<table><caption>Table 13: Detailed performance of the exact algorithm on instances from (Gehring and Homberger, 1999)</caption><thead><tr><th>Instance</th><th>|A<sup>max</sup>|</th><th>K̂</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap Time (s)</th></tr></thead></table>

<table><caption>Table 14: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>Γ<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>|A<sup>max</sup>|</th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff.40.01</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1795</td><td>83.27</td><td>3</td><td>3023.92</td><td>2931.88</td><td>3.14</td><td>108.18</td></tr><tr><td>Cardiff.40.01</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1931</td><td>89.94</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>115.41</td></tr><tr><td>Cardiff.40.01</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2491</td><td>111.19</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>112.07</td></tr><tr><td>Cardiff.40.01</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5261</td><td>147.21</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>147.91</td></tr><tr><td>Cardiff.40.01</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2366</td><td>138.05</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>138.87</td></tr><tr><td>Cardiff.40.01</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2501</td><td>113.29</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>141.00</td></tr><tr><td>Cardiff.40.01</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2636</td><td>121.99</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>152.10</td></tr><tr><td>Cardiff.40.01</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5283</td><td>175.87</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>231.41</td></tr><tr><td>Cardiff.40.01</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>6601</td><td>213.12</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>276.06</td></tr><tr><td>Cardiff.40.01</td><td>3</td><td>8</td><td>8</td><td>1</td><td>5715</td><td>180.78</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>181.72</td></tr><tr><td>Cardiff.40.01</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>16141</td><td>208.76</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>282.59</td></tr><tr><td>Cardiff.40.01</td><td>3</td><td>15</td><td>10</td><td>1</td><td>10714</td><td>197.94</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>273.71</td></tr><tr><td>Cardiff.40.01</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>10714</td><td>190.00</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>252.57</td></tr><tr><td>Cardiff.40.02</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>74.15</td><td>1</td><td>3258.43</td><td>3217.42</td><td>1.27</td><td>74.65</td></tr><tr><td>Cardiff.40.02</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1940</td><td>76.30</td><td>1</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>76.65</td></tr><tr><td>Cardiff.40.02</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2691</td><td>79.61</td><td>1</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>80.37</td></tr><tr><td>Cardiff.40.02</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6439</td><td>119.73</td><td>3</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>368.83</td></tr><tr><td>Cardiff.40.02</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2521</td><td>94.48</td><td>3</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>193.52</td></tr><tr><td>Cardiff.40.02</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2707</td><td>99.99</td><td>1</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>100.56</td></tr><tr><td>Cardiff.40.02</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2831</td><td>73.55</td><td>3</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>163.43</td></tr><tr><td>Cardiff.40.02</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6743</td><td>110.46</td><td>7</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>1222.35</td></tr><tr><td>Cardiff.40.02</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7965</td><td>117.88</td><td>13</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>1812.41</td></tr><tr><td>Cardiff.40.02</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7431</td><td>110.16</td><td>11</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>1928.13</td></tr><tr><td>Cardiff.40.02</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>94606</td><td>104.14</td><td>37</td><td>-</td><td>3217.42</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.02</td><td>3</td><td>15</td><td>10</td><td>1</td><td>15732</td><td>143.74</td><td>5</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>1813.37</td></tr><tr><td>Cardiff.40.02</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>44541</td><td>71.34</td><td>43</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff.40.03</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>64.23</td><td>3</td><td>2761.12</td><td>2682.5</td><td>2.93</td><td>92.10</td></tr><tr><td>Cardiff.40.03</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1932</td><td>83.51</td><td>1</td><td>2686.92</td><td>2682.5</td><td>0.16</td><td>84.03</td></tr><tr><td>Cardiff.40.03</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2573</td><td>101.58</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>193.17</td></tr><tr><td>Cardiff.40.03</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6071</td><td>150.94</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>277.87</td></tr><tr><td>Cardiff.40.03</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2441</td><td>83.80</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>138.85</td></tr><tr><td>Cardiff.40.03</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2605</td><td>107.42</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>186.08</td></tr><tr><td>Cardiff.40.03</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2676</td><td>119.35</td><td>1</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>119.95</td></tr><tr><td>Cardiff.40.03</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6311</td><td>126.94</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>252.25</td></tr><tr><td>Cardiff.40.03</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7550</td><td>132.35</td><td>7</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>447.35</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
<figure><img src="image_7.png" /><figcaption>Figure 6: Optimal solution for c102_100.txt</figcaption></figure>

## 8. Conclusion

In this paper, we introduced a new branch-cut-and-price algorithm for the two-echelon vehicle routing problem with drones. This algorithm is based on the enumeration of the drone's round trips between customers and the vehicle parked at another customer. We presented ways to improve the method by reducing the number of drone trips enumerated and by adapting the well-known rounded capacity cuts supported by sensitivity analysis.

Extensive numerical experiments demonstrated the high performance of our method. We solve all literature instances containing up to 35 customers, improving computation times significantly by a factor higher than 10, and optimally
<table><caption>Table 14: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>Γ<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff.40.03</td><td>3</td><td>8</td><td>8</td><td>1</td><td>6983</td><td>141.43</td><td>5</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>470.14</td></tr><tr><td>Cardiff.40.03</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>32435</td><td>203.85</td><td>5</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>531.98</td></tr><tr><td>Cardiff.40.03</td><td>3</td><td>15</td><td>10</td><td>1</td><td>14395</td><td>184.13</td><td>21</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>2524.46</td></tr><tr><td>Cardiff.40.03</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>20100</td><td>185.76</td><td>5</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>456.20</td></tr><tr><td>Cardiff.40.04</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1792</td><td>60.52</td><td>5</td><td>5259.18</td><td>5082.62</td><td>3.47</td><td>119.43</td></tr><tr><td>Cardiff.40.04</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1934</td><td>60.83</td><td>5</td><td>5239.48</td><td>5082.62</td><td>3.09</td><td>164.87</td></tr><tr><td>Cardiff.40.04</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2720</td><td>72.19</td><td>3</td><td>5239.48</td><td>5082.62</td><td>3.09</td><td>137.02</td></tr><tr><td>Cardiff.40.04</td><td>2</td><td>5</td><td>8</td><td>1</td><td>7764</td><td>90.31</td><td>39</td><td>5245.75</td><td>5082.62</td><td>3.21</td><td>10800.00</td></tr><tr><td>Cardiff.40.04</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2573</td><td>79.86</td><td>7</td><td>5236.25</td><td>5082.62</td><td>3.02</td><td>224.70</td></tr><tr><td>Cardiff.40.04</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2781</td><td>69.25</td><td>7</td><td>5236.25</td><td>5082.62</td><td>3.02</td><td>196.73</td></tr><tr><td>Cardiff.40.04</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2784</td><td>72.60</td><td>17</td><td>5236.25</td><td>5082.62</td><td>3.02</td><td>434.19</td></tr><tr><td>Cardiff.40.04</td><td>3</td><td>5</td><td>8</td><td>1</td><td>8532</td><td>162.82</td><td>73</td><td>5142.45</td><td>5082.62</td><td>1.18</td><td>10800.00</td></tr><tr><td>Cardiff.40.04</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8641</td><td>167.72</td><td>51</td><td>5178.7</td><td>5082.62</td><td>1.89</td><td>10800.00</td></tr><tr><td>Cardiff.40.04</td><td>3</td><td>8</td><td>8</td><td>1</td><td>9603</td><td>115.39</td><td>49</td><td>-</td><td>5082.62</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.04</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>169680</td><td>429.19</td><td>9</td><td>-</td><td>5082.62</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.04</td><td>3</td><td>15</td><td>10</td><td>1</td><td>26672</td><td>195.76</td><td>45</td><td>5082.62</td><td>5082.62</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff.40.04</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>146716</td><td>396.58</td><td>11</td><td>-</td><td>5082.62</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.05</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1795</td><td>166.61</td><td>3</td><td>3812.85</td><td>3770.9</td><td>1.11</td><td>332.22</td></tr><tr><td>Cardiff.40.05</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1947</td><td>142.14</td><td>3</td><td>3812.85</td><td>3770.9</td><td>1.11</td><td>208.14</td></tr><tr><td>Cardiff.40.05</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2582</td><td>185.46</td><td>3</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>250.84</td></tr><tr><td>Cardiff.40.05</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5696</td><td>266.27</td><td>15</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1436.28</td></tr><tr><td>Cardiff.40.05</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2453</td><td>207.88</td><td>3</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>273.77</td></tr><tr><td>Cardiff.40.05</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2609</td><td>213.88</td><td>3</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>269.74</td></tr><tr><td>Cardiff.40.05</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2758</td><td>223.78</td><td>3</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>294.98</td></tr><tr><td>Cardiff.40.05</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5955</td><td>282.85</td><td>11</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1134.08</td></tr><tr><td>Cardiff.40.05</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7149</td><td>336.73</td><td>9</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1313.44</td></tr><tr><td>Cardiff.40.05</td><td>3</td><td>8</td><td>8</td><td>1</td><td>6492</td><td>300.18</td><td>13</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1614.24</td></tr><tr><td>Cardiff.40.05</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>25801</td><td>319.38</td><td>7</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1614.57</td></tr><tr><td>Cardiff.40.05</td><td>3</td><td>15</td><td>10</td><td>1</td><td>12799</td><td>397.57</td><td>5</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1000.81</td></tr><tr><td>Cardiff.40.05</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>16776</td><td>239.74</td><td>3</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>674.01</td></tr><tr><td>Cardiff.40.06</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1800</td><td>108.36</td><td>1</td><td>3013.15</td><td>2909</td><td>3.58</td><td>108.80</td></tr><tr><td>Cardiff.40.06</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1939</td><td>111.47</td><td>1</td><td>2909.0</td><td>2909</td><td>0.00</td><td>112.15</td></tr><tr><td>Cardiff.40.06</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2671</td><td>167.08</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>263.32</td></tr><tr><td>Cardiff.40.06</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6008</td><td>193.26</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>331.11</td></tr><tr><td>Cardiff.40.06</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2501</td><td>157.41</td><td>1</td><td>2909.0</td><td>2909</td><td>0.00</td><td>158.25</td></tr><tr><td>Cardiff.40.06</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2680</td><td>177.21</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>292.64</td></tr><tr><td>Cardiff.40.06</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2858</td><td>174.96</td><td>1</td><td>2909.0</td><td>2909</td><td>0.00</td><td>175.67</td></tr><tr><td>Cardiff.40.06</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6041</td><td>239.07</td><td>5</td><td>2909.0</td><td>2909</td><td>0.00</td><td>536.92</td></tr><tr><td>Cardiff.40.06</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7529</td><td>235.25</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>387.91</td></tr><tr><td>Cardiff.40.06</td><td>3</td><td>8</td><td>8</td><td>1</td><td>6590</td><td>256.48</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>503.01</td></tr><tr><td>Cardiff.40.06</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>26451</td><td>211.78</td><td>7</td><td>2909.0</td><td>2909</td><td>0.00</td><td>865.43</td></tr><tr><td>Cardiff.40.06</td><td>3</td><td>15</td><td>10</td><td>1</td><td>13386</td><td>262.61</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>425.62</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
solving 10 for the first time.

We also proposed 6 new sets of instances to promote research on VRP-D-type problems. The experiments on our method show that we solve all but one clustered instance with 100 customers and more than half of the clustered instances with 120 customers. In the random dataset with 40 customers and large drone-reachable neighborhoods, 11 instances remain open. To tackle these instances, we proposed a heuristic branch-cut-and-price approach based on eliminating certain arcs in the subproblems. This approach shows excellent results, as the gaps with the best-known solutions are minimal. We also show the improvement induced by adapting the rounded capacity cuts and the SPR criterion.

Testing these new instances highlighted some limitations of our branch-cut-and-price approach. In the largest instances, the size of the sub-problem graph becomes intractable due to the exponential number of parallel arcs representing drone round-trip possibilities. A possible remedy is to model the scheduling problem as part of the RCSP to avoid explicitly enumerating the scheduling solutions. This modification would require special care for the resources, as only one drone is responsible for the duration of the makespan. In the same vein, it would be helpful to find other rules of dominance for the drone arcs.

To enhance the speed of the exact algorithm, an alternative approach would be to develop a problem-specific primal heuristic aimed at quickly identifying high-quality primal bounds. It would also be beneficial to develop instances better suited for truck and drone deliveries, incorporating distinct metrics for drones and trucks, as well as realistic features related to last-mile delivery services.

One could also consider uncertainty regarding traffic congestion. It could also be interesting to compare the gain using the 2E-VRP-D and the VRPD on different sets of instances and objective functions. In addition, most national and metropolitan public authorities are moving towards tighter regulations for deliveries in city centers: more restrictions are being imposed on vehicle access times and, therefore, also on customer deliveries. One could also integrate time window constraints with non-zero ready times into our model. This extension will require special care for drone operations, as drones might need to wait between round trips.

Another perspective is to apply this type of enumeration strategy to problems with a similar structure, such as the park-and-loop vehicle routing problem. In this problem, the vehicle driver parked at a client can make a walking tour to serve customers, avoiding network congestion and gas use.

# Appendix A Calculation of drone-reachable neighborhood

Let $Q^d$ be the drone's maximal capacity in kg. For $i \in V$, $f_i^d$ is set to 0 if $q_i > Q^d$ or if $i$ is not available for deliveries by drone. Otherwise, we set $f_i^d = 1$. We introduce a parameter $\tilde{f}_i^d$ expressing whether a truck parked at customer $i \in V$ can launch drones. A customer's location might not be available for a drone launch if no parking spot is available nearby, for example. In this case, we set $\tilde{f}_i^d = 0$ and $\tilde{f}_i^d = 1$ otherwise. An energy function limits the maximal flight
<table><caption>Table 14: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>Γ<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff.40.06</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>17176</td><td>175.53</td><td>5</td><td>2909.0</td><td>2909</td><td>0.00</td><td>591.90</td></tr><tr><td>Cardiff.40.07</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1796</td><td>77.83</td><td>1</td><td>2510.25</td><td>2491.27</td><td>0.76</td><td>78.45</td></tr><tr><td>Cardiff.40.07</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1947</td><td>81.88</td><td>1</td><td>2510.25</td><td>2491.27</td><td>0.76</td><td>82.69</td></tr><tr><td>Cardiff.40.07</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2756</td><td>96.54</td><td>3</td><td>2508.6</td><td>2491.27</td><td>0.70</td><td>220.03</td></tr><tr><td>Cardiff.40.07</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6981</td><td>141.71</td><td>7</td><td>2498.08</td><td>2491.27</td><td>0.27</td><td>711.42</td></tr><tr><td>Cardiff.40.07</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2579</td><td>115.86</td><td>3</td><td>2508.6</td><td>2491.27</td><td>0.70</td><td>239.77</td></tr><tr><td>Cardiff.40.07</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2781</td><td>112.91</td><td>3</td><td>2508.6</td><td>2491.27</td><td>0.70</td><td>243.98</td></tr><tr><td>Cardiff.40.07</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2884</td><td>116.35</td><td>3</td><td>2508.6</td><td>2491.27</td><td>0.70</td><td>205.18</td></tr><tr><td>Cardiff.40.07</td><td>3</td><td>5</td><td>8</td><td>1</td><td>7195</td><td>173.82</td><td>7</td><td>2498.08</td><td>2491.27</td><td>0.27</td><td>772.11</td></tr><tr><td>Cardiff.40.07</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>9005</td><td>154.60</td><td>3</td><td>2498.08</td><td>2491.27</td><td>0.27</td><td>362.34</td></tr><tr><td>Cardiff.40.07</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7704</td><td>170.55</td><td>3</td><td>2498.08</td><td>2491.27</td><td>0.27</td><td>394.30</td></tr><tr><td>Cardiff.40.07</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>144776</td><td>701.13</td><td>3</td><td>-</td><td>2491.27</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.07</td><td>3</td><td>15</td><td>10</td><td>1</td><td>18094</td><td>224.58</td><td>3</td><td>2491.27</td><td>2491.27</td><td>0.00</td><td>414.07</td></tr><tr><td>Cardiff.40.07</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>70597</td><td>375.00</td><td>9</td><td>-</td><td>2491.27</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.08</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>67.13</td><td>5</td><td>3964.98</td><td>3834.02</td><td>3.42</td><td>288.31</td></tr><tr><td>Cardiff.40.08</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1932</td><td>70.08</td><td>7</td><td>3962.05</td><td>3834.02</td><td>3.34</td><td>263.64</td></tr><tr><td>Cardiff.40.08</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2590</td><td>100.03</td><td>3</td><td>3880.87</td><td>3834.02</td><td>1.22</td><td>194.73</td></tr><tr><td>Cardiff.40.08</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5238</td><td>143.00</td><td>1</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>143.70</td></tr><tr><td>Cardiff.40.08</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2444</td><td>138.10</td><td>3</td><td>3880.87</td><td>3834.02</td><td>1.22</td><td>223.55</td></tr><tr><td>Cardiff.40.08</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2605</td><td>114.78</td><td>3</td><td>3870.2</td><td>3834.02</td><td>0.94</td><td>205.67</td></tr><tr><td>Cardiff.40.08</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2703</td><td>115.98</td><td>3</td><td>3870.2</td><td>3834.02</td><td>0.94</td><td>191.49</td></tr><tr><td>Cardiff.40.08</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5467</td><td>226.22</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>725.98</td></tr><tr><td>Cardiff.40.08</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>6622</td><td>235.22</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>683.52</td></tr><tr><td>Cardiff.40.08</td><td>3</td><td>8</td><td>8</td><td>1</td><td>5922</td><td>217.93</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>751.23</td></tr><tr><td>Cardiff.40.08</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>9510</td><td>229.68</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>799.80</td></tr><tr><td>Cardiff.40.08</td><td>3</td><td>15</td><td>10</td><td>1</td><td>6941</td><td>181.43</td><td>3</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>384.79</td></tr><tr><td>Cardiff.40.08</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>6941</td><td>201.69</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>631.42</td></tr><tr><td>Cardiff.40.09</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1799</td><td>148.26</td><td>3</td><td>4122.2</td><td>3668.2</td><td>12.38</td><td>323.28</td></tr><tr><td>Cardiff.40.09</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1950</td><td>105.21</td><td>3</td><td>4114.32</td><td>3668.2</td><td>12.16</td><td>172.51</td></tr><tr><td>Cardiff.40.09</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2698</td><td>186.22</td><td>5</td><td>3977.35</td><td>3668.2</td><td>8.43</td><td>469.85</td></tr><tr><td>Cardiff.40.09</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6482</td><td>180.19</td><td>33</td><td>3726.48</td><td>3668.2</td><td>1.59</td><td>10800.00</td></tr><tr><td>Cardiff.40.09</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2530</td><td>224.38</td><td>3</td><td>3955.0</td><td>3668.2</td><td>7.82</td><td>367.35</td></tr><tr><td>Cardiff.40.09</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2717</td><td>222.18</td><td>3</td><td>3924.03</td><td>3668.2</td><td>6.97</td><td>334.68</td></tr><tr><td>Cardiff.40.09</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2830</td><td>236.50</td><td>3</td><td>3924.03</td><td>3668.2</td><td>6.97</td><td>369.09</td></tr><tr><td>Cardiff.40.09</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6656</td><td>421.09</td><td>49</td><td>3668.2</td><td>3668.2</td><td>0.00</td><td>5115.00</td></tr><tr><td>Cardiff.40.09</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8011</td><td>446.94</td><td>49</td><td>3719.7</td><td>3668.2</td><td>1.40</td><td>10800.00</td></tr><tr><td>Cardiff.40.09</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7350</td><td>323.74</td><td>31</td><td>3668.2</td><td>3668.2</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff.40.09</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>80282</td><td>380.71</td><td>15</td><td>4639.5</td><td>3668.2</td><td>26.48</td><td>10800.00</td></tr><tr><td>Cardiff.40.09</td><td>3</td><td>15</td><td>10</td><td>1</td><td>15941</td><td>361.56</td><td>65</td><td>3668.2</td><td>3668.2</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff.40.09</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>42829</td><td>362.02</td><td>21</td><td>3876.85</td><td>3668.2</td><td>5.69</td><td>10800.00</td></tr><tr><td>Cardiff.40.10</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1800</td><td>76.35</td><td>1</td><td>2769.2</td><td>2692.08</td><td>2.86</td><td>76.72</td></tr><tr><td>Cardiff.40.10</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1950</td><td>76.03</td><td>3</td><td>2769.2</td><td>2692.08</td><td>2.86</td><td>114.10</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
distance, calculated as follows: $P(q) = (W+m+q)^{\frac{3}{2}} \sqrt{\frac{g^3}{2\rho\zeta\hbar}}$ in Watt, introduced by Dorling et al. (2016) as the hovering power consumption of a h-rotor drone, an upper bound on the general power consumption of a h-rotor drone, and based on Leishman (2006). W is the frame weight (kg), m the battery weight (kg), q the payload (kg), g is the force due to gravity (N), ρ the fluid density of air in (kg/m³) and ζ the area of spinning blade (m²). We note $B_c$ the drone's battery capacity in watt-hours. Let g = 9.81 N/kg and ρ = 1.204 kg/m³ as in (Dorling et al., 2016).

$$N_i = \{j \in V | (\bar{f}_i^d == 1) \land (f_j^d == 1) \land (P(q_i) * c_{i,j}^d + P(0) * c_{j,i}^d \le B_c) \land (c_{0,i}^v + c_{i,j}^d \le \bar{d}_j) \quad i \in V\}$$

## Appendix B Detailed computational experiments

In the redfollowing tables we present the detailed results of our experiments. We present different information among: the name of the set (Instances), the maximum number of arcs in the subproblem $G^D$ ($|A^D|$) of all instances, the average maximal size of the drone-reachable neighborhoods ($\hat{\mathcal{K}}$), the number of instances solved optimally over the total number instances (Solved), the number of instances for which no feasible solution have been found (No Sol), the average Gap of the instances for which a feasible solution have been found, the average time in seconds required to solve the instances of the dataset (Time) and the average number of nodes processed in the branch-cut-and-price algorithm (Nodes).

<table><caption>Table 11: Detailed performance of the exact algorithm on the small-size instances</caption><thead><tr><th>Instance</th><th>|A<sup>max</sup>|</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_10_01</td><td>217</td><td>0</td><td>0.72</td><td>1</td><td>1223.62</td><td>1223.62</td><td>0</td><td>0.79</td></tr><tr><td>Cardiff_10_02</td><td>134</td><td>0</td><td>0.447</td><td>1</td><td>1905.08</td><td>1905.08</td><td>0</td><td>0.49</td></tr><tr><td>Cardiff_10_03</td><td>147</td><td>0</td><td>0.543</td><td>1</td><td>1412.67</td><td>1412.67</td><td>0</td><td>0.6</td></tr><tr><td>Cardiff_10_04</td><td>136</td><td>0</td><td>0.572</td><td>1</td><td>1633.32</td><td>1633.32</td><td>0</td><td>0.62</td></tr><tr><td>Cardiff_10_05</td><td>136</td><td>0</td><td>0.436</td><td>1</td><td>1682.93</td><td>1682.93</td><td>0</td><td>0.48</td></tr><tr><td>Cardiff_10_06</td><td>155</td><td>0</td><td>0.591</td><td>1</td><td>1221.75</td><td>1221.75</td><td>0</td><td>0.65</td></tr><tr><td>Cardiff_10_07</td><td>129</td><td>0</td><td>0.473</td><td>1</td><td>1931.75</td><td>1931.75</td><td>0</td><td>0.52</td></tr><tr><td>Cardiff_10_08</td><td>143</td><td>0</td><td>0.615</td><td>1</td><td>1578.15</td><td>1578.15</td><td>0</td><td>0.67</td></tr><tr><td>Cardiff_10_09</td><td>126</td><td>0</td><td>0.456</td><td>1</td><td>2552.03</td><td>2552.03</td><td>0</td><td>0.49</td></tr><tr><td>Cardiff_10_10</td><td>125</td><td>0</td><td>0.46</td><td>1</td><td>2045.18</td><td>2045.18</td><td>0</td><td>0.5</td></tr><tr><td>Cardiff_10_11</td><td>137</td><td>0</td><td>0.424</td><td>1</td><td>2095.25</td><td>2095.25</td><td>0</td><td>0.46</td></tr><tr><td>Cardiff_10_12</td><td>161</td><td>0</td><td>0.578</td><td>1</td><td>1737.25</td><td>1737.25</td><td>0</td><td>0.63</td></tr><tr><td>Cardiff_10_13</td><td>136</td><td>0</td><td>0.5</td><td>1</td><td>1485.88</td><td>1485.88</td><td>0</td><td>0.57</td></tr><tr><td>Cardiff_10_14</td><td>125</td><td>0</td><td>0.441</td><td>1</td><td>1926.62</td><td>1926.62</td><td>0</td><td>0.5</td></tr><tr><td>Cardiff_10_15</td><td>202</td><td>0</td><td>0.479</td><td>1</td><td>1814.33</td><td>1814.33</td><td>0</td><td>0.53</td></tr><tr><td>Cardiff_10_16</td><td>148</td><td>0</td><td>0.602</td><td>1</td><td>1140.05</td><td>1140.05</td><td>0</td><td>0.69</td></tr></tbody><tfoot><tr><td colspan="9">Continued on next page</td></tr></tfoot></table>
<table><caption>Table 14: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>Γ<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff.40.10</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2669</td><td>85.22</td><td>1</td><td>2711.32</td><td>2692.08</td><td>0.71</td><td>86.05</td></tr><tr><td>Cardiff.40.10</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5995</td><td>141.77</td><td>3</td><td>2711.32</td><td>2692.08</td><td>0.71</td><td>276.20</td></tr><tr><td>Cardiff.40.10</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2515</td><td>99.54</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>100.29</td></tr><tr><td>Cardiff.40.10</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2690</td><td>100.58</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>100.99</td></tr><tr><td>Cardiff.40.10</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2799</td><td>103.25</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>103.87</td></tr><tr><td>Cardiff.40.10</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6222</td><td>151.79</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>152.67</td></tr><tr><td>Cardiff.40.10</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7334</td><td>173.19</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>174.24</td></tr><tr><td>Cardiff.40.10</td><td>3</td><td>8</td><td>8</td><td>1</td><td>6779</td><td>136.26</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>136.99</td></tr><tr><td>Cardiff.40.10</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>55901</td><td>167.17</td><td>5</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>521.83</td></tr><tr><td>Cardiff.40.10</td><td>3</td><td>15</td><td>10</td><td>1</td><td>12351</td><td>156.87</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>157.60</td></tr><tr><td>Cardiff.40.10</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>28248</td><td>210.33</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>211.15</td></tr><tr><td>Cardiff.40.11</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1792</td><td>5.47</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>5.69</td></tr><tr><td>Cardiff.40.11</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1921</td><td>4.57</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>4.79</td></tr><tr><td>Cardiff.40.11</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2619</td><td>9.09</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>9.75</td></tr><tr><td>Cardiff.40.11</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6236</td><td>10.38</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>10.86</td></tr><tr><td>Cardiff.40.11</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2467</td><td>8.26</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>8.76</td></tr><tr><td>Cardiff.40.11</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2635</td><td>8.60</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>9.02</td></tr><tr><td>Cardiff.40.11</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2774</td><td>8.18</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>8.48</td></tr><tr><td>Cardiff.40.11</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6535</td><td>10.62</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>10.95</td></tr><tr><td>Cardiff.40.11</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8065</td><td>12.39</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>13.12</td></tr><tr><td>Cardiff.40.11</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7188</td><td>13.01</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>13.37</td></tr><tr><td>Cardiff.40.11</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>48327</td><td>32.05</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>33.12</td></tr><tr><td>Cardiff.40.11</td><td>3</td><td>15</td><td>10</td><td>1</td><td>15181</td><td>16.39</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>17.03</td></tr><tr><td>Cardiff.40.11</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>27035</td><td>23.10</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>23.63</td></tr><tr><td>Cardiff.40.12</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1792</td><td>54.70</td><td>3</td><td>2692.03</td><td>2642.87</td><td>1.86</td><td>72.94</td></tr><tr><td>Cardiff.40.12</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1929</td><td>53.43</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>66.04</td></tr><tr><td>Cardiff.40.12</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2577</td><td>60.04</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>105.03</td></tr><tr><td>Cardiff.40.12</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5911</td><td>99.59</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>145.91</td></tr><tr><td>Cardiff.40.12</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2435</td><td>81.01</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>129.47</td></tr><tr><td>Cardiff.40.12</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2596</td><td>85.92</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>140.96</td></tr><tr><td>Cardiff.40.12</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2720</td><td>87.54</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>142.77</td></tr><tr><td>Cardiff.40.12</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5911</td><td>98.25</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>138.24</td></tr><tr><td>Cardiff.40.12</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7484</td><td>109.45</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>168.09</td></tr><tr><td>Cardiff.40.12</td><td>3</td><td>8</td><td>8</td><td>1</td><td>6505</td><td>109.39</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>159.03</td></tr><tr><td>Cardiff.40.12</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>81967</td><td>173.31</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>251.61</td></tr><tr><td>Cardiff.40.12</td><td>3</td><td>15</td><td>10</td><td>1</td><td>14174</td><td>108.45</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>165.07</td></tr><tr><td>Cardiff.40.12</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>35393</td><td>157.84</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>217.98</td></tr><tr><td>Cardiff.40.13</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>76.77</td><td>1</td><td>2999.0</td><td>2827.82</td><td>6.05</td><td>77.11</td></tr><tr><td>Cardiff.40.13</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1935</td><td>74.68</td><td>1</td><td>2999.0</td><td>2827.82</td><td>6.05</td><td>75.12</td></tr><tr><td>Cardiff.40.13</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2676</td><td>116.97</td><td>1</td><td>2883.55</td><td>2827.82</td><td>1.97</td><td>117.87</td></tr><tr><td>Cardiff.40.13</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6437</td><td>141.25</td><td>57</td><td>2864.38</td><td>2827.82</td><td>1.29</td><td>4819.00</td></tr><tr><td>Cardiff.40.13</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2528</td><td>141.22</td><td>3</td><td>2881.38</td><td>2827.82</td><td>1.89</td><td>254.77</td></tr></tbody><tfoot><tr><td colspan="12" style="text-align: right;">Continued on next page</td></tr></tfoot></table>
<table><caption>Table 11: Detailed performance of the exact algorithm on the small-size instances</caption><thead><tr><th>Instance</th><th>A<sup>max</sup></th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_10_17</td><td>129</td><td>0</td><td>0.449</td><td>1</td><td>1733.83</td><td>1733.83</td><td>0</td><td>0.5</td></tr><tr><td>Cardiff_10_18</td><td>137</td><td>0</td><td>0.456</td><td>1</td><td>1960.93</td><td>1960.93</td><td>0</td><td>0.51</td></tr><tr><td>Cardiff_10_19</td><td>136</td><td>0</td><td>0.478</td><td>1</td><td>1533.67</td><td>1533.67</td><td>0</td><td>0.53</td></tr><tr><td>Cardiff_10_20</td><td>135</td><td>0</td><td>0.502</td><td>1</td><td>1366.42</td><td>1366.42</td><td>0</td><td>0.59</td></tr><tr><td>Cardiff_15_01</td><td>993</td><td>0</td><td>3.59</td><td>1</td><td>1332</td><td>1332</td><td>0</td><td>3.66</td></tr><tr><td>Cardiff_15_02</td><td>383</td><td>0</td><td>0.773</td><td>1</td><td>1970.62</td><td>1970.62</td><td>0</td><td>0.83</td></tr><tr><td>Cardiff_15_03</td><td>292</td><td>0</td><td>1.099</td><td>1</td><td>1971.38</td><td>1971.38</td><td>0</td><td>1.19</td></tr><tr><td>Cardiff_15_04</td><td>320</td><td>0</td><td>0.799</td><td>1</td><td>2188.32</td><td>2188.32</td><td>0</td><td>0.84</td></tr><tr><td>Cardiff_15_05</td><td>311</td><td>0</td><td>0.727</td><td>1</td><td>1831.27</td><td>1831.27</td><td>0</td><td>0.79</td></tr><tr><td>Cardiff_15_06</td><td>408</td><td>0</td><td>1.395</td><td>1</td><td>1695.17</td><td>1695.17</td><td>0</td><td>1.5</td></tr><tr><td>Cardiff_15_07</td><td>318</td><td>0</td><td>0.755</td><td>1</td><td>2050.67</td><td>2050.67</td><td>0</td><td>0.82</td></tr><tr><td>Cardiff_15_08</td><td>318</td><td>0</td><td>1.091</td><td>1</td><td>1689.55</td><td>1689.55</td><td>0</td><td>1.17</td></tr><tr><td>Cardiff_15_09</td><td>322</td><td>0</td><td>0.687</td><td>1</td><td>2765.68</td><td>2765.68</td><td>0</td><td>0.74</td></tr><tr><td>Cardiff_15_10</td><td>271</td><td>0</td><td>0.9</td><td>1</td><td>2984.98</td><td>2984.98</td><td>0</td><td>0.94</td></tr><tr><td>Cardiff_15_11</td><td>319</td><td>0</td><td>0.824</td><td>1</td><td>2242.98</td><td>2242.98</td><td>0</td><td>0.89</td></tr><tr><td>Cardiff_15_12</td><td>379</td><td>0</td><td>0.991</td><td>1</td><td>2155.83</td><td>2155.83</td><td>0</td><td>1.06</td></tr><tr><td>Cardiff_15_13</td><td>369</td><td>0</td><td>1.512</td><td>1</td><td>1606.55</td><td>1606.55</td><td>0</td><td>1.59</td></tr><tr><td>Cardiff_15_14</td><td>300</td><td>0</td><td>4.598</td><td>1</td><td>2369.88</td><td>2369.88</td><td>0</td><td>4.76</td></tr><tr><td>Cardiff_15_15</td><td>728</td><td>0</td><td>1.228</td><td>1</td><td>1883.45</td><td>1883.45</td><td>0</td><td>1.29</td></tr><tr><td>Cardiff_15_16</td><td>522</td><td>0</td><td>1.129</td><td>1</td><td>1756.85</td><td>1756.85</td><td>0</td><td>1.22</td></tr><tr><td>Cardiff_15_17</td><td>293</td><td>0</td><td>0.583</td><td>1</td><td>1858.17</td><td>1858.17</td><td>0</td><td>0.64</td></tr><tr><td>Cardiff_15_18</td><td>330</td><td>0</td><td>0.893</td><td>1</td><td>2288.73</td><td>2288.73</td><td>0</td><td>0.99</td></tr><tr><td>Cardiff_15_19</td><td>303</td><td>0</td><td>0.69</td><td>1</td><td>1762.17</td><td>1762.17</td><td>0</td><td>0.76</td></tr><tr><td>Cardiff_15_20</td><td>306</td><td>0</td><td>0.871</td><td>1</td><td>1697.1</td><td>1697.1</td><td>0</td><td>0.95</td></tr><tr><td>Cardiff_25_01</td><td>1622</td><td>0</td><td>78.333</td><td>1</td><td>2233.87</td><td>2233.87</td><td>0</td><td>78.81</td></tr><tr><td>Cardiff_25_02</td><td>1688</td><td>0.3</td><td>47.381</td><td>3</td><td>1979.95</td><td>1979.95</td><td>0</td><td>64.68</td></tr><tr><td>Cardiff_25_03</td><td>985</td><td>0.7</td><td>28.089</td><td>3</td><td>2389.7</td><td>2389.7</td><td>0</td><td>40.9</td></tr><tr><td>Cardiff_25_04</td><td>1280</td><td>5.8</td><td>31.931</td><td>3</td><td>2797.63</td><td>2797.63</td><td>0</td><td>66.87</td></tr><tr><td>Cardiff_25_05</td><td>1481</td><td>0</td><td>27.47</td><td>1</td><td>2062.97</td><td>2062.97</td><td>0</td><td>27.72</td></tr><tr><td>Cardiff_25_06</td><td>1140</td><td>0</td><td>24.194</td><td>1</td><td>2075.48</td><td>2075.48</td><td>0</td><td>24.52</td></tr><tr><td>Cardiff_25_07</td><td>1212</td><td>1.3</td><td>31.748</td><td>3</td><td>2112.6</td><td>2112.6</td><td>0</td><td>44.93</td></tr><tr><td>Cardiff_25_08</td><td>1119</td><td>0</td><td>20.74</td><td>1</td><td>2605.48</td><td>2605.48</td><td>0</td><td>20.91</td></tr><tr><td>Cardiff_25_09</td><td>1634</td><td>1.4</td><td>33.46</td><td>3</td><td>2055.22</td><td>2055.22</td><td>0</td><td>48.93</td></tr><tr><td>Cardiff_25_10</td><td>1605</td><td>2.7</td><td>75.233</td><td>5</td><td>2217.12</td><td>2217.12</td><td>0</td><td>296.04</td></tr><tr><td>Cardiff_25_11</td><td>5207</td><td>0.7</td><td>85.909</td><td>3</td><td>2051.12</td><td>2051.12</td><td>0</td><td>99.0</td></tr><tr><td>Cardiff_25_12</td><td>1245</td><td>7</td><td>18.103</td><td>5</td><td>4775.93</td><td>4775.93</td><td>0</td><td>157.68</td></tr><tr><td>Cardiff_25_13</td><td>2730</td><td>0</td><td>57.655</td><td>1</td><td>2248.63</td><td>2248.63</td><td>0</td><td>58.04</td></tr><tr><td>Cardiff_25_14</td><td>900</td><td>4</td><td>57.477</td><td>3</td><td>2530.68</td><td>2530.68</td><td>0</td><td>257.38</td></tr><tr><td>Cardiff_25_15</td><td>1240</td><td>0.7</td><td>35.323</td><td>3</td><td>2871.6</td><td>2871.6</td><td>0</td><td>51.14</td></tr><tr><td>Cardiff_25_16</td><td>1553</td><td>1.5</td><td>29.461</td><td>3</td><td>2503.27</td><td>2503.27</td><td>0</td><td>40.64</td></tr><tr><td>Cardiff_25_17</td><td>3780</td><td>0</td><td>65.629</td><td>1</td><td>2275.83</td><td>2275.83</td><td>0</td><td>65.9</td></tr></tbody><tfoot><tr><td colspan="9" style="text-align: center;">Continued on next page</td></tr></tfoot></table>
<table><caption>Table 14: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>Γ<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff.40.13</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2717</td><td>101.87</td><td>1</td><td>2827.82</td><td>2827.82</td><td>0.00</td><td>102.28</td></tr><tr><td>Cardiff.40.13</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2853</td><td>99.53</td><td>1</td><td>2827.82</td><td>2827.82</td><td>0.00</td><td>100.08</td></tr><tr><td>Cardiff.40.13</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6635</td><td>142.07</td><td>79</td><td>2827.82</td><td>2827.82</td><td>0.00</td><td>6390.00</td></tr><tr><td>Cardiff.40.13</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8202</td><td>152.43</td><td>67</td><td>-</td><td>2827.82</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.13</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7251</td><td>151.86</td><td>73</td><td>2827.82</td><td>2827.82</td><td>0.00</td><td>8276.00</td></tr><tr><td>Cardiff.40.13</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>121449</td><td>206.87</td><td>23</td><td>2913.13</td><td>2827.82</td><td>3.02</td><td>10800.00</td></tr><tr><td>Cardiff.40.13</td><td>3</td><td>15</td><td>10</td><td>1</td><td>16815</td><td>208.34</td><td>113</td><td>2827.82</td><td>2827.82</td><td>0.00</td><td>8293.00</td></tr><tr><td>Cardiff.40.13</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>60077</td><td>156.43</td><td>41</td><td>-</td><td>2827.82</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.14</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1796</td><td>75.74</td><td>15</td><td>3091.18</td><td>2910.9</td><td>6.19</td><td>960.53</td></tr><tr><td>Cardiff.40.14</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1929</td><td>93.03</td><td>45</td><td>3053.88</td><td>2910.9</td><td>4.91</td><td>2932.49</td></tr><tr><td>Cardiff.40.14</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2680</td><td>78.02</td><td>63</td><td>3028.5</td><td>2910.9</td><td>4.04</td><td>3480.14</td></tr><tr><td>Cardiff.40.14</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6624</td><td>117.48</td><td>63</td><td>3023.08</td><td>2910.9</td><td>3.85</td><td>10800.00</td></tr><tr><td>Cardiff.40.14</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2515</td><td>108.57</td><td>139</td><td>2957.28</td><td>2910.9</td><td>1.59</td><td>9388.00</td></tr><tr><td>Cardiff.40.14</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2705</td><td>112.64</td><td>55</td><td>2957.28</td><td>2910.9</td><td>1.59</td><td>3692.00</td></tr><tr><td>Cardiff.40.14</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2819</td><td>120.63</td><td>39</td><td>2957.28</td><td>2910.9</td><td>1.59</td><td>2816.44</td></tr><tr><td>Cardiff.40.14</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6992</td><td>170.78</td><td>53</td><td>-</td><td>2910.9</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.14</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8269</td><td>192.80</td><td>63</td><td>-</td><td>2910.9</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.14</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7750</td><td>187.90</td><td>81</td><td>-</td><td>2910.9</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.14</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>246924</td><td>1796.16</td><td>1</td><td>-</td><td>2910.9</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.14</td><td>3</td><td>15</td><td>10</td><td>1</td><td>21082</td><td>102.81</td><td>113</td><td>2910.9</td><td>2910.9</td><td>0.00</td><td>7905.00</td></tr><tr><td>Cardiff.40.14</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>116234</td><td>1094.78</td><td>3</td><td>-</td><td>2910.9</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.15</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1797</td><td>82.77</td><td>1</td><td>2760.08</td><td>2707.12</td><td>1.96</td><td>83.05</td></tr><tr><td>Cardiff.40.15</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1942</td><td>106.92</td><td>1</td><td>2760.08</td><td>2707.12</td><td>1.96</td><td>107.20</td></tr><tr><td>Cardiff.40.15</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2643</td><td>125.59</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>205.99</td></tr><tr><td>Cardiff.40.15</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6574</td><td>174.10</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>318.79</td></tr><tr><td>Cardiff.40.15</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2506</td><td>118.92</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>186.76</td></tr><tr><td>Cardiff.40.15</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2680</td><td>134.02</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>201.04</td></tr><tr><td>Cardiff.40.15</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2730</td><td>132.68</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>198.58</td></tr><tr><td>Cardiff.40.15</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6721</td><td>172.12</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>330.60</td></tr><tr><td>Cardiff.40.15</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8005</td><td>180.66</td><td>9</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>966.44</td></tr><tr><td>Cardiff.40.15</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7296</td><td>186.29</td><td>5</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>597.70</td></tr><tr><td>Cardiff.40.15</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>37408</td><td>185.77</td><td>41</td><td>2716.77</td><td>2707.12</td><td>0.36</td><td>10800.00</td></tr><tr><td>Cardiff.40.15</td><td>3</td><td>15</td><td>10</td><td>1</td><td>15169</td><td>133.81</td><td>25</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>3442.63</td></tr><tr><td>Cardiff.40.15</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>23134</td><td>200.91</td><td>35</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>6986.00</td></tr><tr><td>Cardiff.40.16</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1796</td><td>152.34</td><td>3</td><td>4095.77</td><td>3353.42</td><td>22.14</td><td>325.30</td></tr><tr><td>Cardiff.40.16</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1938</td><td>139.04</td><td>3</td><td>3378.82</td><td>3353.42</td><td>0.76</td><td>246.38</td></tr><tr><td>Cardiff.40.16</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2634</td><td>157.76</td><td>3</td><td>3378.82</td><td>3353.42</td><td>0.76</td><td>290.33</td></tr><tr><td>Cardiff.40.16</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6861</td><td>251.24</td><td>37</td><td>3415.72</td><td>3353.42</td><td>1.86</td><td>10800.00</td></tr><tr><td>Cardiff.40.16</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2483</td><td>223.02</td><td>3</td><td>3378.82</td><td>3353.42</td><td>0.76</td><td>387.75</td></tr><tr><td>Cardiff.40.16</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2660</td><td>146.76</td><td>3</td><td>3353.42</td><td>3353.42</td><td>0.00</td><td>271.65</td></tr><tr><td>Cardiff.40.16</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2771</td><td>161.23</td><td>3</td><td>3353.42</td><td>3353.42</td><td>0.00</td><td>291.54</td></tr><tr><td>Cardiff.40.16</td><td>3</td><td>5</td><td>8</td><td>1</td><td>7072</td><td>278.11</td><td>49</td><td>3353.42</td><td>3353.42</td><td>0.00</td><td>10800.00</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
<table><caption>Table 11: Detailed performance of the exact algorithm on the small-size instances</caption><thead><tr><th>Instance</th><th>A<sup>max</sup></th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_25_18</td><td>922</td><td>0.6</td><td>56.438</td><td>3</td><td>2167.9</td><td>2167.9</td><td>0</td><td>125.93</td></tr><tr><td>Cardiff_25_19</td><td>1796</td><td>1.7</td><td>55.092</td><td>3</td><td>2257.8</td><td>2257.8</td><td>0</td><td>71.74</td></tr><tr><td>Cardiff_25_20</td><td>2449</td><td>0</td><td>82.744</td><td>1</td><td>2816.63</td><td>2816.63</td><td>0</td><td>83.14</td></tr><tr><td>c101_35</td><td>2460</td><td>0.7</td><td>20.556</td><td>3</td><td>1896.5</td><td>1896.5</td><td>0</td><td>113.09</td></tr><tr><td>c102_35</td><td>2460</td><td>0.5</td><td>27.488</td><td>5</td><td>1892.1</td><td>1892.1</td><td>0</td><td>729.18</td></tr><tr><td>c103_35</td><td>2460</td><td>0.6</td><td>17.262</td><td>3</td><td>1889.2</td><td>1889.2</td><td>0</td><td>32.16</td></tr><tr><td>c104_35</td><td>2472</td><td>0.8</td><td>50.63</td><td>25</td><td>1888.6</td><td>1888.6</td><td>0</td><td>1406.2</td></tr><tr><td>c105_35</td><td>2464</td><td>0.5</td><td>38.436</td><td>3</td><td>1896.5</td><td>1896.5</td><td>0</td><td>257.74</td></tr><tr><td>c106_35</td><td>2460</td><td>0.6</td><td>34.21</td><td>5</td><td>1896.5</td><td>1896.5</td><td>0</td><td>241.3</td></tr><tr><td>c107_35</td><td>2490</td><td>0.6</td><td>37.053</td><td>3</td><td>1896.5</td><td>1896.5</td><td>0</td><td>162.77</td></tr><tr><td>c108_35</td><td>2460</td><td>0.7</td><td>28.446</td><td>5</td><td>1893</td><td>1893</td><td>0</td><td>408.04</td></tr><tr><td>c109_35</td><td>2490</td><td>0.5</td><td>121.423</td><td>21</td><td>1893</td><td>1893</td><td>0</td><td>1656.22</td></tr></tbody></table>

Note that the instance *Cardiff_40_11* is not feasible under our assumptions.

<table><caption>Table 12: Detailed performance of the exact algorithm on instances adapted from (Chen et al., 2021)</caption><thead><tr><th>Instance</th><th>A<sup>max</sup></th><th>K̂</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_01</td><td>13034</td><td>10</td><td>0.3</td><td>214.127</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0</td><td>306.84</td></tr><tr><td>Cardiff_40_02</td><td>95883</td><td>14</td><td>20.1</td><td>92.803</td><td>37</td><td>3044.72</td><td>3217.42</td><td>5.7</td><td>10800</td></tr><tr><td>Cardiff_40_03</td><td>30318</td><td>12</td><td>2.7</td><td>168.228</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0</td><td>351.02</td></tr><tr><td>Cardiff_40_04</td><td>169680</td><td>15</td><td>-</td><td>401.227</td><td>9</td><td>4292.31</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>Cardiff_40_05</td><td>25801</td><td>11</td><td>1.7</td><td>329.68</td><td>11</td><td>3770.9</td><td>3770.9</td><td>0</td><td>2141.71</td></tr><tr><td>Cardiff_40_06</td><td>26451</td><td>12</td><td>12.5</td><td>203.151</td><td>19</td><td>2909</td><td>2909</td><td>0</td><td>1633.04</td></tr><tr><td>Cardiff_40_07</td><td>89523</td><td>15</td><td>-</td><td>674.039</td><td>3</td><td>2093.42</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>Cardiff_40_08</td><td>9510</td><td>9</td><td>0.6</td><td>191.295</td><td>3</td><td>3834.02</td><td>3834.02</td><td>0</td><td>358.6</td></tr><tr><td>Cardiff_40_09</td><td>81734</td><td>14</td><td>35.1</td><td>381.086</td><td>11</td><td>3580.1</td><td>4484.18</td><td>25.3</td><td>10800</td></tr><tr><td>Cardiff_40_10</td><td>55913</td><td>14</td><td>1.3</td><td>171.288</td><td>3</td><td>2692.08</td><td>2692.08</td><td>0</td><td>573.32</td></tr><tr><td>Cardiff_40_11</td><td>48327</td><td>12</td><td>0</td><td>29.336</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0</td><td>30.12</td></tr><tr><td>Cardiff_40_12</td><td>38128</td><td>14</td><td>0.7</td><td>200.695</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0</td><td>276.22</td></tr><tr><td>Cardiff_40_13</td><td>121649</td><td>14</td><td>21.9</td><td>196.029</td><td>23</td><td>2723.1</td><td>2913.13</td><td>7</td><td>10800</td></tr><tr><td>Cardiff_40_14</td><td>247124</td><td>15</td><td>-</td><td>1716.28</td><td>1</td><td>2236.37</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>Cardiff_40_15</td><td>33041</td><td>12</td><td>20.3</td><td>181.949</td><td>39</td><td>2606.74</td><td>2707.12</td><td>3.9</td><td>10800</td></tr><tr><td>Cardiff_40_16</td><td>153756</td><td>15</td><td>-</td><td>785.406</td><td>5</td><td>2927.97</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>Cardiff_40_17</td><td>24463</td><td>13</td><td>3.2</td><td>278.477</td><td>23</td><td>2733.69</td><td>2781.87</td><td>1.8</td><td>10800</td></tr><tr><td>Cardiff_40_18</td><td>93744</td><td>14</td><td>-</td><td>224.516</td><td>21</td><td>2707.07</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>Cardiff_40_19</td><td>10767</td><td>11</td><td>1.9</td><td>198.707</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0</td><td>368.26</td></tr><tr><td>Cardiff_40_20</td><td>85341</td><td>14</td><td>-</td><td>214.132</td><td>23</td><td>2649.34</td><td>-</td><td>-</td><td>10800</td></tr></tbody></table>
<table><caption>Table 14: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>Γ<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff.40.16</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8688</td><td>351.24</td><td>27</td><td>3366.97</td><td>3353.42</td><td>0.40</td><td>10800.00</td></tr><tr><td>Cardiff.40.16</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7898</td><td>296.23</td><td>61</td><td>3410.52</td><td>3353.42</td><td>1.70</td><td>10800.00</td></tr><tr><td>Cardiff.40.16</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>152985</td><td>835.01</td><td>5</td><td>-</td><td>3353.42</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.16</td><td>3</td><td>15</td><td>10</td><td>1</td><td>19971</td><td>335.19</td><td>15</td><td>3366.97</td><td>3353.42</td><td>0.40</td><td>10800.00</td></tr><tr><td>Cardiff.40.16</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>65872</td><td>480.78</td><td>9</td><td>-</td><td>3353.42</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.17</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>92.36</td><td>3</td><td>2831.3</td><td>2749.83</td><td>2.96</td><td>115.20</td></tr><tr><td>Cardiff.40.17</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1939</td><td>87.32</td><td>1</td><td>2777.07</td><td>2749.83</td><td>0.99</td><td>87.80</td></tr><tr><td>Cardiff.40.17</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2624</td><td>128.11</td><td>1</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>129.20</td></tr><tr><td>Cardiff.40.17</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5241</td><td>189.10</td><td>5</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>676.60</td></tr><tr><td>Cardiff.40.17</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2474</td><td>162.52</td><td>3</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>235.68</td></tr><tr><td>Cardiff.40.17</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2642</td><td>160.60</td><td>1</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>161.46</td></tr><tr><td>Cardiff.40.17</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2738</td><td>164.62</td><td>1</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>165.30</td></tr><tr><td>Cardiff.40.17</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5350</td><td>225.94</td><td>3</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>364.92</td></tr><tr><td>Cardiff.40.17</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>6334</td><td>204.08</td><td>7</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>928.89</td></tr><tr><td>Cardiff.40.17</td><td>3</td><td>8</td><td>8</td><td>1</td><td>5787</td><td>191.46</td><td>3</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>307.75</td></tr><tr><td>Cardiff.40.17</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>24600</td><td>280.43</td><td>33</td><td>-</td><td>2749.83</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.17</td><td>3</td><td>15</td><td>10</td><td>1</td><td>9307</td><td>233.03</td><td>7</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>1051.50</td></tr><tr><td>Cardiff.40.17</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>16770</td><td>256.00</td><td>9</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>4918.00</td></tr><tr><td>Cardiff.40.18</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1787</td><td>120.56</td><td>3</td><td>2898.75</td><td>2888.65</td><td>0.35</td><td>264.26</td></tr><tr><td>Cardiff.40.18</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1915</td><td>82.22</td><td>3</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>146.25</td></tr><tr><td>Cardiff.40.18</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2579</td><td>88.51</td><td>5</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>268.48</td></tr><tr><td>Cardiff.40.18</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6586</td><td>110.40</td><td>57</td><td>2941.17</td><td>2888.65</td><td>1.82</td><td>10800.00</td></tr><tr><td>Cardiff.40.18</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2435</td><td>120.02</td><td>5</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>378.09</td></tr><tr><td>Cardiff.40.18</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2593</td><td>109.83</td><td>5</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>355.63</td></tr><tr><td>Cardiff.40.18</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2711</td><td>117.91</td><td>3</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>190.47</td></tr><tr><td>Cardiff.40.18</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6763</td><td>155.29</td><td>75</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>9097.00</td></tr><tr><td>Cardiff.40.18</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8311</td><td>165.19</td><td>37</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>4932.00</td></tr><tr><td>Cardiff.40.18</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7454</td><td>153.60</td><td>57</td><td>2902.2</td><td>2888.65</td><td>0.47</td><td>10800.00</td></tr><tr><td>Cardiff.40.18</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>93353</td><td>233.75</td><td>21</td><td>-</td><td>2888.65</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.18</td><td>3</td><td>15</td><td>10</td><td>1</td><td>17614</td><td>94.82</td><td>93</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff.40.18</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>48958</td><td>156.16</td><td>29</td><td>-</td><td>2888.65</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.19</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1800</td><td>100.68</td><td>3</td><td>2807.1</td><td>2784.05</td><td>0.83</td><td>206.02</td></tr><tr><td>Cardiff.40.19</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1956</td><td>125.08</td><td>3</td><td>2807.1</td><td>2784.05</td><td>0.83</td><td>272.73</td></tr><tr><td>Cardiff.40.19</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2690</td><td>181.37</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>345.11</td></tr><tr><td>Cardiff.40.19</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5057</td><td>147.83</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>312.69</td></tr><tr><td>Cardiff.40.19</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2541</td><td>174.93</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>298.16</td></tr><tr><td>Cardiff.40.19</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2710</td><td>172.47</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>306.01</td></tr><tr><td>Cardiff.40.19</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2801</td><td>156.48</td><td>7</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>557.54</td></tr><tr><td>Cardiff.40.19</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5075</td><td>158.20</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>261.90</td></tr><tr><td>Cardiff.40.19</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>6009</td><td>167.29</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>297.71</td></tr><tr><td>Cardiff.40.19</td><td>3</td><td>8</td><td>8</td><td>1</td><td>5412</td><td>169.81</td><td>11</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>924.35</td></tr><tr><td>Cardiff.40.19</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>11376</td><td>209.09</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>374.94</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
<table><caption>Table 13: Detailed performance of the exact algorithm on 100-customer instances</caption><thead><tr><th>Instance</th><th>A<sup>max</sup></th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap Time (s)</th></tr></thead><tbody><tr><td>c101_100</td><td>18845</td><td>0.3</td><td>88.031</td><td>5</td><td>5298.76</td><td>5298.76</td><td>643.78</td></tr><tr><td>c102_100</td><td>18845</td><td>0.4</td><td>86.379</td><td>7</td><td>5298.36</td><td>5298.36</td><td>751.62</td></tr><tr><td>c103_100</td><td>18898</td><td>0.4</td><td>104.734</td><td>43</td><td>5296.46</td><td>5296.46</td><td>4008.0</td></tr><tr><td>c104_100</td><td>20064</td><td>1.4</td><td>141.282</td><td>121</td><td>5274.95</td><td>5339.06</td><td>1.2 10800</td></tr><tr><td>c105_100</td><td>18849</td><td>0.3</td><td>90.378</td><td>19</td><td>5298.76</td><td>5298.76</td><td>3249.86</td></tr><tr><td>c106_100</td><td>18844</td><td>0.4</td><td>90.421</td><td>9</td><td>5298.76</td><td>5298.76</td><td>1144.6</td></tr><tr><td>c107_100</td><td>18875</td><td>0.3</td><td>80.05</td><td>5</td><td>5298.76</td><td>5298.76</td><td>769.38</td></tr><tr><td>c108_100</td><td>18845</td><td>0.4</td><td>93.02</td><td>15</td><td>5295.36</td><td>5295.36</td><td>1712.0</td></tr><tr><td>c109_100</td><td>19018</td><td>0.4</td><td>125.412</td><td>49</td><td>5295.16</td><td>5295.16</td><td>5127.0</td></tr></tbody></table>

<table><caption>Table 14: Detailed performance of the exact algorithm on instances from (Gehring and Homberger, 1999)</caption><thead><tr><th>Instance</th><th>A<sup>max</sup></th><th>K̂</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap Time (s)</th></tr></thead><tbody><tr><td>120_C1_2_1</td><td>14931</td><td>3 0.4</td><td>45.306</td><td>7</td><td>9090</td><td>9090</td><td>0</td><td>251.78</td></tr><tr><td>120_C1_2_2</td><td>14931</td><td>3 0.3</td><td>87.072</td><td>29</td><td>8920.5</td><td>8920.5</td><td>0</td><td>1827.92</td></tr><tr><td>120_C1_2_3</td><td>14931</td><td>3 1035</td><td>185.251</td><td>143</td><td>8815.06</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>120_C1_2_4</td><td>14931</td><td>3 1046.7</td><td>163.474</td><td>153</td><td>8728.17</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>120_C1_2_5</td><td>14931</td><td>3 0.5</td><td>58.236</td><td>19</td><td>8986.2</td><td>8986.2</td><td>0</td><td>1454.68</td></tr><tr><td>120_C1_2_6</td><td>14931</td><td>3 0.9</td><td>91.461</td><td>17</td><td>8988.4</td><td>8988.4</td><td>0</td><td>1899.7</td></tr><tr><td>120_C1_2_7</td><td>14931</td><td>3 0.5</td><td>67.444</td><td>29</td><td>8958.6</td><td>8958.6</td><td>0</td><td>2438.2</td></tr><tr><td>120_C1_2_8</td><td>14931</td><td>3 0.3</td><td>166.804</td><td>9</td><td>8817.9</td><td>8817.9</td><td>0</td><td>642.36</td></tr><tr><td>120_C1_2_9</td><td>14931</td><td>3 0.3</td><td>171.819</td><td>51</td><td>8790.62</td><td>8790.62</td><td>0</td><td>3394.73</td></tr><tr><td>120_C1_2_10</td><td>14931</td><td>3 1044.6</td><td>193.899</td><td>131</td><td>8741.16</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>130_C1_2_1</td><td>17614</td><td>4 0.6</td><td>61.628</td><td>11</td><td>9325.92</td><td>9325.92</td><td>0</td><td>744.67</td></tr><tr><td>130_C1_2_2</td><td>17614</td><td>4 0.3</td><td>105.671</td><td>11</td><td>9141.2</td><td>9141.2</td><td>0</td><td>787.67</td></tr><tr><td>130_C1_2_3</td><td>17614</td><td>4 1005.5</td><td>147.702</td><td>105</td><td>9054.61</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>130_C1_2_4</td><td>17617</td><td>4 1015.2</td><td>162.767</td><td>125</td><td>8973.53</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>130_C1_2_5</td><td>17614</td><td>4 0.5</td><td>87.648</td><td>29</td><td>9209.62</td><td>9209.62</td><td>0</td><td>3294.54</td></tr><tr><td>130_C1_2_6</td><td>17614</td><td>4 0.8</td><td>119.465</td><td>109</td><td>9222.4</td><td>9222.4</td><td>0</td><td>9784.0</td></tr><tr><td>130_C1_2_7</td><td>17614</td><td>4 0.6</td><td>122.121</td><td>21</td><td>9197.92</td><td>9197.92</td><td>0</td><td>2199.14</td></tr><tr><td>130_C1_2_8</td><td>17614</td><td>4 0.7</td><td>148.914</td><td>153</td><td>9053.06</td><td>9091.7</td><td>0.4</td><td>10800</td></tr><tr><td>130_C1_2_9</td><td>17614</td><td>4 1008.9</td><td>177.902</td><td>107</td><td>9029.23</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>130_C1_2_10</td><td>17614</td><td>4 1013.6</td><td>215.358</td><td>103</td><td>8985.44</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>140_C1_2_1</td><td>20366</td><td>4 0.6</td><td>82.444</td><td>51</td><td>9970.42</td><td>9970.42</td><td>0</td><td>2840.77</td></tr><tr><td>140_C1_2_2</td><td>20366</td><td>4 0.5</td><td>135.393</td><td>129</td><td>9786.12</td><td>9817.38</td><td>0.3</td><td>10800</td></tr><tr><td>140_C1_2_3</td><td>20366</td><td>4 931.4</td><td>192.591</td><td>125</td><td>9710.4</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>140_C1_2_4</td><td>20369</td><td>4 939</td><td>181.705</td><td>87</td><td>9632.6</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>140_C1_2_5</td><td>20366</td><td>4 0.4</td><td>94.988</td><td>25</td><td>9848.82</td><td>9848.82</td><td>0</td><td>1981.57</td></tr></tbody></table>

Continued on next page
<table><caption>Table 14: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>Γ<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff.40.19</td><td>3</td><td>15</td><td>10</td><td>1</td><td>7577</td><td>211.69</td><td>7</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>650.65</td></tr><tr><td>Cardiff.40.19</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>8484</td><td>189.95</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>345.95</td></tr><tr><td>Cardiff.40.20</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>104.94</td><td>41</td><td>3167.3</td><td>3083.32</td><td>2.72</td><td>4142.00</td></tr><tr><td>Cardiff.40.20</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1937</td><td>94.93</td><td>53</td><td>3167.3</td><td>3083.32</td><td>2.72</td><td>4879.00</td></tr><tr><td>Cardiff.40.20</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2668</td><td>104.20</td><td>3</td><td>3083.32</td><td>3083.32</td><td>0.00</td><td>249.27</td></tr><tr><td>Cardiff.40.20</td><td>2</td><td>5</td><td>8</td><td>1</td><td>7541</td><td>126.64</td><td>51</td><td>3083.32</td><td>3083.32</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff.40.20</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2503</td><td>152.96</td><td>3</td><td>3083.32</td><td>3083.32</td><td>0.00</td><td>295.26</td></tr><tr><td>Cardiff.40.20</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2685</td><td>142.13</td><td>3</td><td>3083.32</td><td>3083.32</td><td>0.00</td><td>315.32</td></tr><tr><td>Cardiff.40.20</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2798</td><td>138.74</td><td>3</td><td>3083.32</td><td>3083.32</td><td>0.00</td><td>283.32</td></tr><tr><td>Cardiff.40.20</td><td>3</td><td>5</td><td>8</td><td>1</td><td>7844</td><td>162.42</td><td>71</td><td>3217.35</td><td>3083.32</td><td>4.35</td><td>10800.00</td></tr><tr><td>Cardiff.40.20</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>9585</td><td>183.54</td><td>51</td><td>3102.13</td><td>3083.32</td><td>0.61</td><td>10800.00</td></tr><tr><td>Cardiff.40.20</td><td>3</td><td>8</td><td>8</td><td>1</td><td>8665</td><td>198.26</td><td>47</td><td>3109.15</td><td>3083.32</td><td>0.84</td><td>10800.00</td></tr><tr><td>Cardiff.40.20</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>89884</td><td>223.75</td><td>23</td><td>-</td><td>3083.32</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff.40.20</td><td>3</td><td>15</td><td>10</td><td>1</td><td>20544</td><td>273.60</td><td>55</td><td>3089.5</td><td>3083.32</td><td>0.20</td><td>10800.00</td></tr><tr><td>Cardiff.40.20</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>55292</td><td>162.79</td><td>31</td><td>-</td><td>3083.32</td><td>-</td><td>10800.00</td></tr></tbody></table>

<table><caption>Table 15: Detailed experiments on the impact of the ARCC</caption><thead><tr><th>Instance</th><th>ARCC</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>120.C1.2.01</td><td>yes</td><td>0</td><td>58.04</td><td>1</td><td>9090</td><td>9090</td><td>0</td><td>58.94</td></tr><tr><td>120.C1.2.01</td><td>no</td><td>0</td><td>43.98</td><td>1</td><td>9090</td><td>9090</td><td>0</td><td>44.63</td></tr><tr><td>120.C1.2.02</td><td>yes</td><td>0</td><td>162.93</td><td>1</td><td>8920.5</td><td>8920.5</td><td>0</td><td>163.87</td></tr><tr><td>120.C1.2.02</td><td>no</td><td>0</td><td>145.72</td><td>1</td><td>8920.5</td><td>8920.5</td><td>0</td><td>146.54</td></tr><tr><td>120.C1.2.03</td><td>yes</td><td>0.2</td><td>250.16</td><td>5</td><td>8843.52</td><td>8843.52</td><td>0</td><td>428.45</td></tr><tr><td>120.C1.2.03</td><td>no</td><td>0.3</td><td>185.19</td><td>9</td><td>8843.52</td><td>8843.52</td><td>0</td><td>433.68</td></tr><tr><td>120.C1.2.04</td><td>yes</td><td>0.7</td><td>240.19</td><td>187</td><td>8740.64</td><td>8784.92</td><td>0.51</td><td>10800</td></tr><tr><td>120.C1.2.04</td><td>no</td><td>0.6</td><td>165.93</td><td>241</td><td>8740</td><td>8784.92</td><td>0.51</td><td>10800</td></tr><tr><td>120.C1.2.05</td><td>yes</td><td>0</td><td>240.02</td><td>1</td><td>8986.2</td><td>8986.2</td><td>0</td><td>241.07</td></tr><tr><td>120.C1.2.05</td><td>no</td><td>0</td><td>237.6</td><td>1</td><td>8986.2</td><td>8986.2</td><td>0</td><td>238.7</td></tr><tr><td>120.C1.2.06</td><td>yes</td><td>0.3</td><td>395.59</td><td>9</td><td>8988.4</td><td>8988.4</td><td>0</td><td>847.64</td></tr><tr><td>120.C1.2.06</td><td>no</td><td>0.3</td><td>341.83</td><td>9</td><td>8988.4</td><td>8988.4</td><td>0</td><td>908.45</td></tr><tr><td>120.C1.2.07</td><td>yes</td><td>0.1</td><td>210.22</td><td>3</td><td>8958.6</td><td>8958.6</td><td>0</td><td>375.54</td></tr><tr><td>120.C1.2.07</td><td>no</td><td>0.1</td><td>242.94</td><td>3</td><td>8958.6</td><td>8958.6</td><td>0</td><td>419.64</td></tr><tr><td>120.C1.2.08</td><td>yes</td><td>0.1</td><td>229.57</td><td>11</td><td>8817.9</td><td>8817.9</td><td>0</td><td>375.16</td></tr><tr><td>120.C1.2.08</td><td>no</td><td>0.1</td><td>175.54</td><td>15</td><td>8817.9</td><td>8817.9</td><td>0</td><td>529.05</td></tr><tr><td>120.C1.2.09</td><td>yes</td><td>0</td><td>281.36</td><td>1</td><td>8790.62</td><td>8790.62</td><td>0</td><td>282.26</td></tr><tr><td>120.C1.2.09</td><td>no</td><td>0</td><td>189.73</td><td>1</td><td>8790.62</td><td>8790.62</td><td>0</td><td>190.56</td></tr><tr><td>120.C1.2.10</td><td>yes</td><td>0.7</td><td>264.75</td><td>97</td><td>8740.41</td><td>8794.92</td><td>0.62</td><td>10800</td></tr><tr><td>120.C1.2.10</td><td>no</td><td>0.7</td><td>155.31</td><td>125</td><td>8737.92</td><td>8794.92</td><td>0.65</td><td>10800</td></tr><tr><td>130.C1.2.01</td><td>yes</td><td>0</td><td>193.32</td><td>1</td><td>9325.92</td><td>9325.92</td><td>0</td><td>194.05</td></tr></tbody></table>

Continued on next page
<table><caption>Table 14: Detailed performance of the exact algorithm on instances from (Gehring and Homberger, 1999)</caption><thead><tr><th>Instance</th><th>A<sup>max</sup></th><th>K</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>140_C1_2_6</td><td>20366</td><td>4</td><td>1.1</td><td>121.619</td><td>89</td><td>9812.82</td><td>9891.3</td><td>0.8</td><td>10800</td></tr><tr><td>140_C1_2_7</td><td>20366</td><td>4</td><td>0.3</td><td>152.451</td><td>21</td><td>9836.32</td><td>9836.32</td><td>0</td><td>1867.67</td></tr><tr><td>140_C1_2_8</td><td>20366</td><td>4</td><td>0.6</td><td>193.816</td><td>103</td><td>9707.63</td><td>9753.78</td><td>0.5</td><td>10800</td></tr><tr><td>140_C1_2_9</td><td>20366</td><td>4</td><td>933</td><td>215.832</td><td>107</td><td>9683.85</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>140_C1_2_10</td><td>20366</td><td>4</td><td>939.2</td><td>211.671</td><td>105</td><td>9636.41</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>150_C1_2_1</td><td>23331</td><td>4</td><td>0.4</td><td>95.102</td><td>35</td><td>10699.3</td><td>10699.3</td><td>0</td><td>1539.33</td></tr><tr><td>150_C1_2_2</td><td>23331</td><td>4</td><td>0.6</td><td>202.898</td><td>103</td><td>10551.2</td><td>10599.8</td><td>0.5</td><td>10800</td></tr><tr><td>150_C1_2_3</td><td>23331</td><td>4</td><td>1.6</td><td>160.827</td><td>137</td><td>10453.6</td><td>10611.5</td><td>1.5</td><td>10800</td></tr><tr><td>150_C1_2_4</td><td>23334</td><td>4</td><td>860.4</td><td>221.244</td><td>91</td><td>10425.2</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>150_C1_2_5</td><td>23331</td><td>4</td><td>0.6</td><td>107.043</td><td>123</td><td>10582.5</td><td>10628.2</td><td>0.4</td><td>10800</td></tr><tr><td>150_C1_2_6</td><td>23331</td><td>4</td><td>0.5</td><td>170.548</td><td>159</td><td>10561.4</td><td>10595.1</td><td>0.3</td><td>10800</td></tr><tr><td>150_C1_2_7</td><td>23331</td><td>4</td><td>0.5</td><td>131.694</td><td>113</td><td>10602.5</td><td>10602.5</td><td>0</td><td>5905.0</td></tr><tr><td>150_C1_2_8</td><td>23331</td><td>4</td><td>856.6</td><td>215.009</td><td>105</td><td>10468.6</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>150_C1_2_9</td><td>23331</td><td>4</td><td>860.5</td><td>236.564</td><td>105</td><td>10416.2</td><td>-</td><td>-</td><td>10800</td></tr><tr><td>150_C1_2_10</td><td>23331</td><td>4</td><td>865</td><td>210.899</td><td>107</td><td>10381</td><td>-</td><td>-</td><td>10800</td></tr></tbody></table>

<table><caption>Table 15: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>D<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_01</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1795</td><td>83.27</td><td>3</td><td>3023.92</td><td>2931.88</td><td>3.14</td><td>108.18</td></tr><tr><td>Cardiff_40_01</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1931</td><td>89.94</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>115.41</td></tr><tr><td>Cardiff_40_01</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2491</td><td>111.19</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>112.07</td></tr><tr><td>Cardiff_40_01</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5261</td><td>147.21</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>147.91</td></tr><tr><td>Cardiff_40_01</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2366</td><td>138.05</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>138.87</td></tr><tr><td>Cardiff_40_01</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2501</td><td>113.29</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>141.00</td></tr><tr><td>Cardiff_40_01</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2636</td><td>121.99</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>152.10</td></tr><tr><td>Cardiff_40_01</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5283</td><td>175.87</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>231.41</td></tr><tr><td>Cardiff_40_01</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>6601</td><td>213.12</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>276.06</td></tr><tr><td>Cardiff_40_01</td><td>3</td><td>8</td><td>8</td><td>1</td><td>5715</td><td>180.78</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>181.72</td></tr><tr><td>Cardiff_40_01</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>16141</td><td>208.76</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>282.59</td></tr><tr><td>Cardiff_40_01</td><td>3</td><td>15</td><td>10</td><td>1</td><td>10714</td><td>197.94</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>273.71</td></tr><tr><td>Cardiff_40_01</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>10714</td><td>190.00</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>252.57</td></tr><tr><td>Cardiff_40_02</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>74.15</td><td>1</td><td>3258.43</td><td>3217.42</td><td>1.27</td><td>74.65</td></tr><tr><td>Cardiff_40_02</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1940</td><td>76.30</td><td>1</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>76.65</td></tr><tr><td>Cardiff_40_02</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2691</td><td>79.61</td><td>1</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>80.37</td></tr><tr><td>Cardiff_40_02</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6439</td><td>119.73</td><td>3</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>368.83</td></tr><tr><td>Cardiff_40_02</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2521</td><td>94.48</td><td>3</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>193.52</td></tr><tr><td>Cardiff_40_02</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2707</td><td>99.99</td><td>1</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>100.56</td></tr><tr><td>Cardiff_40_02</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2831</td><td>73.55</td><td>3</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>163.43</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
<table><caption>Table 15: Detailed experiments on the impact of the ARCC</caption><thead><tr><th>Instance</th><th>ARCC</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>130.C1.2.01</td><td>no</td><td>0</td><td>188.75</td><td>1</td><td>9325.92</td><td>9325.92</td><td>0</td><td>189.49</td></tr><tr><td>130.C1.2.02</td><td>yes</td><td>0</td><td>201.23</td><td>1</td><td>9141.2</td><td>9141.2</td><td>0</td><td>202.12</td></tr><tr><td>130.C1.2.02</td><td>no</td><td>0</td><td>169.74</td><td>1</td><td>9141.2</td><td>9141.2</td><td>0</td><td>170.74</td></tr><tr><td>130.C1.2.03</td><td>yes</td><td>0.7</td><td>198.25</td><td>241</td><td>9056.65</td><td>9119</td><td>0.69</td><td>10800</td></tr><tr><td>130.C1.2.03</td><td>no</td><td>0.7</td><td>199.17</td><td>167</td><td>9059.79</td><td>9119</td><td>0.65</td><td>10800</td></tr><tr><td>130.C1.2.04</td><td>yes</td><td>0.8</td><td>254.91</td><td>223</td><td>8993.56</td><td>9056.21</td><td>0.70</td><td>10800</td></tr><tr><td>130.C1.2.04</td><td>no</td><td>0.8</td><td>176.29</td><td>101</td><td>8989.81</td><td>9056.21</td><td>0.74</td><td>10800</td></tr><tr><td>130.C1.2.05</td><td>yes</td><td>0</td><td>264.44</td><td>1</td><td>9209.62</td><td>9209.62</td><td>0</td><td>265.45</td></tr><tr><td>130.C1.2.05</td><td>no</td><td>0</td><td>214.59</td><td>1</td><td>9209.62</td><td>9209.62</td><td>0</td><td>215.36</td></tr><tr><td>130.C1.2.06</td><td>yes</td><td>0.3</td><td>336.13</td><td>33</td><td>9222.4</td><td>9222.4</td><td>0</td><td>2152.1</td></tr><tr><td>130.C1.2.06</td><td>no</td><td>0.3</td><td>403.74</td><td>15</td><td>9222.4</td><td>9222.4</td><td>0</td><td>1633.03</td></tr><tr><td>130.C1.2.07</td><td>yes</td><td>0</td><td>687.49</td><td>3</td><td>9197.92</td><td>9197.92</td><td>0</td><td>1027.5</td></tr><tr><td>130.C1.2.07</td><td>no</td><td>0</td><td>771.28</td><td>3</td><td>9197.92</td><td>9197.92</td><td>0</td><td>1236.02</td></tr><tr><td>130.C1.2.08</td><td>yes</td><td>0.4</td><td>375.96</td><td>141</td><td>9082.79</td><td>9091.7</td><td>0.10</td><td>10800</td></tr><tr><td>130.C1.2.08</td><td>no</td><td>0.3</td><td>432.57</td><td>137</td><td>9066.88</td><td>9091.7</td><td>0.27</td><td>10800</td></tr><tr><td>130.C1.2.09</td><td>yes</td><td>0.6</td><td>261.74</td><td>119</td><td>9028.84</td><td>9077.5</td><td>0.54</td><td>10800</td></tr><tr><td>130.C1.2.09</td><td>no</td><td>0.6</td><td>236.97</td><td>129</td><td>9029.86</td><td>9077.5</td><td>0.53</td><td>10800</td></tr><tr><td>130.C1.2.10</td><td>yes</td><td>0.8</td><td>277.84</td><td>119</td><td>8992</td><td>9060.5</td><td>0.76</td><td>10800</td></tr><tr><td>130.C1.2.10</td><td>no</td><td>0.8</td><td>193.69</td><td>121</td><td>8990.42</td><td>9060.5</td><td>0.78</td><td>10800</td></tr><tr><td>140.C1.2.01</td><td>yes</td><td>0</td><td>268.45</td><td>1</td><td>9970.42</td><td>9970.42</td><td>0</td><td>269.33</td></tr><tr><td>140.C1.2.01</td><td>no</td><td>0</td><td>224.69</td><td>3</td><td>9970.42</td><td>9970.42</td><td>0</td><td>259.88</td></tr><tr><td>140.C1.2.02</td><td>yes</td><td>0.4</td><td>323.74</td><td>53</td><td>9817.38</td><td>9817.38</td><td>0</td><td>3780.0</td></tr><tr><td>140.C1.2.02</td><td>no</td><td>0.4</td><td>241.88</td><td>53</td><td>9817.38</td><td>9817.38</td><td>0</td><td>3656.0</td></tr><tr><td>140.C1.2.03</td><td>yes</td><td>0.8</td><td>271.7</td><td>115</td><td>9722.55</td><td>9784.7</td><td>0.64</td><td>10800</td></tr><tr><td>140.C1.2.03</td><td>no</td><td>0.8</td><td>174.26</td><td>119</td><td>9715.29</td><td>9784.7</td><td>0.71</td><td>10800</td></tr><tr><td>140.C1.2.04</td><td>yes</td><td>1.4</td><td>288.78</td><td>143</td><td>9637.97</td><td>9762.48</td><td>1.29</td><td>10800</td></tr><tr><td>140.C1.2.04</td><td>no</td><td>1.4</td><td>220.5</td><td>119</td><td>9637.72</td><td>9762.48</td><td>1.29</td><td>10800</td></tr><tr><td>140.C1.2.05</td><td>yes</td><td>0</td><td>262.62</td><td>1</td><td>9848.82</td><td>9848.82</td><td>0</td><td>263.61</td></tr><tr><td>140.C1.2.05</td><td>no</td><td>0</td><td>219.09</td><td>1</td><td>9848.82</td><td>9848.82</td><td>0</td><td>220.18</td></tr><tr><td>140.C1.2.06</td><td>yes</td><td>0.1</td><td>638.89</td><td>3</td><td>9853.5</td><td>9853.5</td><td>0</td><td>881.09</td></tr><tr><td>140.C1.2.06</td><td>no</td><td>0.1</td><td>598.12</td><td>3</td><td>9853.5</td><td>9853.5</td><td>0</td><td>809.91</td></tr><tr><td>140.C1.2.07</td><td>yes</td><td>0</td><td>325.88</td><td>3</td><td>9836.32</td><td>9836.32</td><td>0</td><td>363.95</td></tr><tr><td>140.C1.2.07</td><td>no</td><td>0</td><td>229.26</td><td>3</td><td>9836.32</td><td>9836.32</td><td>0</td><td>304.98</td></tr><tr><td>140.C1.2.08</td><td>yes</td><td>0.4</td><td>374.68</td><td>165</td><td>9726.07</td><td>9754.28</td><td>0.29</td><td>10800</td></tr><tr><td>140.C1.2.08</td><td>no</td><td>0.5</td><td>274.15</td><td>129</td><td>9716.74</td><td>9754.28</td><td>0.39</td><td>10800</td></tr><tr><td>140.C1.2.09</td><td>yes</td><td>0.8</td><td>271.95</td><td>157</td><td>9684.21</td><td>9754</td><td>0.72</td><td>10800</td></tr><tr><td>140.C1.2.09</td><td>no</td><td>0.9</td><td>258.01</td><td>181</td><td>9690.01</td><td>9754</td><td>0.66</td><td>10800</td></tr><tr><td>140.C1.2.10</td><td>yes</td><td>2.9</td><td>296.33</td><td>113</td><td>9639.97</td><td>9900</td><td>2.70</td><td>10800</td></tr><tr><td>140.C1.2.10</td><td>no</td><td>2.9</td><td>185.31</td><td>115</td><td>9638.62</td><td>9900</td><td>2.71</td><td>10800</td></tr></tbody></table>
<table><caption>Table 15: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>D<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_02</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6743</td><td>110.46</td><td>7</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>1222.35</td></tr><tr><td>Cardiff_40_02</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7965</td><td>117.88</td><td>13</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>1812.41</td></tr><tr><td>Cardiff_40_02</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7431</td><td>110.16</td><td>11</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>1928.13</td></tr><tr><td>Cardiff_40_02</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>94606</td><td>104.14</td><td>37</td><td>-</td><td>3217.42</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_02</td><td>3</td><td>15</td><td>10</td><td>1</td><td>15732</td><td>143.74</td><td>5</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>1813.37</td></tr><tr><td>Cardiff_40_02</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>44541</td><td>71.34</td><td>43</td><td>3217.42</td><td>3217.42</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff_40_03</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>64.23</td><td>3</td><td>2761.12</td><td>2682.5</td><td>2.93</td><td>92.10</td></tr><tr><td>Cardiff_40_03</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1932</td><td>83.51</td><td>1</td><td>2686.92</td><td>2682.5</td><td>0.16</td><td>84.03</td></tr><tr><td>Cardiff_40_03</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2573</td><td>101.58</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>193.17</td></tr><tr><td>Cardiff_40_03</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6071</td><td>150.94</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>277.87</td></tr><tr><td>Cardiff_40_03</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2441</td><td>83.80</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>138.85</td></tr><tr><td>Cardiff_40_03</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2605</td><td>107.42</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>186.08</td></tr><tr><td>Cardiff_40_03</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2676</td><td>119.35</td><td>1</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>119.95</td></tr><tr><td>Cardiff_40_03</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6311</td><td>126.94</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>252.25</td></tr><tr><td>Cardiff_40_03</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7550</td><td>132.35</td><td>7</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>447.35</td></tr><tr><td>Cardiff_40_03</td><td>3</td><td>8</td><td>8</td><td>1</td><td>6983</td><td>141.43</td><td>5</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>470.14</td></tr><tr><td>Cardiff_40_03</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>32435</td><td>203.85</td><td>5</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>531.98</td></tr><tr><td>Cardiff_40_03</td><td>3</td><td>15</td><td>10</td><td>1</td><td>14395</td><td>184.13</td><td>21</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>2524.46</td></tr><tr><td>Cardiff_40_03</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>20100</td><td>185.76</td><td>5</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>456.20</td></tr><tr><td>Cardiff_40_04</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1792</td><td>60.52</td><td>5</td><td>5259.18</td><td>5082.62</td><td>3.47</td><td>119.43</td></tr><tr><td>Cardiff_40_04</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1934</td><td>60.83</td><td>5</td><td>5239.48</td><td>5082.62</td><td>3.09</td><td>164.87</td></tr><tr><td>Cardiff_40_04</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2720</td><td>72.19</td><td>3</td><td>5239.48</td><td>5082.62</td><td>3.09</td><td>137.02</td></tr><tr><td>Cardiff_40_04</td><td>2</td><td>5</td><td>8</td><td>1</td><td>7764</td><td>90.31</td><td>39</td><td>5245.75</td><td>5082.62</td><td>3.21</td><td>10800.00</td></tr><tr><td>Cardiff_40_04</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2573</td><td>79.86</td><td>7</td><td>5236.25</td><td>5082.62</td><td>3.02</td><td>224.70</td></tr><tr><td>Cardiff_40_04</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2781</td><td>69.25</td><td>7</td><td>5236.25</td><td>5082.62</td><td>3.02</td><td>196.73</td></tr><tr><td>Cardiff_40_04</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2784</td><td>72.60</td><td>17</td><td>5236.25</td><td>5082.62</td><td>3.02</td><td>434.19</td></tr><tr><td>Cardiff_40_04</td><td>3</td><td>5</td><td>8</td><td>1</td><td>8532</td><td>162.82</td><td>73</td><td>5142.45</td><td>5082.62</td><td>1.18</td><td>10800.00</td></tr><tr><td>Cardiff_40_04</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8641</td><td>167.72</td><td>51</td><td>5178.7</td><td>5082.62</td><td>1.89</td><td>10800.00</td></tr><tr><td>Cardiff_40_04</td><td>3</td><td>8</td><td>8</td><td>1</td><td>9603</td><td>115.39</td><td>49</td><td>-</td><td>5082.62</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_04</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>169680</td><td>429.19</td><td>9</td><td>-</td><td>5082.62</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_04</td><td>3</td><td>15</td><td>10</td><td>1</td><td>26672</td><td>195.76</td><td>45</td><td>5082.62</td><td>5082.62</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff_40_04</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>146716</td><td>396.58</td><td>11</td><td>-</td><td>5082.62</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_05</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1795</td><td>166.61</td><td>3</td><td>3812.85</td><td>3770.9</td><td>1.11</td><td>332.22</td></tr><tr><td>Cardiff_40_05</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1947</td><td>142.14</td><td>3</td><td>3812.85</td><td>3770.9</td><td>1.11</td><td>208.14</td></tr><tr><td>Cardiff_40_05</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2582</td><td>185.46</td><td>3</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>250.84</td></tr><tr><td>Cardiff_40_05</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5696</td><td>266.27</td><td>15</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1436.28</td></tr><tr><td>Cardiff_40_05</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2453</td><td>207.88</td><td>3</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>273.77</td></tr><tr><td>Cardiff_40_05</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2609</td><td>213.88</td><td>3</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>269.74</td></tr><tr><td>Cardiff_40_05</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2758</td><td>223.78</td><td>3</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>294.98</td></tr><tr><td>Cardiff_40_05</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5955</td><td>282.85</td><td>11</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1134.08</td></tr><tr><td>Cardiff_40_05</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7149</td><td>336.73</td><td>9</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1313.44</td></tr><tr><td>Cardiff_40_05</td><td>3</td><td>8</td><td>8</td><td>1</td><td>6492</td><td>300.18</td><td>13</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1614.24</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
<table><caption>Table 16: Detailed experiments on the impact of the SPR</caption><thead><tr><th>Instance</th><th>SPR</th><th>A<sup>max</sup></th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff.40.01</td><td>yes</td><td>13034</td><td>0</td><td>268.41</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0</td><td>269.49</td></tr><tr><td>Cardiff.40.01</td><td>no</td><td>13174</td><td>0</td><td>297.93</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0</td><td>298.89</td></tr><tr><td>Cardiff.40.02</td><td>yes</td><td>95883</td><td>20.1</td><td>88.12</td><td>45</td><td>2827.85</td><td>3217.43</td><td>13.8</td><td>10800</td></tr><tr><td>Cardiff.40.02</td><td>no</td><td>97648</td><td>20.1</td><td>117.31</td><td>29</td><td>2774.49</td><td>3217.42</td><td>16</td><td>10800</td></tr><tr><td>Cardiff.40.03</td><td>yes</td><td>30318</td><td>0</td><td>400.03</td><td>1</td><td>2682.5</td><td>2682.5</td><td>0</td><td>401.32</td></tr><tr><td>Cardiff.40.03</td><td>no</td><td>30721</td><td>9.1</td><td>264.48</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0</td><td>542.77</td></tr><tr><td>Cardiff.40.04</td><td>yes</td><td>169680</td><td>20.2</td><td>317.5</td><td>9</td><td>4282.36</td><td>5082.63</td><td>18.7</td><td>10800</td></tr><tr><td>Cardiff.40.04</td><td>no</td><td>178022</td><td>20.2</td><td>478.01</td><td>7</td><td>4281.08</td><td>5082.63</td><td>18.7</td><td>10800</td></tr><tr><td>Cardiff.40.05</td><td>yes</td><td>25801</td><td>1.6</td><td>543.24</td><td>27</td><td>3770.9</td><td>3770.9</td><td>0</td><td>6574.0</td></tr><tr><td>Cardiff.40.05</td><td>no</td><td>26586</td><td>1.6</td><td>603.97</td><td>23</td><td>3770.9</td><td>3770.9</td><td>0</td><td>4977.0</td></tr><tr><td>Cardiff.40.06</td><td>yes</td><td>26451</td><td>0</td><td>491.63</td><td>1</td><td>2909</td><td>2909</td><td>0</td><td>492.73</td></tr><tr><td>Cardiff.40.06</td><td>no</td><td>27449</td><td>0</td><td>559.3</td><td>1</td><td>2909</td><td>2909</td><td>0</td><td>560.32</td></tr><tr><td>Cardiff.40.07</td><td>yes</td><td>89523</td><td>19.8</td><td>696.68</td><td>3</td><td>2093.42</td><td>2491.28</td><td>19</td><td>10800</td></tr><tr><td>Cardiff.40.07</td><td>no</td><td>91461</td><td>19.8</td><td>1008.99</td><td>1</td><td>2080.22</td><td>2491.28</td><td>19.8</td><td>10800</td></tr><tr><td>Cardiff.40.08</td><td>yes</td><td>9510</td><td>0</td><td>215.16</td><td>1</td><td>3834.02</td><td>3834.02</td><td>0</td><td>215.85</td></tr><tr><td>Cardiff.40.08</td><td>no</td><td>9671</td><td>0</td><td>258.93</td><td>1</td><td>3834.02</td><td>3834.02</td><td>0</td><td>259.65</td></tr><tr><td>Cardiff.40.09</td><td>yes</td><td>81734</td><td>12.7</td><td>1084.47</td><td>9</td><td>3569.6</td><td>3668.21</td><td>2.8</td><td>10800</td></tr><tr><td>Cardiff.40.09</td><td>no</td><td>84161</td><td>13.1</td><td>1156.82</td><td>11</td><td>3541.86</td><td>3668.21</td><td>3.6</td><td>10800</td></tr><tr><td>Cardiff.40.10</td><td>yes</td><td>55913</td><td>0</td><td>220.62</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0</td><td>221.98</td></tr><tr><td>Cardiff.40.10</td><td>no</td><td>59456</td><td>0</td><td>297.74</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0</td><td>299.62</td></tr><tr><td>Cardiff.40.11</td><td>yes</td><td>48327</td><td>0</td><td>5.94</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0</td><td>6.59</td></tr><tr><td>Cardiff.40.11</td><td>no</td><td>51524</td><td>0</td><td>6.89</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0</td><td>8.0</td></tr><tr><td>Cardiff.40.12</td><td>yes</td><td>38128</td><td>0</td><td>280.93</td><td>1</td><td>2642.87</td><td>2642.87</td><td>0</td><td>282.13</td></tr><tr><td>Cardiff.40.12</td><td>no</td><td>38637</td><td>0</td><td>351.3</td><td>1</td><td>2642.87</td><td>2642.87</td><td>0</td><td>353.38</td></tr><tr><td>Cardiff.40.13</td><td>yes</td><td>121649</td><td>18.4</td><td>199.97</td><td>17</td><td>2742.72</td><td>2827.83</td><td>3.1</td><td>10800</td></tr><tr><td>Cardiff.40.13</td><td>no</td><td>123340</td><td>18.4</td><td>274.22</td><td>15</td><td>2742.19</td><td>2827.83</td><td>3.1</td><td>10800</td></tr><tr><td>Cardiff.40.14</td><td>yes</td><td>247124</td><td>30.2</td><td>1794.42</td><td>1</td><td>2236.37</td><td>2910.91</td><td>30.2</td><td>10800</td></tr><tr><td>Cardiff.40.14</td><td>no</td><td>260625</td><td>30.2</td><td>3466.11</td><td>1</td><td>2236.37</td><td>2910.91</td><td>30.2</td><td>10800</td></tr><tr><td>Cardiff.40.15</td><td>yes</td><td>33041</td><td>19.9</td><td>281.4</td><td>37</td><td>2549.95</td><td>2707.12</td><td>6.2</td><td>10800</td></tr><tr><td>Cardiff.40.15</td><td>no</td><td>33301</td><td>20</td><td>351.13</td><td>35</td><td>2643.72</td><td>2707.13</td><td>2.4</td><td>10800</td></tr><tr><td>Cardiff.40.16</td><td>yes</td><td>153756</td><td>18</td><td>844.32</td><td>3</td><td>2904.8</td><td>3353.43</td><td>15.4</td><td>10800</td></tr><tr><td>Cardiff.40.16</td><td>no</td><td>156619</td><td>19.1</td><td>1134.11</td><td>3</td><td>2881.14</td><td>3353.43</td><td>16.4</td><td>10800</td></tr><tr><td>Cardiff.40.17</td><td>yes</td><td>24463</td><td>1.8</td><td>678.22</td><td>13</td><td>2735.28</td><td>2749.84</td><td>0.5</td><td>10800</td></tr><tr><td>Cardiff.40.17</td><td>no</td><td>24917</td><td>1.9</td><td>916.07</td><td>13</td><td>2722.56</td><td>2749.84</td><td>1</td><td>10800</td></tr><tr><td>Cardiff.40.18</td><td>yes</td><td>93744</td><td>31</td><td>213.52</td><td>21</td><td>2676.43</td><td>2888.66</td><td>7.9</td><td>10800</td></tr><tr><td>Cardiff.40.18</td><td>no</td><td>95960</td><td>31</td><td>291.94</td><td>15</td><td>2509.3</td><td>2888.66</td><td>15.1</td><td>10800</td></tr><tr><td>Cardiff.40.19</td><td>yes</td><td>10767</td><td>0</td><td>264.74</td><td>1</td><td>2784.05</td><td>2784.05</td><td>0</td><td>265.26</td></tr><tr><td>Cardiff.40.19</td><td>no</td><td>10810</td><td>0</td><td>262.37</td><td>1</td><td>2784.05</td><td>2784.05</td><td>0</td><td>263.17</td></tr><tr><td>Cardiff.40.20</td><td>yes</td><td>85341</td><td>27.2</td><td>219.7</td><td>21</td><td>2586.44</td><td>3083.33</td><td>19.2</td><td>10800</td></tr><tr><td>Cardiff.40.20</td><td>no</td><td>87042</td><td>27.2</td><td>322.25</td><td>13</td><td>2594.19</td><td>3083.33</td><td>18.9</td><td>10800</td></tr><tr><td>c100_01</td><td>yes</td><td>18845</td><td>0</td><td>55.84</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>56.75</td></tr></tbody></table>

Continued on next page
<table><caption>Table 15: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>D<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_05</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>25801</td><td>319.38</td><td>7</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1614.57</td></tr><tr><td>Cardiff_40_05</td><td>3</td><td>15</td><td>10</td><td>1</td><td>12799</td><td>397.57</td><td>5</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1000.81</td></tr><tr><td>Cardiff_40_05</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>16776</td><td>239.74</td><td>3</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>674.01</td></tr><tr><td>Cardiff_40_06</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1800</td><td>108.36</td><td>1</td><td>3013.15</td><td>2909</td><td>3.58</td><td>108.80</td></tr><tr><td>Cardiff_40_06</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1939</td><td>111.47</td><td>1</td><td>2909.0</td><td>2909</td><td>0.00</td><td>112.15</td></tr><tr><td>Cardiff_40_06</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2671</td><td>167.08</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>263.32</td></tr><tr><td>Cardiff_40_06</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6008</td><td>193.26</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>331.11</td></tr><tr><td>Cardiff_40_06</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2501</td><td>157.41</td><td>1</td><td>2909.0</td><td>2909</td><td>0.00</td><td>158.25</td></tr><tr><td>Cardiff_40_06</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2680</td><td>177.21</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>292.64</td></tr><tr><td>Cardiff_40_06</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2858</td><td>174.96</td><td>1</td><td>2909.0</td><td>2909</td><td>0.00</td><td>175.67</td></tr><tr><td>Cardiff_40_06</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6041</td><td>239.07</td><td>5</td><td>2909.0</td><td>2909</td><td>0.00</td><td>536.92</td></tr><tr><td>Cardiff_40_06</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7529</td><td>235.25</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>387.91</td></tr><tr><td>Cardiff_40_06</td><td>3</td><td>8</td><td>8</td><td>1</td><td>6590</td><td>256.48</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>503.01</td></tr><tr><td>Cardiff_40_06</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>26451</td><td>211.78</td><td>7</td><td>2909.0</td><td>2909</td><td>0.00</td><td>865.43</td></tr><tr><td>Cardiff_40_06</td><td>3</td><td>15</td><td>10</td><td>1</td><td>13386</td><td>262.61</td><td>3</td><td>2909.0</td><td>2909</td><td>0.00</td><td>425.62</td></tr><tr><td>Cardiff_40_06</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>17176</td><td>175.53</td><td>5</td><td>2909.0</td><td>2909</td><td>0.00</td><td>591.90</td></tr><tr><td>Cardiff_40_07</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1796</td><td>77.83</td><td>1</td><td>2510.25</td><td>2491.27</td><td>0.76</td><td>78.45</td></tr><tr><td>Cardiff_40_07</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1947</td><td>81.88</td><td>1</td><td>2510.25</td><td>2491.27</td><td>0.76</td><td>82.69</td></tr><tr><td>Cardiff_40_07</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2756</td><td>96.54</td><td>3</td><td>2508.6</td><td>2491.27</td><td>0.70</td><td>220.03</td></tr><tr><td>Cardiff_40_07</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6981</td><td>141.71</td><td>7</td><td>2498.08</td><td>2491.27</td><td>0.27</td><td>711.42</td></tr><tr><td>Cardiff_40_07</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2579</td><td>115.86</td><td>3</td><td>2508.6</td><td>2491.27</td><td>0.70</td><td>239.77</td></tr><tr><td>Cardiff_40_07</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2781</td><td>112.91</td><td>3</td><td>2508.6</td><td>2491.27</td><td>0.70</td><td>243.98</td></tr><tr><td>Cardiff_40_07</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2884</td><td>116.35</td><td>3</td><td>2508.6</td><td>2491.27</td><td>0.70</td><td>205.18</td></tr><tr><td>Cardiff_40_07</td><td>3</td><td>5</td><td>8</td><td>1</td><td>7195</td><td>173.82</td><td>7</td><td>2498.08</td><td>2491.27</td><td>0.27</td><td>772.11</td></tr><tr><td>Cardiff_40_07</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>9005</td><td>154.60</td><td>3</td><td>2498.08</td><td>2491.27</td><td>0.27</td><td>362.34</td></tr><tr><td>Cardiff_40_07</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7704</td><td>170.55</td><td>3</td><td>2498.08</td><td>2491.27</td><td>0.27</td><td>394.30</td></tr><tr><td>Cardiff_40_07</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>144776</td><td>701.13</td><td>3</td><td>-</td><td>2491.27</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_07</td><td>3</td><td>15</td><td>10</td><td>1</td><td>18094</td><td>224.58</td><td>3</td><td>2491.27</td><td>2491.27</td><td>0.00</td><td>414.07</td></tr><tr><td>Cardiff_40_07</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>70597</td><td>375.00</td><td>9</td><td>-</td><td>2491.27</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_08</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>67.13</td><td>5</td><td>3964.98</td><td>3834.02</td><td>3.42</td><td>288.31</td></tr><tr><td>Cardiff_40_08</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1932</td><td>70.08</td><td>7</td><td>3962.05</td><td>3834.02</td><td>3.34</td><td>263.64</td></tr><tr><td>Cardiff_40_08</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2590</td><td>100.03</td><td>3</td><td>3880.87</td><td>3834.02</td><td>1.22</td><td>194.73</td></tr><tr><td>Cardiff_40_08</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5238</td><td>143.00</td><td>1</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>143.70</td></tr><tr><td>Cardiff_40_08</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2444</td><td>138.10</td><td>3</td><td>3880.87</td><td>3834.02</td><td>1.22</td><td>223.55</td></tr><tr><td>Cardiff_40_08</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2605</td><td>114.78</td><td>3</td><td>3870.2</td><td>3834.02</td><td>0.94</td><td>205.67</td></tr><tr><td>Cardiff_40_08</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2703</td><td>115.98</td><td>3</td><td>3870.2</td><td>3834.02</td><td>0.94</td><td>191.49</td></tr><tr><td>Cardiff_40_08</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5467</td><td>226.22</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>725.98</td></tr><tr><td>Cardiff_40_08</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>6622</td><td>235.22</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>683.52</td></tr><tr><td>Cardiff_40_08</td><td>3</td><td>8</td><td>8</td><td>1</td><td>5922</td><td>217.93</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>751.23</td></tr><tr><td>Cardiff_40_08</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>9510</td><td>229.68</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>799.80</td></tr><tr><td>Cardiff_40_08</td><td>3</td><td>15</td><td>10</td><td>1</td><td>6941</td><td>181.43</td><td>3</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>384.79</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
<table><caption>Table 16: Detailed experiments on the impact of the SPR</caption><thead><tr><th>Instance</th><th>SPR</th><th>A<sup>max</sup></th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>c100_01</td><td>no</td><td>18845</td><td>0</td><td>57.8</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>58.64</td></tr><tr><td>c100_02</td><td>yes</td><td>18845</td><td>0</td><td>88.01</td><td>1</td><td>5298.36</td><td>5298.36</td><td>0</td><td>88.81</td></tr><tr><td>c100_02</td><td>no</td><td>18845</td><td>0</td><td>84.7</td><td>1</td><td>5298.36</td><td>5298.36</td><td>0</td><td>85.49</td></tr><tr><td>c100_03</td><td>yes</td><td>18898</td><td>0</td><td>139.25</td><td>1</td><td>5296.46</td><td>5296.46</td><td>0</td><td>140.3</td></tr><tr><td>c100_03</td><td>no</td><td>18898</td><td>0</td><td>150.06</td><td>1</td><td>5296.46</td><td>5296.46</td><td>0</td><td>150.89</td></tr><tr><td>c100_04</td><td>yes</td><td>20064</td><td>0.5</td><td>111.65</td><td>39</td><td>5294.66</td><td>5294.66</td><td>0</td><td>1042.88</td></tr><tr><td>c100_04</td><td>no</td><td>20064</td><td>0.5</td><td>99.7</td><td>45</td><td>5294.66</td><td>5294.66</td><td>0</td><td>1629.27</td></tr><tr><td>c100_05</td><td>yes</td><td>18849</td><td>0</td><td>56.7</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>57.6</td></tr><tr><td>c100_05</td><td>no</td><td>18849</td><td>0</td><td>57.66</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>58.43</td></tr><tr><td>c100_06</td><td>yes</td><td>18844</td><td>0</td><td>80.37</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>81.23</td></tr><tr><td>c100_06</td><td>no</td><td>18844</td><td>0</td><td>78.6</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>79.32</td></tr><tr><td>c100_07</td><td>yes</td><td>18875</td><td>0</td><td>65.13</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>66.0</td></tr><tr><td>c100_07</td><td>no</td><td>18875</td><td>0</td><td>66.53</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>67.33</td></tr><tr><td>c100_08</td><td>yes</td><td>18845</td><td>0</td><td>107.34</td><td>1</td><td>5295.36</td><td>5295.36</td><td>0</td><td>108.15</td></tr><tr><td>c100_08</td><td>no</td><td>18845</td><td>0</td><td>114.34</td><td>1</td><td>5295.36</td><td>5295.36</td><td>0</td><td>115.17</td></tr><tr><td>c100_09</td><td>yes</td><td>19018</td><td>0</td><td>218.49</td><td>1</td><td>5295.16</td><td>5295.16</td><td>0</td><td>219.57</td></tr><tr><td>c100_09</td><td>no</td><td>19018</td><td>0</td><td>226.06</td><td>1</td><td>5295.16</td><td>5295.16</td><td>0</td><td>227.08</td></tr></tbody></table>

<table><caption>Table 17: Detailed experiments on the impact of the restricted master heuristics</caption><thead><tr><th>Instance</th><th>RMH</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_01</td><td>yes</td><td>0.3</td><td>214.13</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>306.84</td></tr><tr><td>Cardiff_40_01</td><td>no</td><td>0.5</td><td>234.17</td><td>5</td><td>2931.88</td><td>2931.88</td><td>0.00</td><td>447.26</td></tr><tr><td>Cardiff_40_02</td><td>yes</td><td>21.1</td><td>99.25</td><td>77</td><td>2986.6</td><td>3242.98</td><td>8.58</td><td>10800.00</td></tr><tr><td>Cardiff_40_02</td><td>no</td><td>20.1</td><td>92.80</td><td>37</td><td>3044.72</td><td>3217.42</td><td>5.67</td><td>10800.00</td></tr><tr><td>Cardiff_40_03</td><td>yes</td><td>2.7</td><td>168.23</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>351.02</td></tr><tr><td>Cardiff_40_03</td><td>no</td><td>14.6</td><td>114.83</td><td>21</td><td>2682.5</td><td>2682.5</td><td>0.00</td><td>1287.88</td></tr><tr><td>Cardiff_40_04</td><td>yes</td><td>inf</td><td>401.23</td><td>9</td><td>4292.31</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_04</td><td>no</td><td>9.2</td><td>453.32</td><td>57</td><td>4297.88</td><td>4620.65</td><td>7.51</td><td>10800.00</td></tr><tr><td>Cardiff_40_05</td><td>yes</td><td>1.7</td><td>329.68</td><td>11</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>2141.71</td></tr><tr><td>Cardiff_40_05</td><td>no</td><td>1.8</td><td>378.99</td><td>15</td><td>3770.9</td><td>3770.9</td><td>0.00</td><td>1415.53</td></tr><tr><td>Cardiff_40_06</td><td>yes</td><td>12.5</td><td>203.15</td><td>19</td><td>2909.0</td><td>2909.0</td><td>0.00</td><td>1633.04</td></tr><tr><td>Cardiff_40_06</td><td>no</td><td>14.6</td><td>214.06</td><td>17</td><td>2909.0</td><td>2909.0</td><td>0.00</td><td>1067.80</td></tr><tr><td>Cardiff_40_07</td><td>yes</td><td>21.9</td><td>741.64</td><td>53</td><td>2297.3</td><td>2535.67</td><td>10.38</td><td>10800.00</td></tr><tr><td>Cardiff_40_07</td><td>no</td><td>inf</td><td>674.04</td><td>3</td><td>2093.42</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_08</td><td>yes</td><td>0.6</td><td>191.29</td><td>3</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>358.60</td></tr><tr><td>Cardiff_40_08</td><td>no</td><td>0.5</td><td>247.14</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>509.05</td></tr><tr><td>Cardiff_40_09</td><td>yes</td><td>35.1</td><td>381.09</td><td>11</td><td>3580.1</td><td>4484.18</td><td>25.25</td><td>10800.00</td></tr></tbody></table>

Continued on next page
<table><caption>Table 15: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>D<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>|A<sup>max</sup>|</th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_08</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>6941</td><td>201.69</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.00</td><td>631.42</td></tr><tr><td>Cardiff_40_09</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1799</td><td>148.26</td><td>3</td><td>4122.2</td><td>3668.2</td><td>12.38</td><td>323.28</td></tr><tr><td>Cardiff_40_09</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1950</td><td>105.21</td><td>3</td><td>4114.32</td><td>3668.2</td><td>12.16</td><td>172.51</td></tr><tr><td>Cardiff_40_09</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2698</td><td>186.22</td><td>5</td><td>3977.35</td><td>3668.2</td><td>8.43</td><td>469.85</td></tr><tr><td>Cardiff_40_09</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6482</td><td>180.19</td><td>33</td><td>3726.48</td><td>3668.2</td><td>1.59</td><td>10800.00</td></tr><tr><td>Cardiff_40_09</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2530</td><td>224.38</td><td>3</td><td>3955.0</td><td>3668.2</td><td>7.82</td><td>367.35</td></tr><tr><td>Cardiff_40_09</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2717</td><td>222.18</td><td>3</td><td>3924.03</td><td>3668.2</td><td>6.97</td><td>334.68</td></tr><tr><td>Cardiff_40_09</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2830</td><td>236.50</td><td>3</td><td>3924.03</td><td>3668.2</td><td>6.97</td><td>369.09</td></tr><tr><td>Cardiff_40_09</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6656</td><td>421.09</td><td>49</td><td>3668.2</td><td>3668.2</td><td>0.00</td><td>5115.00</td></tr><tr><td>Cardiff_40_09</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8011</td><td>446.94</td><td>49</td><td>3719.7</td><td>3668.2</td><td>1.40</td><td>10800.00</td></tr><tr><td>Cardiff_40_09</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7350</td><td>323.74</td><td>31</td><td>3668.2</td><td>3668.2</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff_40_09</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>80282</td><td>380.71</td><td>15</td><td>4639.5</td><td>3668.2</td><td>26.48</td><td>10800.00</td></tr><tr><td>Cardiff_40_09</td><td>3</td><td>15</td><td>10</td><td>1</td><td>15941</td><td>361.56</td><td>65</td><td>3668.2</td><td>3668.2</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff_40_09</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>42829</td><td>362.02</td><td>21</td><td>3876.85</td><td>3668.2</td><td>5.69</td><td>10800.00</td></tr><tr><td>Cardiff_40_10</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1800</td><td>76.35</td><td>1</td><td>2769.2</td><td>2692.08</td><td>2.86</td><td>76.72</td></tr><tr><td>Cardiff_40_10</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1950</td><td>76.03</td><td>3</td><td>2769.2</td><td>2692.08</td><td>2.86</td><td>114.10</td></tr><tr><td>Cardiff_40_10</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2669</td><td>85.22</td><td>1</td><td>2711.32</td><td>2692.08</td><td>0.71</td><td>86.05</td></tr><tr><td>Cardiff_40_10</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5995</td><td>141.77</td><td>3</td><td>2711.32</td><td>2692.08</td><td>0.71</td><td>276.20</td></tr><tr><td>Cardiff_40_10</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2515</td><td>99.54</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>100.29</td></tr><tr><td>Cardiff_40_10</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2690</td><td>100.58</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>100.99</td></tr><tr><td>Cardiff_40_10</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2799</td><td>103.25</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>103.87</td></tr><tr><td>Cardiff_40_10</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6222</td><td>151.79</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>152.67</td></tr><tr><td>Cardiff_40_10</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7334</td><td>173.19</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>174.24</td></tr><tr><td>Cardiff_40_10</td><td>3</td><td>8</td><td>8</td><td>1</td><td>6779</td><td>136.26</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>136.99</td></tr><tr><td>Cardiff_40_10</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>55901</td><td>167.17</td><td>5</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>521.83</td></tr><tr><td>Cardiff_40_10</td><td>3</td><td>15</td><td>10</td><td>1</td><td>12351</td><td>156.87</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>157.60</td></tr><tr><td>Cardiff_40_10</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>28248</td><td>210.33</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>211.15</td></tr><tr><td>Cardiff_40_11</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1792</td><td>5.47</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>5.69</td></tr><tr><td>Cardiff_40_11</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1921</td><td>4.57</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>4.79</td></tr><tr><td>Cardiff_40_11</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2619</td><td>9.09</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>9.75</td></tr><tr><td>Cardiff_40_11</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6236</td><td>10.38</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>10.86</td></tr><tr><td>Cardiff_40_11</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2467</td><td>8.26</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>8.76</td></tr><tr><td>Cardiff_40_11</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2635</td><td>8.60</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>9.02</td></tr><tr><td>Cardiff_40_11</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2774</td><td>8.18</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>8.48</td></tr><tr><td>Cardiff_40_11</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6535</td><td>10.62</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>10.95</td></tr><tr><td>Cardiff_40_11</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8065</td><td>12.39</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>13.12</td></tr><tr><td>Cardiff_40_11</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7188</td><td>13.01</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>13.37</td></tr><tr><td>Cardiff_40_11</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>48327</td><td>32.05</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>33.12</td></tr><tr><td>Cardiff_40_11</td><td>3</td><td>15</td><td>10</td><td>1</td><td>15181</td><td>16.39</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>17.03</td></tr><tr><td>Cardiff_40_11</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>27035</td><td>23.10</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>23.63</td></tr><tr><td>Cardiff_40_12</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1792</td><td>54.70</td><td>3</td><td>2692.03</td><td>2642.87</td><td>1.86</td><td>72.94</td></tr><tr><td>Cardiff_40_12</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1929</td><td>53.43</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>66.04</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
<table><caption>Table 17: Detailed experiments on the impact of the restricted master heuristics</caption><thead><tr><th>Instance</th><th>RMH</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_09</td><td>no</td><td>17.5</td><td>338.15</td><td>73</td><td>3580.5</td><td>3707.23</td><td>3.54</td><td>10800.00</td></tr><tr><td>Cardiff_40_10</td><td>yes</td><td>1.9</td><td>184.87</td><td>5</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>441.81</td></tr><tr><td>Cardiff_40_10</td><td>no</td><td>1.3</td><td>171.29</td><td>3</td><td>2692.08</td><td>2692.08</td><td>0.00</td><td>573.32</td></tr><tr><td>Cardiff_40_11</td><td>yes</td><td>0</td><td>29.34</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>30.12</td></tr><tr><td>Cardiff_40_11</td><td>no</td><td>0</td><td>32.62</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0.00</td><td>33.43</td></tr><tr><td>Cardiff_40_12</td><td>yes</td><td>0.8</td><td>200.06</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>307.18</td></tr><tr><td>Cardiff_40_12</td><td>no</td><td>0.7</td><td>200.69</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>276.22</td></tr><tr><td>Cardiff_40_13</td><td>yes</td><td>inf</td><td>211.40</td><td>81</td><td>2722.68</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_13</td><td>no</td><td>21.9</td><td>196.03</td><td>23</td><td>2723.1</td><td>2913.13</td><td>6.98</td><td>10800.00</td></tr><tr><td>Cardiff_40_14</td><td>yes</td><td>inf</td><td>1716.28</td><td>1</td><td>2236.37</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_14</td><td>no</td><td>inf</td><td>1914.77</td><td>13</td><td>2435.77</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_15</td><td>22.9</td><td>157.89</td><td>53</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>3757.00</td><td></td></tr><tr><td>Cardiff_40_15</td><td>no</td><td>20.3</td><td>181.95</td><td>39</td><td>2606.74</td><td>2707.12</td><td>3.85</td><td>10800.00</td></tr><tr><td>Cardiff_40_16</td><td>yes</td><td>19.8</td><td>863.33</td><td>61</td><td>3188.12</td><td>3372.57</td><td>5.79</td><td>10800.00</td></tr><tr><td>Cardiff_40_16</td><td>no</td><td>inf</td><td>785.41</td><td>5</td><td>2927.97</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_17</td><td>yes</td><td>2.1</td><td>291.80</td><td>57</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>4976.00</td></tr><tr><td>Cardiff_40_17</td><td>no</td><td>3.2</td><td>278.48</td><td>23</td><td>2733.69</td><td>2781.87</td><td>1.76</td><td>10800.00</td></tr><tr><td>Cardiff_40_18</td><td>yes</td><td>33.0</td><td>254.40</td><td>63</td><td>2731.72</td><td>2932.45</td><td>7.35</td><td>10800.00</td></tr><tr><td>Cardiff_40_18</td><td>no</td><td>inf</td><td>224.52</td><td>21</td><td>2707.07</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_19</td><td>yes</td><td>1.9</td><td>198.71</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>368.26</td></tr><tr><td>Cardiff_40_19</td><td>no</td><td>1.7</td><td>227.32</td><td>17</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>989.55</td></tr><tr><td>Cardiff_40_20</td><td>yes</td><td>32.1</td><td>237.58</td><td>103</td><td>2617.56</td><td>3203.98</td><td>22.40</td><td>10800.00</td></tr><tr><td>Cardiff_40_20</td><td>no</td><td>inf</td><td>214.13</td><td>23</td><td>2649.34</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>c100_01</td><td>0.3</td><td>yes</td><td>88.03</td><td>5</td><td>5298.76</td><td>5298.76</td><td>0.00</td><td>643.78</td></tr><tr><td>c100_01</td><td>0.3</td><td>no</td><td>70.29</td><td>33</td><td>5298.76</td><td>5298.76</td><td>0.00</td><td>3785.00</td></tr><tr><td>c100_02</td><td>0.4</td><td>yes</td><td>86.38</td><td>7</td><td>5298.36</td><td>5298.36</td><td>0.00</td><td>751.62</td></tr><tr><td>c100_02</td><td>0.3</td><td>no</td><td>80.16</td><td>63</td><td>5298.36</td><td>5298.36</td><td>0.00</td><td>2802.46</td></tr><tr><td>c100_03</td><td>0.4</td><td>yes</td><td>111.98</td><td>81</td><td>5296.46</td><td>5296.46</td><td>0.00</td><td>3877.00</td></tr><tr><td>c100_03</td><td>0.4</td><td>no</td><td>104.73</td><td>43</td><td>5296.46</td><td>5296.46</td><td>0.00</td><td>4008.00</td></tr><tr><td>c100_04</td><td>inf</td><td>yes</td><td>151.20</td><td>121</td><td>5274.14</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>c100_04</td><td>1.4</td><td>no</td><td>141.28</td><td>121</td><td>5274.95</td><td>5339.06</td><td>1.22</td><td>10800.00</td></tr><tr><td>c100_05</td><td>0.3</td><td>yes</td><td>93.02</td><td>61</td><td>5298.76</td><td>5298.76</td><td>0.00</td><td>5342.00</td></tr><tr><td>c100_05</td><td>0.3</td><td>no</td><td>90.38</td><td>19</td><td>5298.76</td><td>5298.76</td><td>0.00</td><td>3249.86</td></tr><tr><td>c100_06</td><td>0.4</td><td>yes</td><td>90.42</td><td>9</td><td>5298.76</td><td>5298.76</td><td>0.00</td><td>1144.60</td></tr><tr><td>c100_06</td><td>0.3</td><td>no</td><td>89.64</td><td>23</td><td>5298.76</td><td>5298.76</td><td>0.00</td><td>1840.12</td></tr><tr><td>c100_07</td><td>0.3</td><td>yes</td><td>87.01</td><td>37</td><td>5298.76</td><td>5298.76</td><td>0.00</td><td>3516.10</td></tr><tr><td>c100_07</td><td>0.3</td><td>no</td><td>80.05</td><td>5</td><td>5298.76</td><td>5298.76</td><td>0.00</td><td>769.38</td></tr><tr><td>c100_08</td><td>0.4</td><td>yes</td><td>113.60</td><td>25</td><td>5295.36</td><td>5295.36</td><td>0.00</td><td>1823.05</td></tr><tr><td>c100_08</td><td>0.4</td><td>no</td><td>93.02</td><td>15</td><td>5295.36</td><td>5295.36</td><td>0.00</td><td>1712.00</td></tr><tr><td>c100_09</td><td>0.4</td><td>yes</td><td>125.41</td><td>49</td><td>5295.16</td><td>5295.16</td><td>0.00</td><td>5127.00</td></tr></tbody></table>

Continued on next page
<table><caption>Table 15: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>D<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_12</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2577</td><td>60.04</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>105.03</td></tr><tr><td>Cardiff_40_12</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5911</td><td>99.59</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>145.91</td></tr><tr><td>Cardiff_40_12</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2435</td><td>81.01</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>129.47</td></tr><tr><td>Cardiff_40_12</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2596</td><td>85.92</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>140.96</td></tr><tr><td>Cardiff_40_12</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2720</td><td>87.54</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>142.77</td></tr><tr><td>Cardiff_40_12</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5911</td><td>98.25</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>138.24</td></tr><tr><td>Cardiff_40_12</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>7484</td><td>109.45</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>168.09</td></tr><tr><td>Cardiff_40_12</td><td>3</td><td>8</td><td>8</td><td>1</td><td>6505</td><td>109.39</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>159.03</td></tr><tr><td>Cardiff_40_12</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>81967</td><td>173.31</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>251.61</td></tr><tr><td>Cardiff_40_12</td><td>3</td><td>15</td><td>10</td><td>1</td><td>14174</td><td>108.45</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>165.07</td></tr><tr><td>Cardiff_40_12</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>35393</td><td>157.84</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.00</td><td>217.98</td></tr><tr><td>Cardiff_40_13</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>76.77</td><td>1</td><td>2999.0</td><td>2827.82</td><td>6.05</td><td>77.11</td></tr><tr><td>Cardiff_40_13</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1935</td><td>74.68</td><td>1</td><td>2999.0</td><td>2827.82</td><td>6.05</td><td>75.12</td></tr><tr><td>Cardiff_40_13</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2676</td><td>116.97</td><td>1</td><td>2883.55</td><td>2827.82</td><td>1.97</td><td>117.87</td></tr><tr><td>Cardiff_40_13</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6437</td><td>141.25</td><td>57</td><td>2864.38</td><td>2827.82</td><td>1.29</td><td>4819.00</td></tr><tr><td>Cardiff_40_13</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2528</td><td>141.22</td><td>3</td><td>2881.38</td><td>2827.82</td><td>1.89</td><td>254.77</td></tr><tr><td>Cardiff_40_13</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2717</td><td>101.87</td><td>1</td><td>2827.82</td><td>2827.82</td><td>0.00</td><td>102.28</td></tr><tr><td>Cardiff_40_13</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2853</td><td>99.53</td><td>1</td><td>2827.82</td><td>2827.82</td><td>0.00</td><td>100.08</td></tr><tr><td>Cardiff_40_13</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6635</td><td>142.07</td><td>79</td><td>2827.82</td><td>2827.82</td><td>0.00</td><td>6390.00</td></tr><tr><td>Cardiff_40_13</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8202</td><td>152.43</td><td>67</td><td>-</td><td>2827.82</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_13</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7251</td><td>151.86</td><td>73</td><td>2827.82</td><td>2827.82</td><td>0.00</td><td>8276.00</td></tr><tr><td>Cardiff_40_13</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>121449</td><td>206.87</td><td>23</td><td>2913.13</td><td>2827.82</td><td>3.02</td><td>10800.00</td></tr><tr><td>Cardiff_40_13</td><td>3</td><td>15</td><td>10</td><td>1</td><td>16815</td><td>208.34</td><td>113</td><td>2827.82</td><td>2827.82</td><td>0.00</td><td>8293.00</td></tr><tr><td>Cardiff_40_13</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>60077</td><td>156.43</td><td>41</td><td>-</td><td>2827.82</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_14</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1796</td><td>75.74</td><td>15</td><td>3091.18</td><td>2910.9</td><td>6.19</td><td>960.53</td></tr><tr><td>Cardiff_40_14</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1929</td><td>93.03</td><td>45</td><td>3053.88</td><td>2910.9</td><td>4.91</td><td>2932.49</td></tr><tr><td>Cardiff_40_14</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2680</td><td>78.02</td><td>63</td><td>3028.5</td><td>2910.9</td><td>4.04</td><td>3480.14</td></tr><tr><td>Cardiff_40_14</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6624</td><td>117.48</td><td>63</td><td>3023.08</td><td>2910.9</td><td>3.85</td><td>10800.00</td></tr><tr><td>Cardiff_40_14</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2515</td><td>108.57</td><td>139</td><td>2957.28</td><td>2910.9</td><td>1.59</td><td>9388.00</td></tr><tr><td>Cardiff_40_14</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2705</td><td>112.64</td><td>55</td><td>2957.28</td><td>2910.9</td><td>1.59</td><td>3692.00</td></tr><tr><td>Cardiff_40_14</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2819</td><td>120.63</td><td>39</td><td>2957.28</td><td>2910.9</td><td>1.59</td><td>2816.44</td></tr><tr><td>Cardiff_40_14</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6992</td><td>170.78</td><td>53</td><td>-</td><td>2910.9</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_14</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8269</td><td>192.80</td><td>63</td><td>-</td><td>2910.9</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_14</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7750</td><td>187.90</td><td>81</td><td>-</td><td>2910.9</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_14</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>246924</td><td>1796.16</td><td>1</td><td>-</td><td>2910.9</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_14</td><td>3</td><td>15</td><td>10</td><td>1</td><td>21082</td><td>102.81</td><td>113</td><td>2910.9</td><td>2910.9</td><td>0.00</td><td>7905.00</td></tr><tr><td>Cardiff_40_14</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>116234</td><td>1094.78</td><td>3</td><td>-</td><td>2910.9</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_15</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1797</td><td>82.77</td><td>1</td><td>2760.08</td><td>2707.12</td><td>1.96</td><td>83.05</td></tr><tr><td>Cardiff_40_15</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1942</td><td>106.92</td><td>1</td><td>2760.08</td><td>2707.12</td><td>1.96</td><td>107.20</td></tr><tr><td>Cardiff_40_15</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2643</td><td>125.59</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>205.99</td></tr><tr><td>Cardiff_40_15</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6574</td><td>174.10</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>318.79</td></tr><tr><td>Cardiff_40_15</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2506</td><td>118.92</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>186.76</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
<table><caption>Table 17: Detailed experiments on the impact of the restricted master heuristics</caption><thead><tr><th>Instance</th><th>RMH</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>c100_09</td><td>0.6</td><td>no</td><td>126.27</td><td>69</td><td>5295.16</td><td>5295.16</td><td>0.00</td><td>3874.00</td></tr><tr><td>120_C1.2_01</td><td>yes</td><td>0.4</td><td>43.36</td><td>7</td><td>9090.0</td><td>9090.0</td><td>0.00</td><td>279.21</td></tr><tr><td>120_C1.2_01</td><td>no</td><td>0.4</td><td>45.31</td><td>7</td><td>9090.0</td><td>9090.0</td><td>0.00</td><td>251.78</td></tr><tr><td>120_C1.2_02</td><td>yes</td><td>0.3</td><td>93.16</td><td>83</td><td>8920.5</td><td>8920.5</td><td>0.00</td><td>2895.06</td></tr><tr><td>120_C1.2_02</td><td>no</td><td>0.3</td><td>87.07</td><td>29</td><td>8920.5</td><td>8920.5</td><td>0.00</td><td>1827.92</td></tr><tr><td>120_C1.2_03</td><td>yes</td><td>inf</td><td>185.25</td><td>143</td><td>8815.06</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>120_C1.2_03</td><td>no</td><td>0.7</td><td>158.94</td><td>247</td><td>8812.02</td><td>8868.12</td><td>0.64</td><td>10800.00</td></tr><tr><td>120_C1.2_04</td><td>yes</td><td>inf</td><td>163.47</td><td>153</td><td>8728.17</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>120_C1.2_04</td><td>no</td><td>inf</td><td>155.55</td><td>229</td><td>8718.23</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>120_C1.2_05</td><td>yes</td><td>0.5</td><td>65.29</td><td>21</td><td>8986.2</td><td>8986.2</td><td>0.00</td><td>1552.51</td></tr><tr><td>120_C1.2_05</td><td>no</td><td>0.5</td><td>58.24</td><td>19</td><td>8986.2</td><td>8986.2</td><td>0.00</td><td>1454.68</td></tr><tr><td>120_C1.2_06</td><td>yes</td><td>0.9</td><td>97.45</td><td>99</td><td>8988.4</td><td>8988.4</td><td>0.00</td><td>4892.00</td></tr><tr><td>120_C1.2_06</td><td>no</td><td>0.9</td><td>91.46</td><td>17</td><td>8988.4</td><td>8988.4</td><td>0.00</td><td>1899.70</td></tr><tr><td>120_C1.2_07</td><td>yes</td><td>0.4</td><td>84.31</td><td>29</td><td>8958.6</td><td>8958.6</td><td>0.00</td><td>1845.62</td></tr><tr><td>120_C1.2_07</td><td>no</td><td>0.5</td><td>67.44</td><td>29</td><td>8958.6</td><td>8958.6</td><td>0.00</td><td>2438.20</td></tr><tr><td>120_C1.2_08</td><td>yes</td><td>0.3</td><td>153.67</td><td>135</td><td>8817.9</td><td>8817.9</td><td>0.00</td><td>6501.00</td></tr><tr><td>120_C1.2_08</td><td>no</td><td>0.3</td><td>166.80</td><td>9</td><td>8817.9</td><td>8817.9</td><td>0.00</td><td>642.36</td></tr><tr><td>120_C1.2_09</td><td>yes</td><td>inf</td><td>164.03</td><td>231</td><td>8771.15</td><td>-</td><td>-</td><td>10800.00</td></tr><tr><td>120_C1.2_09</td><td>no</td><td>0.3</td><td>171.82</td><td>51</td><td>8790.62</td><td>8790.62</td><td>0.00</td><td>3394.73</td></tr><tr><td>120_C1.2_10</td><td>yes</td><td>1.0</td><td>191.08</td><td>243</td><td>8729.87</td><td>8808.82</td><td>0.90</td><td>10800.00</td></tr><tr><td>120_C1.2_10</td><td>yes</td><td>inf</td><td>193.90</td><td>131</td><td>8741.16</td><td>-</td><td>-</td><td>10800.00</td></tr></tbody></table>

## Appendix B Calculation of drone-reachable neighborhood

Let $Q^d$ be the drones maximal capacity. For $i \in V$, $f_i^d$ is set to 0 if $q_i > Q^d$ or if $i$ is not available for deliveries by drone. Otherwise we set $f_i^d = 1$. We introduce a parameter $\tilde{f}_i^d = 0$ expressing whether client $i \in V$ is available to launch drone from or not. The latest can be explained because no parking spot is available nearby for example. We set $\tilde{f}_i^d = 0$ in this case and $\tilde{f}_i^d = 1$ otherwise. An energy function limits the maximal flight distance, calculated as follows: $P(q) = (W + m + q)^{\frac{3}{2}} \sqrt{\frac{q^3}{2\rho\zeta h}}$ in Watt, introduced by Dorling et al. (2016) as the hovering power consumption of a h-rotor drone, an upper bound on the general power consumption of a h-rotor drone, and based on Leishman (2006). $W$ is the frame weight (kg), $m$ the battery weight (kg), $q$ the payload (kg), $g$ is the force due to gravity (N), $\rho$ the fluid density of air in (kg/m$^3$) and $\zeta$ the area of spinning blade (m$^2$). We note $B_c$ the drone's battery capacity in
<table><caption>Table 15: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>D<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_15</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2680</td><td>134.02</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>201.04</td></tr><tr><td>Cardiff_40_15</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2730</td><td>132.68</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>198.58</td></tr><tr><td>Cardiff_40_15</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6721</td><td>172.12</td><td>3</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>330.60</td></tr><tr><td>Cardiff_40_15</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8005</td><td>180.66</td><td>9</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>966.44</td></tr><tr><td>Cardiff_40_15</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7296</td><td>186.29</td><td>5</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>597.70</td></tr><tr><td>Cardiff_40_15</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>37408</td><td>185.77</td><td>41</td><td>2716.77</td><td>2707.12</td><td>0.36</td><td>10800.00</td></tr><tr><td>Cardiff_40_15</td><td>3</td><td>15</td><td>10</td><td>1</td><td>15169</td><td>133.81</td><td>25</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>3442.63</td></tr><tr><td>Cardiff_40_15</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>23134</td><td>200.91</td><td>35</td><td>2707.12</td><td>2707.12</td><td>0.00</td><td>6986.00</td></tr><tr><td>Cardiff_40_16</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1796</td><td>152.34</td><td>3</td><td>4095.77</td><td>3353.42</td><td>22.14</td><td>325.30</td></tr><tr><td>Cardiff_40_16</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1938</td><td>139.04</td><td>3</td><td>3378.82</td><td>3353.42</td><td>0.76</td><td>246.38</td></tr><tr><td>Cardiff_40_16</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2634</td><td>157.76</td><td>3</td><td>3378.82</td><td>3353.42</td><td>0.76</td><td>290.33</td></tr><tr><td>Cardiff_40_16</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6861</td><td>251.24</td><td>37</td><td>3415.72</td><td>3353.42</td><td>1.86</td><td>10800.00</td></tr><tr><td>Cardiff_40_16</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2483</td><td>223.02</td><td>3</td><td>3378.82</td><td>3353.42</td><td>0.76</td><td>387.75</td></tr><tr><td>Cardiff_40_16</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2660</td><td>146.76</td><td>3</td><td>3353.42</td><td>3353.42</td><td>0.00</td><td>271.65</td></tr><tr><td>Cardiff_40_16</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2771</td><td>161.23</td><td>3</td><td>3353.42</td><td>3353.42</td><td>0.00</td><td>291.54</td></tr><tr><td>Cardiff_40_16</td><td>3</td><td>5</td><td>8</td><td>1</td><td>7072</td><td>278.11</td><td>49</td><td>3353.42</td><td>3353.42</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff_40_16</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8688</td><td>351.24</td><td>27</td><td>3366.97</td><td>3353.42</td><td>0.40</td><td>10800.00</td></tr><tr><td>Cardiff_40_16</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7898</td><td>296.23</td><td>61</td><td>3410.52</td><td>3353.42</td><td>1.70</td><td>10800.00</td></tr><tr><td>Cardiff_40_16</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>152985</td><td>835.01</td><td>5</td><td>-</td><td>3353.42</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_16</td><td>3</td><td>15</td><td>10</td><td>1</td><td>19971</td><td>335.19</td><td>15</td><td>3366.97</td><td>3353.42</td><td>0.40</td><td>10800.00</td></tr><tr><td>Cardiff_40_16</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>65872</td><td>480.78</td><td>9</td><td>-</td><td>3353.42</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_17</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>92.36</td><td>3</td><td>2831.3</td><td>2749.83</td><td>2.96</td><td>115.20</td></tr><tr><td>Cardiff_40_17</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1939</td><td>87.32</td><td>1</td><td>2777.07</td><td>2749.83</td><td>0.99</td><td>87.80</td></tr><tr><td>Cardiff_40_17</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2624</td><td>128.11</td><td>1</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>129.20</td></tr><tr><td>Cardiff_40_17</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5241</td><td>189.10</td><td>5</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>676.60</td></tr><tr><td>Cardiff_40_17</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2474</td><td>162.52</td><td>3</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>235.68</td></tr><tr><td>Cardiff_40_17</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2642</td><td>160.60</td><td>1</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>161.46</td></tr><tr><td>Cardiff_40_17</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2738</td><td>164.62</td><td>1</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>165.30</td></tr><tr><td>Cardiff_40_17</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5350</td><td>225.94</td><td>3</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>364.92</td></tr><tr><td>Cardiff_40_17</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>6334</td><td>204.08</td><td>7</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>928.89</td></tr><tr><td>Cardiff_40_17</td><td>3</td><td>8</td><td>8</td><td>1</td><td>5787</td><td>191.46</td><td>3</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>307.75</td></tr><tr><td>Cardiff_40_17</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>24600</td><td>280.43</td><td>33</td><td>-</td><td>2749.83</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_17</td><td>3</td><td>15</td><td>10</td><td>1</td><td>9307</td><td>233.03</td><td>7</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>1051.50</td></tr><tr><td>Cardiff_40_17</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>16770</td><td>256.00</td><td>9</td><td>2749.83</td><td>2749.83</td><td>0.00</td><td>4918.00</td></tr><tr><td>Cardiff_40_18</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1787</td><td>120.56</td><td>3</td><td>2898.75</td><td>2888.65</td><td>0.35</td><td>264.26</td></tr><tr><td>Cardiff_40_18</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1915</td><td>82.22</td><td>3</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>146.25</td></tr><tr><td>Cardiff_40_18</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2579</td><td>88.51</td><td>5</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>268.48</td></tr><tr><td>Cardiff_40_18</td><td>2</td><td>5</td><td>8</td><td>1</td><td>6586</td><td>110.40</td><td>57</td><td>2941.17</td><td>2888.65</td><td>1.82</td><td>10800.00</td></tr><tr><td>Cardiff_40_18</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2435</td><td>120.02</td><td>5</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>378.09</td></tr><tr><td>Cardiff_40_18</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2593</td><td>109.83</td><td>5</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>355.63</td></tr><tr><td>Cardiff_40_18</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2711</td><td>117.91</td><td>3</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>190.47</td></tr><tr><td>Cardiff_40_18</td><td>3</td><td>5</td><td>8</td><td>1</td><td>6763</td><td>155.29</td><td>75</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>9097.00</td></tr></tbody><tfoot><tr><td colspan="12">Continued on next page</td></tr></tfoot></table>
watt-hours. Let $g = 9.81$ N/kg and $\rho = 1.204$ kg/m³ as in (Dorling et al., 2016).

$$C_i = \{j \in V | (\bar{f}_i^d == 1) \land (f_j^d == 1) \land (P(q_i) * c_{i,j}^d + P(0) * c_{j,i}^d \le B_c) \land (c_{0,i}^v + c_{i,j}^d \le \bar{d}_j) \quad i \in V\}$$

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<table><caption>Table 15: Detailed performance of the heuristic</caption><thead><tr><th>Instance</th><th>D<sub>h</sub></th><th>w<sub>h</sub></th><th>k<sub>h</sub></th><th>p<sub>h</sub></th><th>A<sup>max</sup></th><th>Root Time</th><th>Nodes</th><th>PB</th><th>BKS</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_18</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>8311</td><td>165.19</td><td>37</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>4932.00</td></tr><tr><td>Cardiff_40_18</td><td>3</td><td>8</td><td>8</td><td>1</td><td>7454</td><td>153.60</td><td>57</td><td>2902.2</td><td>2888.65</td><td>0.47</td><td>10800.00</td></tr><tr><td>Cardiff_40_18</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>93353</td><td>233.75</td><td>21</td><td>-</td><td>2888.65</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_18</td><td>3</td><td>15</td><td>10</td><td>1</td><td>17614</td><td>94.82</td><td>93</td><td>2888.65</td><td>2888.65</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff_40_18</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>48958</td><td>156.16</td><td>29</td><td>-</td><td>2888.65</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_19</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1800</td><td>100.68</td><td>3</td><td>2807.1</td><td>2784.05</td><td>0.83</td><td>206.02</td></tr><tr><td>Cardiff_40_19</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1956</td><td>125.08</td><td>3</td><td>2807.1</td><td>2784.05</td><td>0.83</td><td>272.73</td></tr><tr><td>Cardiff_40_19</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2690</td><td>181.37</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>345.11</td></tr><tr><td>Cardiff_40_19</td><td>2</td><td>5</td><td>8</td><td>1</td><td>5057</td><td>147.83</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>312.69</td></tr><tr><td>Cardiff_40_19</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2541</td><td>174.93</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>298.16</td></tr><tr><td>Cardiff_40_19</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2710</td><td>172.47</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>306.01</td></tr><tr><td>Cardiff_40_19</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2801</td><td>156.48</td><td>7</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>557.54</td></tr><tr><td>Cardiff_40_19</td><td>3</td><td>5</td><td>8</td><td>1</td><td>5075</td><td>158.20</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>261.90</td></tr><tr><td>Cardiff_40_19</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>6009</td><td>167.29</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>297.71</td></tr><tr><td>Cardiff_40_19</td><td>3</td><td>8</td><td>8</td><td>1</td><td>5412</td><td>169.81</td><td>11</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>924.35</td></tr><tr><td>Cardiff_40_19</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>11376</td><td>209.09</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>374.94</td></tr><tr><td>Cardiff_40_19</td><td>3</td><td>15</td><td>10</td><td>1</td><td>7577</td><td>211.69</td><td>7</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>650.65</td></tr><tr><td>Cardiff_40_19</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>8484</td><td>189.95</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.00</td><td>345.95</td></tr><tr><td>Cardiff_40_20</td><td>2</td><td>2</td><td>2</td><td>1</td><td>1798</td><td>104.94</td><td>41</td><td>3167.3</td><td>3083.32</td><td>2.72</td><td>4142.00</td></tr><tr><td>Cardiff_40_20</td><td>2</td><td>3</td><td>3</td><td>1</td><td>1937</td><td>94.93</td><td>53</td><td>3167.3</td><td>3083.32</td><td>2.72</td><td>4879.00</td></tr><tr><td>Cardiff_40_20</td><td>2</td><td>5</td><td>5</td><td>1</td><td>2668</td><td>104.20</td><td>3</td><td>3083.32</td><td>3083.32</td><td>0.00</td><td>249.27</td></tr><tr><td>Cardiff_40_20</td><td>2</td><td>5</td><td>8</td><td>1</td><td>7541</td><td>126.64</td><td>51</td><td>3083.32</td><td>3083.32</td><td>0.00</td><td>10800.00</td></tr><tr><td>Cardiff_40_20</td><td>3</td><td>3</td><td>5</td><td>1</td><td>2503</td><td>152.96</td><td>3</td><td>3083.32</td><td>3083.32</td><td>0.00</td><td>295.26</td></tr><tr><td>Cardiff_40_20</td><td>3</td><td>5</td><td>5</td><td>1</td><td>2685</td><td>142.13</td><td>3</td><td>3083.32</td><td>3083.32</td><td>0.00</td><td>315.32</td></tr><tr><td>Cardiff_40_20</td><td>3</td><td>5</td><td>5</td><td>inf</td><td>2798</td><td>138.74</td><td>3</td><td>3083.32</td><td>3083.32</td><td>0.00</td><td>283.32</td></tr><tr><td>Cardiff_40_20</td><td>3</td><td>5</td><td>8</td><td>1</td><td>7844</td><td>162.42</td><td>71</td><td>3217.35</td><td>3083.32</td><td>4.35</td><td>10800.00</td></tr><tr><td>Cardiff_40_20</td><td>3</td><td>5</td><td>8</td><td>inf</td><td>9585</td><td>183.54</td><td>51</td><td>3102.13</td><td>3083.32</td><td>0.61</td><td>10800.00</td></tr><tr><td>Cardiff_40_20</td><td>3</td><td>8</td><td>8</td><td>1</td><td>8665</td><td>198.26</td><td>47</td><td>3109.15</td><td>3083.32</td><td>0.84</td><td>10800.00</td></tr><tr><td>Cardiff_40_20</td><td>3</td><td>10</td><td>15</td><td>inf</td><td>89884</td><td>223.75</td><td>23</td><td>-</td><td>3083.32</td><td>-</td><td>10800.00</td></tr><tr><td>Cardiff_40_20</td><td>3</td><td>15</td><td>10</td><td>1</td><td>20544</td><td>273.60</td><td>55</td><td>3089.5</td><td>3083.32</td><td>0.20</td><td>10800.00</td></tr><tr><td>Cardiff_40_20</td><td>3</td><td>15</td><td>15</td><td>inf</td><td>55292</td><td>162.79</td><td>31</td><td>-</td><td>3083.32</td><td>-</td><td>10800.00</td></tr></tbody></table>

<table><caption>Table 16: Detailed experiments on the impact of the ARCC</caption><thead><tr><th>Instance</th><th>ARCC</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>120_C1_2_01</td><td>yes</td><td>0</td><td>58.04</td><td>1</td><td>9090</td><td>9090</td><td>0</td><td>58.94</td></tr><tr><td>120_C1_2_01</td><td>no</td><td>0</td><td>43.98</td><td>1</td><td>9090</td><td>9090</td><td>0</td><td>44.63</td></tr><tr><td>120_C1_2_02</td><td>yes</td><td>0</td><td>162.93</td><td>1</td><td>8920.5</td><td>8920.5</td><td>0</td><td>163.87</td></tr><tr><td>120_C1_2_02</td><td>no</td><td>0</td><td>145.72</td><td>1</td><td>8920.5</td><td>8920.5</td><td>0</td><td>146.54</td></tr><tr><td>120_C1_2_03</td><td>yes</td><td>0.2</td><td>250.16</td><td>5</td><td>8843.52</td><td>8843.52</td><td>0</td><td>428.45</td></tr></tbody></table>

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<table><caption>Table 16: Detailed experiments on the impact of the ARCC</caption><thead><tr><th>Instance</th><th>ARCC</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>120_C1_2_03</td><td>no</td><td>0.3</td><td>185.19</td><td>9</td><td>8843.52</td><td>8843.52</td><td>0</td><td>433.68</td></tr><tr><td>120_C1_2_04</td><td>yes</td><td>0.7</td><td>240.19</td><td>187</td><td>8740.64</td><td>8784.92</td><td>0.51</td><td>10800</td></tr><tr><td>120_C1_2_04</td><td>no</td><td>0.6</td><td>165.93</td><td>241</td><td>8740</td><td>8784.92</td><td>0.51</td><td>10800</td></tr><tr><td>120_C1_2_05</td><td>yes</td><td>0</td><td>240.02</td><td>1</td><td>8986.2</td><td>8986.2</td><td>0</td><td>241.07</td></tr><tr><td>120_C1_2_05</td><td>no</td><td>0</td><td>237.6</td><td>1</td><td>8986.2</td><td>8986.2</td><td>0</td><td>238.7</td></tr><tr><td>120_C1_2_06</td><td>yes</td><td>0.3</td><td>395.59</td><td>9</td><td>8988.4</td><td>8988.4</td><td>0</td><td>847.64</td></tr><tr><td>120_C1_2_06</td><td>no</td><td>0.3</td><td>341.83</td><td>9</td><td>8988.4</td><td>8988.4</td><td>0</td><td>908.45</td></tr><tr><td>120_C1_2_07</td><td>yes</td><td>0.1</td><td>210.22</td><td>3</td><td>8958.6</td><td>8958.6</td><td>0</td><td>375.54</td></tr><tr><td>120_C1_2_07</td><td>no</td><td>0.1</td><td>242.94</td><td>3</td><td>8958.6</td><td>8958.6</td><td>0</td><td>419.64</td></tr><tr><td>120_C1_2_08</td><td>yes</td><td>0.1</td><td>229.57</td><td>11</td><td>8817.9</td><td>8817.9</td><td>0</td><td>375.16</td></tr><tr><td>120_C1_2_08</td><td>no</td><td>0.1</td><td>175.54</td><td>15</td><td>8817.9</td><td>8817.9</td><td>0</td><td>529.05</td></tr><tr><td>120_C1_2_09</td><td>yes</td><td>0</td><td>281.36</td><td>1</td><td>8790.62</td><td>8790.62</td><td>0</td><td>282.26</td></tr><tr><td>120_C1_2_09</td><td>no</td><td>0</td><td>189.73</td><td>1</td><td>8790.62</td><td>8790.62</td><td>0</td><td>190.56</td></tr><tr><td>120_C1_2_10</td><td>yes</td><td>0.7</td><td>264.75</td><td>97</td><td>8740.41</td><td>8794.92</td><td>0.62</td><td>10800</td></tr><tr><td>120_C1_2_10</td><td>no</td><td>0.7</td><td>155.31</td><td>125</td><td>8737.92</td><td>8794.92</td><td>0.65</td><td>10800</td></tr><tr><td>130_C1_2_01</td><td>yes</td><td>0</td><td>193.32</td><td>1</td><td>9325.92</td><td>9325.92</td><td>0</td><td>194.05</td></tr><tr><td>130_C1_2_01</td><td>no</td><td>0</td><td>188.75</td><td>1</td><td>9325.92</td><td>9325.92</td><td>0</td><td>189.49</td></tr><tr><td>130_C1_2_02</td><td>yes</td><td>0</td><td>201.23</td><td>1</td><td>9141.2</td><td>9141.2</td><td>0</td><td>202.12</td></tr><tr><td>130_C1_2_02</td><td>no</td><td>0</td><td>169.74</td><td>1</td><td>9141.2</td><td>9141.2</td><td>0</td><td>170.74</td></tr><tr><td>130_C1_2_03</td><td>yes</td><td>0.7</td><td>198.25</td><td>241</td><td>9056.65</td><td>9119</td><td>0.69</td><td>10800</td></tr><tr><td>130_C1_2_03</td><td>no</td><td>0.7</td><td>199.17</td><td>167</td><td>9059.79</td><td>9119</td><td>0.65</td><td>10800</td></tr><tr><td>130_C1_2_04</td><td>yes</td><td>0.8</td><td>254.91</td><td>223</td><td>8993.56</td><td>9056.21</td><td>0.70</td><td>10800</td></tr><tr><td>130_C1_2_04</td><td>no</td><td>0.8</td><td>176.29</td><td>101</td><td>8989.81</td><td>9056.21</td><td>0.74</td><td>10800</td></tr><tr><td>130_C1_2_05</td><td>yes</td><td>0</td><td>264.44</td><td>1</td><td>9209.62</td><td>9209.62</td><td>0</td><td>265.45</td></tr><tr><td>130_C1_2_05</td><td>no</td><td>0</td><td>214.59</td><td>1</td><td>9209.62</td><td>9209.62</td><td>0</td><td>215.36</td></tr><tr><td>130_C1_2_06</td><td>yes</td><td>0.3</td><td>336.13</td><td>33</td><td>9222.4</td><td>9222.4</td><td>0</td><td>2152.1</td></tr><tr><td>130_C1_2_06</td><td>no</td><td>0.3</td><td>403.74</td><td>15</td><td>9222.4</td><td>9222.4</td><td>0</td><td>1633.03</td></tr><tr><td>130_C1_2_07</td><td>yes</td><td>0</td><td>687.49</td><td>3</td><td>9197.92</td><td>9197.92</td><td>0</td><td>1027.5</td></tr><tr><td>130_C1_2_07</td><td>no</td><td>0</td><td>771.28</td><td>3</td><td>9197.92</td><td>9197.92</td><td>0</td><td>1236.02</td></tr><tr><td>130_C1_2_08</td><td>yes</td><td>0.4</td><td>375.96</td><td>141</td><td>9082.79</td><td>9091.7</td><td>0.10</td><td>10800</td></tr><tr><td>130_C1_2_08</td><td>no</td><td>0.3</td><td>432.57</td><td>137</td><td>9066.88</td><td>9091.7</td><td>0.27</td><td>10800</td></tr><tr><td>130_C1_2_09</td><td>yes</td><td>0.6</td><td>261.74</td><td>119</td><td>9028.84</td><td>9077.5</td><td>0.54</td><td>10800</td></tr><tr><td>130_C1_2_09</td><td>no</td><td>0.6</td><td>236.97</td><td>129</td><td>9029.86</td><td>9077.5</td><td>0.53</td><td>10800</td></tr><tr><td>130_C1_2_10</td><td>yes</td><td>0.8</td><td>277.84</td><td>119</td><td>8992</td><td>9060.5</td><td>0.76</td><td>10800</td></tr><tr><td>130_C1_2_10</td><td>no</td><td>0.8</td><td>193.69</td><td>121</td><td>8990.42</td><td>9060.5</td><td>0.78</td><td>10800</td></tr><tr><td>140_C1_2_01</td><td>yes</td><td>0</td><td>268.45</td><td>1</td><td>9970.42</td><td>9970.42</td><td>0</td><td>269.33</td></tr><tr><td>140_C1_2_01</td><td>no</td><td>0</td><td>224.69</td><td>3</td><td>9970.42</td><td>9970.42</td><td>0</td><td>259.88</td></tr><tr><td>140_C1_2_02</td><td>yes</td><td>0.4</td><td>323.74</td><td>53</td><td>9817.38</td><td>9817.38</td><td>0</td><td>3780.0</td></tr><tr><td>140_C1_2_02</td><td>no</td><td>0.4</td><td>241.88</td><td>53</td><td>9817.38</td><td>9817.38</td><td>0</td><td>3656.0</td></tr><tr><td>140_C1_2_03</td><td>yes</td><td>0.8</td><td>271.7</td><td>115</td><td>9722.55</td><td>9784.7</td><td>0.64</td><td>10800</td></tr><tr><td>140_C1_2_03</td><td>no</td><td>0.8</td><td>174.26</td><td>119</td><td>9715.29</td><td>9784.7</td><td>0.71</td><td>10800</td></tr></tbody></table>

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<table><caption>Table 16: Detailed experiments on the impact of the ARCC</caption><thead><tr><th>Instance</th><th>ARCC</th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>140_C1_2_04</td><td>yes</td><td>1.4</td><td>288.78</td><td>143</td><td>9637.97</td><td>9762.48</td><td>1.29</td><td>10800</td></tr><tr><td>140_C1_2_04</td><td>no</td><td>1.4</td><td>220.5</td><td>119</td><td>9637.72</td><td>9762.48</td><td>1.29</td><td>10800</td></tr><tr><td>140_C1_2_05</td><td>yes</td><td>0</td><td>262.62</td><td>1</td><td>9848.82</td><td>9848.82</td><td>0</td><td>263.61</td></tr><tr><td>140_C1_2_05</td><td>no</td><td>0</td><td>219.09</td><td>1</td><td>9848.82</td><td>9848.82</td><td>0</td><td>220.18</td></tr><tr><td>140_C1_2_06</td><td>yes</td><td>0.1</td><td>638.89</td><td>3</td><td>9853.5</td><td>9853.5</td><td>0</td><td>881.09</td></tr><tr><td>140_C1_2_06</td><td>no</td><td>0.1</td><td>598.12</td><td>3</td><td>9853.5</td><td>9853.5</td><td>0</td><td>809.91</td></tr><tr><td>140_C1_2_07</td><td>yes</td><td>0</td><td>325.88</td><td>3</td><td>9836.32</td><td>9836.32</td><td>0</td><td>363.95</td></tr><tr><td>140_C1_2_07</td><td>no</td><td>0</td><td>229.26</td><td>3</td><td>9836.32</td><td>9836.32</td><td>0</td><td>304.98</td></tr><tr><td>140_C1_2_08</td><td>yes</td><td>0.4</td><td>374.68</td><td>165</td><td>9726.07</td><td>9754.28</td><td>0.29</td><td>10800</td></tr><tr><td>140_C1_2_08</td><td>no</td><td>0.5</td><td>274.15</td><td>129</td><td>9716.74</td><td>9754.28</td><td>0.39</td><td>10800</td></tr><tr><td>140_C1_2_09</td><td>yes</td><td>0.8</td><td>271.95</td><td>157</td><td>9684.21</td><td>9754</td><td>0.72</td><td>10800</td></tr><tr><td>140_C1_2_09</td><td>no</td><td>0.9</td><td>258.01</td><td>181</td><td>9690.01</td><td>9754</td><td>0.66</td><td>10800</td></tr><tr><td>140_C1_2_10</td><td>yes</td><td>2.9</td><td>296.33</td><td>113</td><td>9639.97</td><td>9900</td><td>2.70</td><td>10800</td></tr><tr><td>140_C1_2_10</td><td>no</td><td>2.9</td><td>185.31</td><td>115</td><td>9638.62</td><td>9900</td><td>2.71</td><td>10800</td></tr></tbody></table>

<table><caption>Table 17: Detailed experiments on the impact of the SPR</caption><thead><tr><th>Instance</th><th>SPR</th><th>A<sup>max</sup></th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_01</td><td>yes</td><td>13034</td><td>0</td><td>268.41</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0</td><td>269.49</td></tr><tr><td>Cardiff_40_01</td><td>no</td><td>13174</td><td>0</td><td>297.93</td><td>1</td><td>2931.88</td><td>2931.88</td><td>0</td><td>298.89</td></tr><tr><td>Cardiff_40_02</td><td>yes</td><td>95883</td><td>20.1</td><td>88.12</td><td>45</td><td>2827.85</td><td>3217.43</td><td>13.8</td><td>10800</td></tr><tr><td>Cardiff_40_02</td><td>no</td><td>97648</td><td>20.1</td><td>117.31</td><td>29</td><td>2774.49</td><td>3217.42</td><td>16</td><td>10800</td></tr><tr><td>Cardiff_40_03</td><td>yes</td><td>30318</td><td>0</td><td>400.03</td><td>1</td><td>2682.5</td><td>2682.5</td><td>0</td><td>401.32</td></tr><tr><td>Cardiff_40_03</td><td>no</td><td>30721</td><td>9.1</td><td>264.48</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0</td><td>542.77</td></tr><tr><td>Cardiff_40_04</td><td>yes</td><td>169680</td><td>20.2</td><td>317.5</td><td>9</td><td>4282.36</td><td>5082.63</td><td>18.7</td><td>10800</td></tr><tr><td>Cardiff_40_04</td><td>no</td><td>178022</td><td>20.2</td><td>478.01</td><td>7</td><td>4281.08</td><td>5082.63</td><td>18.7</td><td>10800</td></tr><tr><td>Cardiff_40_05</td><td>yes</td><td>25801</td><td>1.6</td><td>543.24</td><td>27</td><td>3770.9</td><td>3770.9</td><td>0</td><td>6574.0</td></tr><tr><td>Cardiff_40_05</td><td>no</td><td>26586</td><td>1.6</td><td>603.97</td><td>23</td><td>3770.9</td><td>3770.9</td><td>0</td><td>4977.0</td></tr><tr><td>Cardiff_40_06</td><td>yes</td><td>26451</td><td>0</td><td>491.63</td><td>1</td><td>2909</td><td>2909</td><td>0</td><td>492.73</td></tr><tr><td>Cardiff_40_06</td><td>no</td><td>27449</td><td>0</td><td>559.3</td><td>1</td><td>2909</td><td>2909</td><td>0</td><td>560.32</td></tr><tr><td>Cardiff_40_07</td><td>yes</td><td>89523</td><td>19.8</td><td>696.68</td><td>3</td><td>2093.42</td><td>2491.28</td><td>19</td><td>10800</td></tr><tr><td>Cardiff_40_07</td><td>no</td><td>91461</td><td>19.8</td><td>1008.99</td><td>1</td><td>2080.22</td><td>2491.28</td><td>19.8</td><td>10800</td></tr><tr><td>Cardiff_40_08</td><td>yes</td><td>9510</td><td>0</td><td>215.16</td><td>1</td><td>3834.02</td><td>3834.02</td><td>0</td><td>215.85</td></tr><tr><td>Cardiff_40_08</td><td>no</td><td>9671</td><td>0</td><td>258.93</td><td>1</td><td>3834.02</td><td>3834.02</td><td>0</td><td>259.65</td></tr><tr><td>Cardiff_40_09</td><td>yes</td><td>81734</td><td>12.7</td><td>1084.47</td><td>9</td><td>3569.6</td><td>3668.21</td><td>2.8</td><td>10800</td></tr><tr><td>Cardiff_40_09</td><td>no</td><td>84161</td><td>13.1</td><td>1156.82</td><td>11</td><td>3541.86</td><td>3668.21</td><td>3.6</td><td>10800</td></tr><tr><td>Cardiff_40_10</td><td>yes</td><td>55913</td><td>0</td><td>220.62</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0</td><td>221.98</td></tr><tr><td>Cardiff_40_10</td><td>no</td><td>59456</td><td>0</td><td>297.74</td><td>1</td><td>2692.08</td><td>2692.08</td><td>0</td><td>299.62</td></tr><tr><td>Cardiff_40_11</td><td>yes</td><td>48327</td><td>0</td><td>5.94</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0</td><td>6.59</td></tr></tbody></table>

Continued on next page
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Diego Pecin, Artur Pessoa, Marcus Poggi, and Eduardo Uchoa. Im-
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<table><caption>Table 17: Detailed experiments on the impact of the SPR</caption><thead><tr><th>Instance</th><th>SPR</th><th>A<sup>max</sup></th><th>Root Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_11</td><td>no</td><td>51524</td><td>0</td><td>6.89</td><td>1</td><td>unfeasible</td><td>unfeasible</td><td>0</td><td>8.0</td></tr><tr><td>Cardiff_40_12</td><td>yes</td><td>38128</td><td>0</td><td>280.93</td><td>1</td><td>2642.87</td><td>2642.87</td><td>0</td><td>282.13</td></tr><tr><td>Cardiff_40_12</td><td>no</td><td>38637</td><td>0</td><td>351.3</td><td>1</td><td>2642.87</td><td>2642.87</td><td>0</td><td>353.38</td></tr><tr><td>Cardiff_40_13</td><td>yes</td><td>121649</td><td>18.4</td><td>199.97</td><td>17</td><td>2742.72</td><td>2827.83</td><td>3.1</td><td>10800</td></tr><tr><td>Cardiff_40_13</td><td>no</td><td>123340</td><td>18.4</td><td>274.22</td><td>15</td><td>2742.19</td><td>2827.83</td><td>3.1</td><td>10800</td></tr><tr><td>Cardiff_40_14</td><td>yes</td><td>247124</td><td>30.2</td><td>1794.42</td><td>1</td><td>2236.37</td><td>2910.91</td><td>30.2</td><td>10800</td></tr><tr><td>Cardiff_40_14</td><td>no</td><td>260625</td><td>30.2</td><td>3466.11</td><td>1</td><td>2236.37</td><td>2910.91</td><td>30.2</td><td>10800</td></tr><tr><td>Cardiff_40_15</td><td>yes</td><td>33041</td><td>19.9</td><td>281.4</td><td>37</td><td>2549.95</td><td>2707.12</td><td>6.2</td><td>10800</td></tr><tr><td>Cardiff_40_15</td><td>no</td><td>33301</td><td>20</td><td>351.13</td><td>35</td><td>2643.72</td><td>2707.13</td><td>2.4</td><td>10800</td></tr><tr><td>Cardiff_40_16</td><td>yes</td><td>153756</td><td>18</td><td>844.32</td><td>3</td><td>2904.8</td><td>3353.43</td><td>15.4</td><td>10800</td></tr><tr><td>Cardiff_40_16</td><td>no</td><td>156619</td><td>19.1</td><td>1134.11</td><td>3</td><td>2881.14</td><td>3353.43</td><td>16.4</td><td>10800</td></tr><tr><td>Cardiff_40_17</td><td>yes</td><td>24463</td><td>1.8</td><td>678.22</td><td>13</td><td>2735.28</td><td>2749.84</td><td>0.5</td><td>10800</td></tr><tr><td>Cardiff_40_17</td><td>no</td><td>24917</td><td>1.9</td><td>916.07</td><td>13</td><td>2722.56</td><td>2749.84</td><td>1</td><td>10800</td></tr><tr><td>Cardiff_40_18</td><td>yes</td><td>93744</td><td>31</td><td>213.52</td><td>21</td><td>2676.43</td><td>2888.66</td><td>7.9</td><td>10800</td></tr><tr><td>Cardiff_40_18</td><td>no</td><td>95960</td><td>31</td><td>291.94</td><td>15</td><td>2509.3</td><td>2888.66</td><td>15.1</td><td>10800</td></tr><tr><td>Cardiff_40_19</td><td>yes</td><td>10767</td><td>0</td><td>264.74</td><td>1</td><td>2784.05</td><td>2784.05</td><td>0</td><td>265.26</td></tr><tr><td>Cardiff_40_19</td><td>no</td><td>10810</td><td>0</td><td>262.37</td><td>1</td><td>2784.05</td><td>2784.05</td><td>0</td><td>263.17</td></tr><tr><td>Cardiff_40_20</td><td>yes</td><td>85341</td><td>27.2</td><td>219.7</td><td>21</td><td>2586.44</td><td>3083.33</td><td>19.2</td><td>10800</td></tr><tr><td>Cardiff_40_20</td><td>no</td><td>87042</td><td>27.2</td><td>322.25</td><td>13</td><td>2594.19</td><td>3083.33</td><td>18.9</td><td>10800</td></tr><tr><td>c100_01</td><td>yes</td><td>18845</td><td>0</td><td>55.84</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>56.75</td></tr><tr><td>c100_01</td><td>no</td><td>18845</td><td>0</td><td>57.8</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>58.64</td></tr><tr><td>c100_02</td><td>yes</td><td>18845</td><td>0</td><td>88.01</td><td>1</td><td>5298.36</td><td>5298.36</td><td>0</td><td>88.81</td></tr><tr><td>c100_02</td><td>no</td><td>18845</td><td>0</td><td>84.7</td><td>1</td><td>5298.36</td><td>5298.36</td><td>0</td><td>85.49</td></tr><tr><td>c100_03</td><td>yes</td><td>18898</td><td>0</td><td>139.25</td><td>1</td><td>5296.46</td><td>5296.46</td><td>0</td><td>140.3</td></tr><tr><td>c100_03</td><td>no</td><td>18898</td><td>0</td><td>150.06</td><td>1</td><td>5296.46</td><td>5296.46</td><td>0</td><td>150.89</td></tr><tr><td>c100_04</td><td>yes</td><td>20064</td><td>0.5</td><td>111.65</td><td>39</td><td>5294.66</td><td>5294.66</td><td>0</td><td>1042.88</td></tr><tr><td>c100_04</td><td>no</td><td>20064</td><td>0.5</td><td>99.7</td><td>45</td><td>5294.66</td><td>5294.66</td><td>0</td><td>1629.27</td></tr><tr><td>c100_05</td><td>yes</td><td>18849</td><td>0</td><td>56.7</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>57.6</td></tr><tr><td>c100_05</td><td>no</td><td>18849</td><td>0</td><td>57.66</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>58.43</td></tr><tr><td>c100_06</td><td>yes</td><td>18844</td><td>0</td><td>80.37</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>81.23</td></tr><tr><td>c100_06</td><td>no</td><td>18844</td><td>0</td><td>78.6</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>79.32</td></tr><tr><td>c100_07</td><td>yes</td><td>18875</td><td>0</td><td>65.13</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>66.0</td></tr><tr><td>c100_07</td><td>no</td><td>18875</td><td>0</td><td>66.53</td><td>1</td><td>5298.76</td><td>5298.76</td><td>0</td><td>67.33</td></tr><tr><td>c100_08</td><td>yes</td><td>18845</td><td>0</td><td>107.34</td><td>1</td><td>5295.36</td><td>5295.36</td><td>0</td><td>108.15</td></tr><tr><td>c100_08</td><td>no</td><td>18845</td><td>0</td><td>114.34</td><td>1</td><td>5295.36</td><td>5295.36</td><td>0</td><td>115.17</td></tr><tr><td>c100_09</td><td>yes</td><td>19018</td><td>0</td><td>218.49</td><td>1</td><td>5295.16</td><td>5295.16</td><td>0</td><td>219.57</td></tr><tr><td>c100_09</td><td>no</td><td>19018</td><td>0</td><td>226.06</td><td>1</td><td>5295.16</td><td>5295.16</td><td>0</td><td>227.08</td></tr></tbody></table>
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<table><caption>Table 18: Detailed experiments on the impact of the restricted master heuristics</caption><thead><tr><th>Instance</th><th>RMH</th><th>Root</th><th>Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>Cardiff_40_01 yes</td><td>0.3</td><td>214.13</td><td>3</td><td>2931.88</td><td>3</td><td>2931.88</td><td>2931.88</td><td>0.0</td><td>306.84</td></tr><tr><td>Cardiff_40_01 no</td><td>0.5</td><td>234.17</td><td>5</td><td>2931.88</td><td>5</td><td>2931.88</td><td>2931.88</td><td>0.0</td><td>447.26</td></tr><tr><td>Cardiff_40_02 yes</td><td>20.1</td><td>92.8</td><td>37</td><td>3044.72</td><td>37</td><td>3044.72</td><td>3217.42</td><td>5.67</td><td>10800.0</td></tr><tr><td>Cardiff_40_02 no</td><td>21.1</td><td>99.25</td><td>77</td><td>2986.6</td><td>77</td><td>2986.6</td><td>3242.98</td><td>8.58</td><td>10800.0</td></tr><tr><td>Cardiff_40_03 yes</td><td>2.7</td><td>168.23</td><td>3</td><td>2682.5</td><td>3</td><td>2682.5</td><td>2682.5</td><td>0.0</td><td>351.02</td></tr><tr><td>Cardiff_40_03 no</td><td>14.6</td><td>114.83</td><td>21</td><td>2682.5</td><td>21</td><td>2682.5</td><td>2682.5</td><td>0.0</td><td>1287.88</td></tr><tr><td>Cardiff_40_04 yes</td><td>inf</td><td>401.23</td><td>9</td><td>4292.31</td><td>9</td><td>4292.31</td><td>-</td><td>-</td><td>10800.0</td></tr><tr><td>Cardiff_40_04 no</td><td>9.2</td><td>453.32</td><td>57</td><td>4297.88</td><td>57</td><td>4297.88</td><td>4620.65</td><td>7.51</td><td>10800.0</td></tr><tr><td>Cardiff_40_05 yes</td><td>1.7</td><td>329.68</td><td>11</td><td>3770.9</td><td>11</td><td>3770.9</td><td>3770.9</td><td>0.0</td><td>2141.71</td></tr><tr><td>Cardiff_40_05 no</td><td>1.8</td><td>378.99</td><td>15</td><td>3770.9</td><td>15</td><td>3770.9</td><td>3770.9</td><td>0.0</td><td>1415.53</td></tr><tr><td>Cardiff_40_06 yes</td><td>12.5</td><td>203.15</td><td>19</td><td>2909.0</td><td>19</td><td>2909.0</td><td>2909.0</td><td>0.0</td><td>1633.04</td></tr><tr><td>Cardiff_40_06 no</td><td>14.6</td><td>214.06</td><td>17</td><td>2909.0</td><td>17</td><td>2909.0</td><td>2909.0</td><td>0.0</td><td>1067.8</td></tr><tr><td>Cardiff_40_07 yes</td><td>inf</td><td>674.04</td><td>3</td><td>2093.42</td><td>3</td><td>2093.42</td><td>-</td><td>-</td><td>10800.0</td></tr><tr><td>Cardiff_40_07 no</td><td>21.9</td><td>741.64</td><td>53</td><td>2297.3</td><td>53</td><td>2297.3</td><td>2535.67</td><td>10.38</td><td>10800.0</td></tr><tr><td>Cardiff_40_08 yes</td><td>0.6</td><td>191.29</td><td>3</td><td>3834.02</td><td>3</td><td>3834.02</td><td>3834.02</td><td>0.0</td><td>358.6</td></tr><tr><td>Cardiff_40_08 no</td><td>0.5</td><td>247.14</td><td>5</td><td>3834.02</td><td>5</td><td>3834.02</td><td>3834.02</td><td>0.0</td><td>509.05</td></tr><tr><td>Cardiff_40_09 yes</td><td>35.1</td><td>381.09</td><td>11</td><td>3580.1</td><td>11</td><td>3580.1</td><td>4484.18</td><td>25.25</td><td>10800.0</td></tr><tr><td>Cardiff_40_09 no</td><td>17.5</td><td>338.15</td><td>73</td><td>3580.5</td><td>73</td><td>3580.5</td><td>3707.23</td><td>3.54</td><td>10800.0</td></tr><tr><td>Cardiff_40_10 yes</td><td>1.3</td><td>171.29</td><td>3</td><td>2692.08</td><td>3</td><td>2692.08</td><td>2692.08</td><td>0.0</td><td>573.32</td></tr><tr><td>Cardiff_40_10 no</td><td>1.9</td><td>184.87</td><td>5</td><td>2692.08</td><td>5</td><td>2692.08</td><td>2692.08</td><td>0.0</td><td>441.81</td></tr><tr><td>Cardiff_40_11 yes</td><td>0.0</td><td>29.34</td><td>1</td><td>unfeasible</td><td>1</td><td>unfeasible</td><td>0.0</td><td>0.0</td><td>30.12</td></tr><tr><td>Cardiff_40_11 no</td><td>0.0</td><td>32.62</td><td>1</td><td>unfeasible</td><td>1</td><td>unfeasible</td><td>0.0</td><td>0.0</td><td>33.43</td></tr><tr><td>Cardiff_40_12 yes</td><td>0.7</td><td>200.69</td><td>3</td><td>2642.87</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.0</td><td>276.22</td></tr><tr><td>Cardiff_40_12 no</td><td>0.8</td><td>200.06</td><td>3</td><td>2642.87</td><td>3</td><td>2642.87</td><td>2642.87</td><td>0.0</td><td>307.18</td></tr><tr><td>Cardiff_40_13 yes</td><td>21.9</td><td>196.03</td><td>23</td><td>2723.1</td><td>23</td><td>2723.1</td><td>2913.13</td><td>6.98</td><td>10800.0</td></tr><tr><td>Cardiff_40_13 no</td><td>inf</td><td>211.4</td><td>81</td><td>2722.68</td><td>81</td><td>2722.68</td><td>-</td><td>-</td><td>10800.0</td></tr><tr><td>Cardiff_40_14 yes</td><td>inf</td><td>1716.28</td><td>1</td><td>2236.37</td><td>1</td><td>2236.37</td><td>-</td><td>-</td><td>10800.0</td></tr><tr><td>Cardiff_40_14 no</td><td>inf</td><td>1914.77</td><td>13</td><td>2435.77</td><td>13</td><td>2435.77</td><td>-</td><td>-</td><td>10800.0</td></tr><tr><td>Cardiff_40_15 yes</td><td>20.3</td><td>181.95</td><td>39</td><td>2606.74</td><td>39</td><td>2606.74</td><td>2707.12</td><td>3.85</td><td>10800.0</td></tr><tr><td>Cardiff_40_15 no</td><td>22.9</td><td>157.89</td><td>53</td><td>2707.12</td><td>53</td><td>2707.12</td><td>2707.12</td><td>0.0</td><td>3757.0</td></tr><tr><td>Cardiff_40_16 yes</td><td>inf</td><td>785.41</td><td>5</td><td>2927.97</td><td>5</td><td>2927.97</td><td>-</td><td>-</td><td>10800.0</td></tr><tr><td>Cardiff_40_16 no</td><td>19.8</td><td>863.33</td><td>61</td><td>3188.12</td><td>61</td><td>3188.12</td><td>3372.57</td><td>5.79</td><td>10800.0</td></tr><tr><td>Cardiff_40_17 yes</td><td>3.2</td><td>278.48</td><td>23</td><td>2733.69</td><td>23</td><td>2733.69</td><td>2781.87</td><td>1.76</td><td>10800.0</td></tr><tr><td>Cardiff_40_17 no</td><td>2.1</td><td>291.8</td><td>57</td><td>2749.83</td><td>57</td><td>2749.83</td><td>2749.83</td><td>0.0</td><td>4976.0</td></tr><tr><td>Cardiff_40_18 yes</td><td>inf</td><td>224.52</td><td>21</td><td>2707.07</td><td>21</td><td>2707.07</td><td>-</td><td>-</td><td>10800.0</td></tr><tr><td>Cardiff_40_18 no</td><td>33.0</td><td>254.4</td><td>63</td><td>2731.72</td><td>63</td><td>2731.72</td><td>2932.45</td><td>7.35</td><td>10800.0</td></tr><tr><td>Cardiff_40_19 yes</td><td>1.9</td><td>198.71</td><td>3</td><td>2784.05</td><td>3</td><td>2784.05</td><td>2784.05</td><td>0.0</td><td>368.26</td></tr><tr><td>Cardiff_40_19 no</td><td>1.7</td><td>227.32</td><td>17</td><td>2784.05</td><td>17</td><td>2784.05</td><td>2784.05</td><td>0.0</td><td>989.55</td></tr><tr><td>Cardiff_40_20 yes</td><td>inf</td><td>214.13</td><td>23</td><td>2649.34</td><td>23</td><td>2649.34</td><td>-</td><td>-</td><td>10800.0</td></tr><tr><td>Cardiff_40_20 no</td><td>32.1</td><td>237.58</td><td>103</td><td>2617.56</td><td>103</td><td>2617.56</td><td>3203.98</td><td>22.4</td><td>10800.0</td></tr></tbody></table>

Continued on next page
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Yunqiang Yin, Ling Qing, Dujuan Wang, T. C. E. Cheng, and Joshua Ignatius. Exact solution method for vehicle-and-drone cooperative delivery routing of blood products. Computers & Operations Research, 164:106559, April 2024. ISSN 0305-0548. doi:10.1016/j.cor.2024.106559. URL https://www.sciencedirect.com/science/article/pii/S0305054824000315.

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<table><caption>Table 18: Detailed experiments on the impact of the restricted master heuristics</caption><thead><tr><th>Instance</th><th>RMH</th><th>Root</th><th>Gap</th><th>Root Time</th><th>Nodes</th><th>DB</th><th>PB</th><th>Gap</th><th>Time (s)</th></tr></thead><tbody><tr><td>c100_01</td><td>yes</td><td>0.3</td><td>88.03</td><td>5</td><td>5298.76</td><td>5298.76</td><td>0.0</td><td>643.78</td><td></td></tr><tr><td>c100_01</td><td>no</td><td>0.3</td><td>70.29</td><td>33</td><td>5298.76</td><td>5298.76</td><td>0.0</td><td>3785.0</td><td></td></tr><tr><td>c100_02</td><td>yes</td><td>0.4</td><td>86.38</td><td>7</td><td>5298.36</td><td>5298.36</td><td>0.0</td><td>751.62</td><td></td></tr><tr><td>c100_02</td><td>no</td><td>0.3</td><td>80.16</td><td>63</td><td>5298.36</td><td>5298.36</td><td>0.0</td><td>2802.46</td><td></td></tr><tr><td>c100_03</td><td>yes</td><td>0.4</td><td>104.73</td><td>43</td><td>5296.46</td><td>5296.46</td><td>0.0</td><td>4008.0</td><td></td></tr><tr><td>c100_03</td><td>no</td><td>0.4</td><td>111.98</td><td>81</td><td>5296.46</td><td>5296.46</td><td>0.0</td><td>3877.0</td><td></td></tr><tr><td>c100_04</td><td>yes</td><td>1.4</td><td>141.28</td><td>121</td><td>5274.95</td><td>5339.06</td><td>1.22</td><td>10800.0</td><td></td></tr><tr><td>c100_04</td><td>no</td><td>inf</td><td>151.2</td><td>121</td><td>5274.14</td><td>-</td><td>-</td><td>10800.0</td><td></td></tr><tr><td>c100_05</td><td>yes</td><td>0.3</td><td>90.38</td><td>19</td><td>5298.76</td><td>5298.76</td><td>0.0</td><td>3249.86</td><td></td></tr><tr><td>c100_05</td><td>no</td><td>0.3</td><td>93.02</td><td>61</td><td>5298.76</td><td>5298.76</td><td>0.0</td><td>5342.0</td><td></td></tr><tr><td>c100_06</td><td>yes</td><td>0.4</td><td>90.42</td><td>9</td><td>5298.76</td><td>5298.76</td><td>0.0</td><td>1144.6</td><td></td></tr><tr><td>c100_06</td><td>no</td><td>0.3</td><td>89.64</td><td>23</td><td>5298.76</td><td>5298.76</td><td>0.0</td><td>1840.12</td><td></td></tr><tr><td>c100_07</td><td>yes</td><td>0.3</td><td>80.05</td><td>5</td><td>5298.76</td><td>5298.76</td><td>0.0</td><td>769.38</td><td></td></tr><tr><td>c100_07</td><td>no</td><td>0.3</td><td>87.01</td><td>37</td><td>5298.76</td><td>5298.76</td><td>0.0</td><td>3516.1</td><td></td></tr><tr><td>c100_08</td><td>yes</td><td>0.4</td><td>93.02</td><td>15</td><td>5295.36</td><td>5295.36</td><td>0.0</td><td>1712.0</td><td></td></tr><tr><td>c100_08</td><td>no</td><td>0.4</td><td>113.6</td><td>25</td><td>5295.36</td><td>5295.36</td><td>0.0</td><td>1823.05</td><td></td></tr><tr><td>c100_09</td><td>yes</td><td>0.4</td><td>125.41</td><td>49</td><td>5295.16</td><td>5295.16</td><td>0.0</td><td>5127.0</td><td></td></tr><tr><td>c100_09</td><td>no</td><td>0.6</td><td>126.27</td><td>69</td><td>5295.16</td><td>5295.16</td><td>0.0</td><td>3874.0</td><td></td></tr><tr><td>120_C1_2_01</td><td>yes</td><td>0.4</td><td>45.31</td><td>7</td><td>9090.0</td><td>9090.0</td><td>0.0</td><td>251.78</td><td></td></tr><tr><td>120_C1_2_01</td><td>no</td><td>0.4</td><td>43.36</td><td>7</td><td>9090.0</td><td>9090.0</td><td>0.0</td><td>279.21</td><td></td></tr><tr><td>120_C1_2_02</td><td>yes</td><td>0.3</td><td>87.07</td><td>29</td><td>8920.5</td><td>8920.5</td><td>0.0</td><td>1827.92</td><td></td></tr><tr><td>120_C1_2_02</td><td>no</td><td>0.3</td><td>93.16</td><td>83</td><td>8920.5</td><td>8920.5</td><td>0.0</td><td>2895.06</td><td></td></tr><tr><td>120_C1_2_03</td><td>yes</td><td>inf</td><td>185.25</td><td>143</td><td>8815.06</td><td>-</td><td>-</td><td>10800.0</td><td></td></tr><tr><td>120_C1_2_03</td><td>no</td><td>0.7</td><td>158.94</td><td>247</td><td>8812.02</td><td>8868.12</td><td>0.64</td><td>10800.0</td><td></td></tr><tr><td>120_C1_2_04</td><td>yes</td><td>inf</td><td>163.47</td><td>153</td><td>8728.17</td><td>-</td><td>-</td><td>10800.0</td><td></td></tr><tr><td>120_C1_2_04</td><td>no</td><td>inf</td><td>155.55</td><td>229</td><td>8718.23</td><td>-</td><td>-</td><td>10800.0</td><td></td></tr><tr><td>120_C1_2_05</td><td>yes</td><td>0.5</td><td>58.24</td><td>19</td><td>8986.2</td><td>8986.2</td><td>0.0</td><td>1454.68</td><td></td></tr><tr><td>120_C1_2_05</td><td>no</td><td>0.5</td><td>65.29</td><td>21</td><td>8986.2</td><td>8986.2</td><td>0.0</td><td>1552.51</td><td></td></tr><tr><td>120_C1_2_06</td><td>yes</td><td>0.9</td><td>91.46</td><td>17</td><td>8988.4</td><td>8988.4</td><td>0.0</td><td>1899.7</td><td></td></tr><tr><td>120_C1_2_06</td><td>no</td><td>0.9</td><td>97.45</td><td>99</td><td>8988.4</td><td>8988.4</td><td>0.0</td><td>4892.0</td><td></td></tr><tr><td>120_C1_2_07</td><td>yes</td><td>0.5</td><td>67.44</td><td>29</td><td>8958.6</td><td>8958.6</td><td>0.0</td><td>2438.2</td><td></td></tr><tr><td>120_C1_2_07</td><td>no</td><td>0.4</td><td>84.31</td><td>29</td><td>8958.6</td><td>8958.6</td><td>0.0</td><td>1845.62</td><td></td></tr><tr><td>120_C1_2_08</td><td>yes</td><td>0.3</td><td>166.8</td><td>9</td><td>8817.9</td><td>8817.9</td><td>0.0</td><td>642.36</td><td></td></tr><tr><td>120_C1_2_08</td><td>no</td><td>0.3</td><td>153.67</td><td>135</td><td>8817.9</td><td>8817.9</td><td>0.0</td><td>6501.0</td><td></td></tr><tr><td>120_C1_2_09</td><td>yes</td><td>0.3</td><td>171.82</td><td>51</td><td>8790.62</td><td>8790.62</td><td>0.0</td><td>3394.73</td><td></td></tr><tr><td>120_C1_2_09</td><td>no</td><td>inf</td><td>164.03</td><td>231</td><td>8771.15</td><td>-</td><td>-</td><td>10800.0</td><td></td></tr><tr><td>120_C1_2_10</td><td>yes</td><td>inf</td><td>193.9</td><td>131</td><td>8741.16</td><td>-</td><td>-</td><td>10800.0</td><td></td></tr><tr><td>120_C1_2_10</td><td>no</td><td>1.0</td><td>191.08</td><td>243</td><td>8729.87</td><td>8808.82</td><td>0.9</td><td>10800.0</td><td></td></tr></tbody></table>
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