Research Article
Facility Location with Tree Topology and Radial Distance Constraints
Table 1
Numerical results for
and
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| # | | | Den. | | | | CPU (s) | | CPU (s) | | | CPU (s) | | CPU (s) | (%) | (%) |
| Instances using radial coverage of 0.2 km | 1 | 500 | 50 | 11.26 | 14 | 56.20 | 113 | 9.61 | 47.63 | 0.78 | 56.20 | 83 | 6.60 | 55.03 | 1.79 | 15.25 | 2.08 | 2 | 600 | 50 | 10.61 | 17 | 63.83 | 123 | 10.33 | 54.63 | 0.98 | 63.83 | 12 | 5.59 | 63.26 | 1.65 | 14.41 | 0.89 | 3 | 700 | 50 | 11.02 | 14 | 84.28 | 166 | 15.46 | 73.40 | 1.14 | 84.28 | 13 | 8.44 | 83.15 | 2.64 | 12.91 | 1.35 | 4 | 800 | 50 | 11.02 | 16 | 85.13 | 65 | 11.81 | 75.25 | 1.39 | 85.13 | 89 | 8.99 | 84.79 | 3.07 | 11.61 | 0.40 | 5 | 1000 | 50 | 10.86 | 16 | 105.24 | 573 | 29.09 | 90.41 | 1.90 | 105.24 | 142 | 16.47 | 104.14 | 3.90 | 14.09 | 1.04 | 6 | 500 | 100 | 10.53 | 20 | 49.81 | 387 | 24.65 | 35.85 | 1.51 | 49.81 | 277 | 22.79 | 47.97 | 7.57 | 28.03 | 3.69 | 7 | 600 | 100 | 10.40 | 21 | 56.95 | 307 | 47.41 | 40.21 | 1.97 | 56.95 | 130 | 27.83 | 55.16 | 9.19 | 29.39 | 3.14 | 8 | 700 | 100 | 10.24 | 20 | 67.01 | 4402 | 260.79 | 47.29 | 2.28 | 67.01 | 5547 | 236.14 | 64.46 | 15.02 | 29.43 | 3.80 | 9 | 800 | 100 | 10.59 | 20 | 76.62 | 633 | 94.77 | 56.29 | 2.61 | 76.62 | 176 | 54.16 | 74.49 | 17.74 | 26.53 | 2.78 | 10 | 1000 | 100 | 10.20 | 20 | 93.87 | 225 | 91.34 | 68.47 | 3.79 | 93.87 | 159 | 73.87 | 91.93 | 24.74 | 27.05 | 2.06 | 11 | 500 | 200 | 10.19 | 23 | 45.05 | 2331 | 727.94 | 26.17 | 4.41 | 45.05 | 219 | 406.80 | 41.67 | 107.66 | 41.91 | 7.50 | 12 | 600 | 200 | 9.97 | 25 | 52.38 | 599 | 405.91 | 29.89 | 4.95 | 52.38 | 273 | 257.96 | 49.50 | 135.94 | 42.93 | 5.50 | 13 | 700 | 200 | 10.20 | 23 | 62.07 | 1898 | 884.70 | 35.45 | 5.73 | 62.07 | 175 | 640.04 | 58.50 | 193.37 | 42.90 | 5.75 | 14 | 800 | 200 | 10.47 | 22 | 70.70 | 4269 | 4296.99 | 38.52 | 6.58 | 70.70 | 346 | 986.03 | 66.93 | 246.15 | 45.51 | 5.33 | 15 | 1000 | 200 | 10.08 | 23 | 87.50 | 2441 | 1653.07 | 49.17 | 9.86 | 87.50 | 1226 | 1324.35 | 83.87 | 358.33 | 43.81 | 4.16 | 16 | 1000 | 300 | 10.35 | 24 | 85.16 | 222 | 7200 | 41.25 | 18.95 | 84.99 | 101 | 7200 | - | 1008.92 | 51.56 | - | 17 | 1200 | 300 | 10.81 | 25 | 102.77 | 127 | 7200 | 48.09 | 23.99 | 102.25 | 51 | 7200 | | | 53.20 | | 18 | 1300 | 300 | 11.01 | 21 | 119.96 | 90 | 7200 | 54.21 | 27.86 | 633.94 | 8 | 7200 | | | 54.81 | | 19 | 1400 | 300 | 10.70 | 24 | 119.61 | 127 | 7200 | 55.51 | 29.75 | 117.08 | 30 | 7200 | | | 53.59 | | 20 | 1500 | 300 | 10.59 | 1 | 766.47 | 11 | 7200 | 60.52 | 31.06 | 765.22 | 2 | 7200 | | | 92.10 | |
| Instances using radial coverage of 0.5 km | 1 | 500 | 50 | 51.18 | 5 | 99.83 | 15 | 16.74 | 46.17 | 0.83 | 99.83 | 3 | 13.12 | 96.61 | 3.87 | 53.75 | 3.23 | 2 | 600 | 50 | 44.08 | 4 | 122.36 | 0 | 14.12 | 62.68 | 0.97 | 122.36 | 0 | 11.43 | 121.36 | 4.87 | 48.78 | 0.82 | 3 | 700 | 50 | 53.39 | 4 | 138.68 | 0 | 17.04 | 70.69 | 1.59 | 138.68 | 0 | 15.35 | 138.03 | 5.96 | 49.03 | 0.47 | 4 | 800 | 50 | 46.12 | 4 | 163.48 | 38 | 29.89 | 77.24 | 1.36 | 163.48 | 11 | 24.80 | 158.58 | 8.98 | 52.75 | 2.99 | 5 | 1000 | 50 | 51.92 | 5 | 201.94 | 0 | 29.91 | 98.40 | 2.33 | 201.94 | 0 | 26.66 | 201.22 | 13.82 | 51.27 | 0.35 | 6 | 500 | 100 | 48.91 | 5 | 97.20 | 0 | 65.99 | 35.74 | 1.72 | 97.20 | 0 | 60.15 | 96.14 | 21.78 | 63.23 | 1.09 | 7 | 600 | 100 | 49.33 | 5 | 116.65 | 40 | 101.18 | 44.57 | 2.04 | 116.65 | 0 | 98.19 | 113.68 | 30.03 | 61.79 | 2.54 | 8 | 700 | 100 | 43.54 | 6 | 131.50 | 0 | 106.99 | 46.58 | 2.53 | 131.50 | 0 | 102.31 | 130.60 | 45.29 | 64.58 | 0.69 | 9 | 800 | 100 | 47.64 | 5 | 157.34 | 15 | 154.19 | 59.78 | 2.98 | 157.34 | 3 | 148.20 | 154.90 | 50.81 | 62.00 | 1.55 | 10 | 1000 | 100 | 52.61 | 5 | 192.27 | 27 | 231.91 | 68.04 | 3.65 | 192.27 | 7 | 222.71 | 189.23 | 88.52 | 64.61 | 1.58 | 11 | 500 | 200 | 48.30 | 6 | 93.32 | 0 | 419.36 | 26.51 | 4.90 | 93.32 | 0 | 522.18 | 91.83 | 249.68 | 71.59 | 1.60 | 12 | 600 | 200 | 47.85 | 6 | 110.63 | 37 | 777.41 | 30.98 | 5.58 | 110.63 | 33 | 740.69 | 108.48 | 401.20 | 72.00 | 1.94 | 13 | 700 | 200 | 49.38 | 6 | 133.28 | 55 | 1158.32 | 35.24 | 7.60 | 133.28 | 19 | 1061.54 | 129.97 | 548.92 | 73.56 | 2.48 | 14 | 800 | 200 | 47.90 | 6 | 152.25 | 39 | 1273.34 | 41.22 | 10.16 | 152.25 | 4 | 1174.40 | 149.29 | 640.60 | 72.93 | 1.94 | 15 | 1000 | 200 | 47.48 | 6 | 188.15 | 36 | 2104.82 | 49.17 | 12.39 | 188.15 | 13 | 1664.89 | 182.83 | 1005.08 | 73.87 | 2.83 | 16 | 1000 | 300 | 46.43 | 6 | 184.02 | 91 | 6892.81 | 40.91 | 23.32 | 184.02 | 18 | 5364.37 | | | 77.77 | | 17 | 1200 | 300 | 48.88 | 1 | 551.27 | 0 | 7200 | 49.02 | 24.77 | 219.90 | 17 | 6747.17 | | | 91.11 | | 18 | 1300 | 300 | 47.10 | 1 | 768.33 | 0 | 7200 | 53.42 | 38.84 | 237.04 | 0 | 6044.67 | | | 93.05 | | 19 | 1400 | 300 | 47.21 | 1 | 701.78 | 0 | 7200 | 56.48 | 43.06 | 701.78 | 0 | 7200 | | | 91.95 | | 20 | 1500 | 300 | 48.17 | 1 | 728.30 | 0 | 7200 | 61.02 | 53.02 | 728.30 | 0 | 7200 | | | 91.62 | |
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Instance not solved. -, CPLEX could not solve the problem. |