Table 9 Values of OVT, nkϕ= 1 and nkϕ= 0 in the small instances without decomposition and in large instances 3 and 5 decomposed with ΓI, kI and η = 0.9, for which #subp = 2 and %sol = 100%: reference configuration with chargeable overtime; configuration in which the continuity of care is reinforced through (30); configuration in which all clients are unwilling to pay overtime

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

Group Inst roverall Percentage   With chargeable With chargeable overtime and Without chargeable
    of ϕc = 1   overtime (reference) (30) in objective function overtime (ϕc = 0∀cC)
     OVT nkϕ= 1 nkϕ= 0 OVT nkϕ= 1 nkϕ= 0 OVT nkϕ= 1 nkϕ= 0
Small 1 0.464 83.3% 49 2.5 ± 1.2 2.7 ± 2.1 67 2.3 ± 1.5 3.0 ± 2.6 137 2.5 ± 1.2 3.0 ± 2.6
  2 0.548 88.9% 22 2.5 ± 1.2 3.5 ± 3.5 26 1.8 ± 0.9 4.5 ± 4.9 93 2.6 ± 1.5 3.0 ± 2.8
  3 0.636 44.4% 62 3.5 ± 1.7 2.4 ± 0.8 57 2.3 ± 1.0 2.2 ± 1.1 116 4.0 ± 1.7 2.4 ± 0.8
  4 0.657 77.8% 12 2.6 ± 1.2 2.0 ± 1.4 32 1.9 ± 1.0 2.3 ± 1.9 84 2.7 ± 1.3 2.0 ± 1.4
  5 0.666 88.9% 7 3.3 ± 1.2 1.0 ± 0.0 69 2.8 ± 1.2 1.0 ± 0.0 129 3.3 ± 1.1 1.0 ± 0.0
  6 0.675 77.8% 60 2.9 ± 1.5 2.3 ± 0.5 52 2.3 ± 1.0 2.5 ± 0.6 146 2.7 ± 1.4 2.3 ± 0.5
  7 0.681 61.1% 24 2.5 ± 0.9 2.9 ± 1.9 52 2.0 ± 1.0 2.7 ± 2.1 93 3.0 ± 0.9 3.0 ± 1.8
  8 0.712 66.7% 111 3.9 ± 1.9 2.7 ± 2.4 207 4.4 ± 2.4 3.5 ± 1.6 247 3.8 ± 1.9 2.2 ± 1.8
  9 0.741 72.2% 62 3.2 ± 1.6 2.8 ± 1.5 16 2.1 ± 0.9 3.4 ± 1.5 132 3.5 ± 1.8 3.2 ± 1.8
  10 0.761 66.7% 98 2.9 ± 1.1 5.3 ± 3.1 139 2.9 ± 1.3 5.0 ± 3.1 188 2.7 ± 1.0 5.0 ± 2.8
Large 3 0.619 60.0% 116 2.6 ± 1.2 2.7 ± 0.9 103 1.2 ± 0.9 2.8 ± 2.2 162 2.9 ± 1.4 2.7 ± 0.8
  5 0.665 80.0% 141 3.7 ± 2.2 3.5 ± 2.2 102 2.3 ± 1.4 3.3 ± 1.9 200 3.0 ± 1.4 3.2 ± 1.8