TABLE 10
FROM:
Efficient heuristics for the rectilinear distance capacitated multi-facility Weber problem
N Aras, M Orbay and I K Altinel
BACK TO ARTICLETable 10. Results of the LH when upper bounds are obtained by solving the transportation problem
| Instance | Best value | BLB | BUB | Sharpness of the BLB | Sharpness of the BUB | CPU time (s) |
|---|---|---|---|---|---|---|
| 8 | 793 | 740.14 | 793 | 6.67 | 0.00 | 2.88 |
| 9 | 9619 | 9550.98 | 9649 | 0.71 | 0.31 | 24.08 |
| 15 | 3427 | 3347.99 | 3501 | 2.31 | 2.16 | 5.42 |
| 16 | 259 | 243.43 | 407 | 6.01 | 57.14 | 6.94 |
| 23 | 238 | 224.81 | 238 | 5.54 | 0.00 | 5.28 |
| 26 | 284 | 274.31 | 436 | 3.41 | 53.52 | 12.80 |
| 29 | 729 | 716.94 | 729 | 1.65 | 0.00 | 33.47 |
| 30 | 745 | 734.20 | 760 | 1.45 | 2.01 | 77.91 |
| I1 | 7233 | 7187.47 | 7233 | 0.63 | 0.00 | 145.95 |
| I2 | 5690 | 5678.32 | 6911 | 0.21 | 21.46 | 171.41 |
| I3 | 4297 | 4234.00 | 4297 | 1.47 | 0.00 | 144.84 |
| I4 | 3512 | 3380.37 | 3723 | 3.75 | 6.01 | 183.33 |
| I5 | 2967 | 2721.27 | 4448 | 8.28 | 49.92 | 115.11 |
| I6 | 2322 | 2158.28 | 4103 | 7.05 | 76.70 | 195.95 |
| I7 | 7521 | 7377.99 | 7561 | 1.90 | 0.53 | 226.92 |
| I8 | 5634 | 5371.34 | 6480 | 4.66 | 15.02 | 247.95 |
| I9 | 4756 | 4251.22 | 6248 | 10.61 | 31.37 | 250.38 |
| I10 | 3713 | 3468.58 | 9639 | 6.58 | 159.60 | 283.53 |
| I11 | 3358 | 2817.56 | 10 367 | 16.09 | 208.73 | 273.09 |
| I12 | 3124 | 2546.77 | 5685 | 18.48 | 81.98 | 262.47 |
| I13 | 13 575 | 13099.09 | 14 353 | 3.51 | 5.73 | 452.34 |
| I14 | 11 234 | 11011.36 | 13 412 | 1.98 | 19.39 | 457.50 |
| I15 | 9439 | 9281.81 | 9552 | 1.67 | 1.20 | 451.80 |
| I16 | 8604 | 8375.51 | 10 650 | 2.66 | 23.78 | 491.88 |
| I17 | 7250 | 7041.55 | 8217 | 2.88 | 13.34 | 500.47 |
| I18 | 6614 | 6431.19 | 6640 | 2.76 | 0.39 | 539.59 |
| I19 | 20 762 | 20562.87 | 21 363 | 0.96 | 2.89 | 1388.98 |
| I20 | 18 721 | 18363.85 | 19 776 | 1.91 | 5.64 | 3237.38 |
| I21 | 29 507 | 23672.54 | 45 584 | 19.77 | 54.49 | 4031.91 |
| I22 | 30 075 | 24223.42 | 48 365 | 19.46 | 60.81 | 4007.53 |
| I23 | 34 844 | 19740.00 | 79 604 | 43.35 | 128.46 | 4044.77 |
| I24 | 33 008 | 18301.00 | 77 162 | 44.56 | 133.77 | 4019.58 |
| I25 | 36 318 | 18016.25 | 75 027 | 50.39 | 106.58 | 4042.36 |
| Avg. | 9.19 | 40.09 | 919.27 |
