 56.20 | 6.60 | 14 | 56.20 | 20.47 | 0 | 14 | 56.20 | 1.38 | 0 | 2 | 600 | 50 | 63.83 | 5.59 | 17 | 63.83 | 96.66 | 0 | 17 | 63.83 | 0.98 | 0 | 3 | 700 | 50 | 84.28 | 8.44 | 15 | 84.45 | 106.28 | 0.20 | 14 | 84.28 | 7.29 | 0 | 4 | 800 | 50 | 85.13 | 8.99 | 16 | 86.67 | 21.14 | 1.81 | 16 | 85.13 | 0.81 | 0 | 5 | 1000 | 50 | 105.24 | 16.47 | 16 | 105.89 | 82.76 | 0.62 | 16 | 105.24 | 0.77 | 0 | 6 | 500 | 100 | 49.81 | 22.79 | 19 | 50.71 | 7.04 | 1.81 | 20 | 49.81 | 8.39 | 0 | 7 | 600 | 100 | 56.95 | 27.83 | 19 | 58.78 | 20.20 | 3.21 | 21 | 56.95 | 5.37 | 0 | 8 | 700 | 100 | 67.01 | 236.14 | 19 | 68.54 | 130.87 | 2.29 | 20 | 67.01 | 13.99 | 0 | 9 | 800 | 100 | 76.62 | 54.16 | 19 | 78.71 | 3.69 | 2.72 | 20 | 76.62 | 11.19 | 0 | 10 | 1000 | 100 | 93.87 | 73.87 | 20 | 94.38 | 62.83 | 0.55 | 20 | 93.87 | 50.80 | 0 | 11 | 500 | 200 | 45.05 | 406.80 | 22 | 46.95 | 27.22 | 4.20 | 23 | 45.05 | 20.44 | 0 | 12 | 600 | 200 | 52.38 | 257.96 | 24 | 54.95 | 48.33 | 4.90 | 23 | 52.45 | 70.66 | 0.12 | 13 | 700 | 200 | 62.07 | 640.04 | 22 | 65.85 | 21.57 | 6.08 | 23 | 62.07 | 161.15 | 0 | 14 | 800 | 200 | 70.70 | 986.03 | 22 | 72.09 | 79.85 | 1.97 | 22 | 70.70 | 253.45 | 0 | 15 | 1000 | 200 | 87.50 | 1324.35 | 21 | 90.59 | 124.55 | 3.53 | 23 | 87.50 | 103.51 | 0 | 16 | 1000 | 300 | 84.99 | 7200 | 21 | 89.53 | 12.73 | 5.34 | 25 | 86.20 | 55.58 | 1.42 | 17 | 1200 | 300 | 102.25 | 7200 | 24 | 105.52 | 133.29 | 3.20 | 25 | 102.75 | 89.55 | 0.49 | 18 | 1300 | 300 | 119.96 | 7200 | 24 | 113.76 | 32.19 | −5.16 | 24 | 112.00 | 43.53 | −6.63 | 19 | 1400 | 300 | 117.08 | 7200 | 23 | 121.14 | 34.62 | 3.47 | 24 | 117.98 | 116.98 | 0.77 | 20 | 1500 | 300 | 765.22 | 7200 | 22 | 133.02 | 67.43 | −82.61 | 25 | 129.33 | 95.53 | −83.09 |
| Instances using radial coverage of 0.5 km | 1 | 500 | 50 | 99.83 | 13.12 | 5 | 99.83 | 0.50 | 0 | 5 | 99.83 | 0.31 | 0 | 2 | 600 | 50 | 122.36 | 11.43 | 4 | 122.36 | 4.72 | 0 | 4 | 122.36 | 0.54 | 0 | 3 | 700 | 50 | 138.68 | 15.35 | 4 | 142.21 | 0.66 | 2.55 | 4 | 138.68 | 15.22 | 0 | 4 | 800 | 50 | 163.48 | 24.80 | 4 | 164.51 | 0.30 | 0.63 | 4 | 163.48 | 63.01 | 0 | 5 | 1000 | 50 | 201.94 | 26.66 | 5 | 201.94 | 2.31 | 0 | 5 | 201.94 | 0.71 | 0 | 6 | 500 | 100 | 97.20 | 60.15 | 5 | 97.20 | 3.81 | 0 | 5 | 97.20 | 6.15 | 0 | 7 | 600 | 100 | 116.65 | 98.19 | 5 | 116.69 | 3.25 | 0.04 | 5 | 116.65 | 11.89 | 0 | 8 | 700 | 100 | 131.50 | 102.31 | 6 | 131.50 | 8.96 | 0 | 6 | 131.50 | 0.67 | 0 | 9 | 800 | 100 | 157.34 | 148.20 | 5 | 157.49 | 5.12 | 0.10 | 5 | 157.34 | 0.59 | 0 | 10 | 1000 | 100 | 192.27 | 222.71 | 5 | 192.27 | 1.04 | 0 | 5 | 192.27 | 26.65 | 0 | 11 | 500 | 200 | 93.32 | 419.36 | 6 | 93.32 | 36.91 | 0 | 6 | 93.32 | 2.56 | 0 | 12 | 600 | 200 | 110.63 | 740.69 | 6 | 110.63 | 2.66 | 0 | 6 | 110.63 | 0.39 | 0 | 13 | 700 | 200 | 133.28 | 1061.54 | 6 | 133.28 | 10.03 | 0 | 6 | 133.28 | 17.64 | 0 | 14 | 800 | 200 | 152.25 | 1174.40 | 6 | 152.78 | 11.47 | 0.35 | 6 | 152.25 | 1.84 | 0 | 15 | 1000 | 200 | 188.15 | 1664.89 | 6 | 188.15 | 28.00 | 0 | 6 | 188.15 | 2.26 | 0 | 16 | 1000 | 300 | 184.02 | 5364.37 | 6 | 184.25 | 17.19 | 0.13 | 6 | 184.72 | 19.32 | 0.38 | 17 | 1200 | 300 | 219.90 | 6747.17 | 6 | 220.81 | 234.57 | 0.41 | 6 | 219.90 | 1.04 | 0 | 18 | 1300 | 300 | 237.04 | 6044.67 | 6 | 237.78 | 60.90 | 0.31 | 6 | 237.04 | 44.37 | 0 | 19 | 1400 | 300 | 701.78 | 7200 | 6 | 256.48 | 74.53 | −63.45 | 6 | 262.47 | 5.84 | −62.59 | 20 | 1500 | 300 | 728.30 | 7200 | 7 | 278.49 | 21.82 | −61.76 | 6 | 282.01 | 10.82 | −61.27 |
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