Table 3 Solution of the entire problem with no cluster-based decomposition: overall objective function (OF); mismatches of strict preferences (mM); mismatches of soft preferences (mF); total overtime paid by the provider OVT; total caregivers’ travel time (TT); computational time to get the solution (CT); percent optimality gap (Gap)

From: Home care vehicle routing problem with chargeable overtime and strict and soft preference matching

Group Inst Output
  (roverall) OF mM mF OVT TT CT Gap
Small 1 (0.464) 232002285.25 37 337 49 57.25 TL 1.8 ⋅ 10− 5%
  2 (0.548) 120002512.75 15 348 22 72.75 TL 1.1 ⋅ 10− 5%
  3 (0.636) 219002612.75 32 343 62 76.75 TL 1.6 ⋅ 10− 5%
  4 (0.657) 272002906 35 398 12 83.00 TL 7.6 ⋅ 10− 6%
  5 (0.666) 138003514.50 20 487 7 69.50 TL 1.7 ⋅ 10− 5%
  6 (0.675) 216002549.75 29 332 60 92.75 TL 1.1 ⋅ 10− 5%
  7 (0.681) 76003424 11 492 24 52.00 TL 2.3 ⋅ 10− 5%
  8 (0.712) 467003686 73 503 111 110.00 TL 3.9%
  9 (0.741) 112002832 14 396 62 55.00 TL 8.5 ⋅ 10− 5%
  10 (0.761) 641003625.75 85 471 98 111.75 TL 1.4 ⋅ 10− 5%
Large 1 (0.458) No solution TL -
  2 (0.619) No solution TL -
  3 (0.629) No solution TL -
  4 (0.658) No solution TL -
  5 (0.665) No solution TL -
  6 (0.676) No solution TL -
  7 (0.682) No solution TL -
  8 (0.744) No solution TL -
  9 (0.770) No solution TL -
  10 (0.850) No solution TL -
  1. TL denotes the time limit of 3600 seconds