Research Article
Solving Capacitated Facility Location Problem Using Lagrangian Decomposition and Volume Algorithm
Table 1
A comparison between the results of the LR and VA and the LD and VA for the small problems sized 100–300.
| Problem size | Algorithm | Method | LB | UB | Time | Passes | Error |
| | LR and VA | LR1 | 9529.44 | 11984.03 | 64.48 | 650 | 20.5 | LR2 | 9529.44 | 11757.42 | 359.4 | 1750 | 18.9 | LR3 | 9529.44 | 11433.22 | 113.8 | 571 | 16.7 | LR4 | 9529.44 | 11433.22 | 41.0 | 423 | 16.7 | LD and VA | LR5 | 11088.854 | 11717.01 | 4.35 | 450 | 5.43 | LR6 | 11088.854 | 11599.43 | 3.8 | 397 | 4.46 | LR7 | 11088.854 | 11433.22 | 4.61 | 482 | 3.03 | LR8 | 11088.854 | 11433.22 | 4.12 | 443 | 3.02 | Best greedy sol. | Filter 4 | 11089.6 | 11634.30 | 55.19 | — | 4.68 |
| | LR and VA | LR1 | 18005.55 | 20677.407 | 681.68 | 1400 | 12.9 | LR2 | 18005.75 | 20447.484 | 680.48 | 1450 | 11.9 | LR3 | 18005.34 | 20083.69 | 822.64 | 617 | 10.3 | LR4 | 18005.75 | 20083.69 | 78.10 | 503 | 10.3 | LD and VA | LR5 | 19542.11 | 19919.04 | 151.54 | 1850 | 1.89 | LR6 | 19542.02 | 19919.05 | 75.06 | 900 | 1.89 | LR7 | 19542.08 | 19919.05 | 116.26 | 1400 | 1.89 | LR8 | 19542.07 | 19792.52 | 95.01 | 1150 | 1.30 | Best greedy sol. | Filter 4 | 19542.3 | 19791.608 | 791.64 | — | 1.30 |
| | LR and VA | LR1 | 26428.89 | 30775.85 | 1552.28 | 1000 | 14.0 | LR2 | 26428.09 | 29854.86 | 774.10 | 500 | 11.5 | LR3 | 26428.85 | 29092.27 | 1000.82 | 647 | 9.2 | LR4 | 26428.86 | 29092.27 | 644.98 | 438 | 9.2 | LD and VA | LR5 | 28351.01 | 29197.79 | 616.77 | 702 | 2.9 | LR6 | 28351.01 | 29065.70 | 1469.08 | 1700 | 2.5 | LR7 | 28351.01 | 28933.05 | 935.91 | 1150 | 2.01 | LR8 | 28351.01 | 28933.05 | 369.46 | 1150 | 2.01 | Best greedy sol. | Filter 4 | 28351.8 | 29125.771 | 5403.93 | — | 2.7 |
|
|