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%
  1. The table has the same structure of Table 4