Table 6 Cluster-based decomposition in large instances 1-5
From: Home care vehicle routing problem with chargeable overtime and strict and soft preference matching
| Instance | Input | Overall output | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (roverall) | Γ | k | η | #subp | %sol | OF | mM | mF | OVT | TT | CT | Gapmax |
| 1 (0.458) | I(2) | I(1) | 1 | 2 | 4% | 6000137 | 3 | 40 | 0 | 7 | 0 | 0.0% |
| II(14) | I(1) | 1 | 10 | 98% | 128002727.25 | 22 | 448 | 98 | 120.25 | 913 | 7.7% | |
| I(2) | II(17) | 1 | 1 | 0% | 0 | 0 | 0 | 0 | 0 | 0 | 0.0% | |
| II(14) | II(7) | 1 | 10 | 98% | 124002280.75 | 26 | 337 | 90 | 114.75 | 2053 | 7.3% | |
| I(2) | I(1) | 0.9 | 2 | 4% | 6000137 | 3 | 40 | 0 | 7 | 0 | 0.0% | |
| II(14) | I(1) | 0.9 | 10 | 99% | 184002580.75 | 36 | 437 | 70 | 134.75 | 912 | 6.0% | |
| I(2) | II(17) | 0.9 | 1 | 0% | 0 | 0 | 0 | 0 | 0 | 0 | 0.0% | |
| II(14) | II(7) | 0.9 | 10 | 98% | 237002083.5 | 45 | 340 | 89 | 112.5 | 1973 | 5.9% | |
| 2 (0.619) | I(3) | I(1) | 1 | 3 | 24% | 54001206.5 | 11 | 179 | 21 | 43.5 | 2 | 0.0% |
| II(15) | I(1) | 1 | 10 | 100% | 373004928.75 | 61 | 685 | 26 | 165.75 | 459 | 0.0% | |
| I(3) | II(13) | 1 | 1 | 0% | 0 | 0 | 0 | 0 | 0 | 0 | 0.0% | |
| II(15) | II(7) | 1 | 7 | 96% | 276003846.5 | 38 | 514 | 100 | 141.5 | 1772 | 6.4% | |
| I(3) | I(1) | 0.9 | 3 | 24% | 54001206.5 | 11 | 179 | 21 | 43.5 | 2 | 0.0% | |
| II(15) | I(1) | 0.9 | 8 | 100% | 325004618.25 | 48 | 628 | 26 | 206.25 | 1381 | 3.6⋅ 10− 6% | |
| I(3) | II(13) | 0.9 | 1 | 0% | 0 | 0 | 0 | 0 | 0 | 0 | 0.0% | |
| 3 (0.629) | II(12) | I(1) | 1 | 9 | 91% | 458004786.5 | 70 | 638 | 86 | 109.5 | 409 | 0.0% |
| I(2) | I(1) | 1 | 2 | 100% | 620002899.50 | 91 | 410 | 116 | 110.50 | 2566 | 3.6⋅ 10− 5% | |
| I(2) | II(11) | 1 | 2 | 12% | 774 | 0 | 96 | 0 | 6 | 2 | 0.0% | |
| II(12) | II(5) | 1 | 9 | 95% | 509003566 | 78 | 489 | 137 | 116 | 584 | 0.0% | |
| II(12) | I(1) | 0.9 | 9 | 100% | 624004280 | 102 | 583 | 88 | 114 | 49 | 0.0% | |
| I(2) | I(1) | 0.9 | 2 | 100% | 620002899.50 | 91 | 410 | 116 | 110.50 | 2580 | 3.6⋅ 10− 5% | |
| I(2) | II(11) | 0.9 | 2 | 12% | 774 | 0 | 96 | 0 | 6 | 2 | 0.0% | |
| II(12) | II(5) | 0.9 | 9 | 100% | 621003804.5 | 93 | 543 | 118 | 112.5 | 143 | 0.0% | |
| 4 (0.658) | I(2) | I(1) | 1 | 2 | 19% | 156000831.5 | 20 | 114 | 14 | 25.5 | 15 | 0.0% |
| II(16) | I(1) | 1 | 8 | 100% | 688005849.25 | 99 | 796 | 142 | 151.25 | 1798 | 1.2⋅ 10− 4% | |
| I(2) | II(13) | 1 | 2 | 0% | 0 | 0 | 0 | 0 | 0 | 0 | 0.0% | |
| II(16) | II(7) | 1 | 8 | 100% | 994005551.25 | 144 | 747 | 94 | 171.25 | 1509 | 9.7⋅ 10− 5% | |
| I(2) | I(1) | 0.9 | 2 | 19% | 156000831.5 | 20 | 114 | 14 | 25.5 | 15 | 0.0% | |
| I(2) | II(13) | 0.9 | 2 | 0% | 0 | 0 | 0 | 0 | 0 | 0 | 0.0% | |
| 5 (0.665) | I(2) | I(1) | 1 | 2 | 100% | 426005714.5 | 63 | 798 | 142 | 149.5 | TL | 3.0% |
| II(16) | I(1) | 1 | 11 | 91% | 866005301.75 | 135 | 725 | 27 | 111.75 | 606 | 2.0⋅ 10− 1% | |
| I(2) | II(13) | 1 | 2 | 31% | 112002257.75 | 14 | 293 | 4 | 21.75 | 1131 | 2.2⋅ 10− 6% | |
| I(2) | I(1) | 0.9 | 2 | 100% | 379006103.75 | 57 | 835 | 141 | 154.75 | TL | 1.3% | |
| I(2) | II(13) | 0.9 | 2 | 34% | 112002225 | 14 | 294 | 4 | 33 | 1230 | 2.0⋅ 10− 6% | |