# A Multi-Strategy ALNS for the VRP with Flexible Time Windows and Delivery Locations
## 5 Results and Discussion
### Evaluation of Question Features
#### 5.3.2 The Effect of Delivery Options
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Init.**} & \multicolumn{2}{c}{**VRP-CS**} & \multicolumn{4}{c}{**VRPSD**} \\ \cline{2-9}  & \(\mathbf{C_{total}}\) & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{total}}\) & \(\mathbf{Gap_{total}}\) & \(\mathbf{C_{1}}\) & \(\mathbf{Gap_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{Gap_{2}}\) \\ \hline C16L50 & 3070.05 & 3065.67 & 4.95 & 3045.33 & 0.81\% & 2959.50 & 3.46\% & 1.71 & **16.23\%** \\ C16L52 & 2467.45 & 2486.33 & 5.28 & 3385.26 & \(\mathbf{-37.20\%}\) & 3273.50 & \(\mathbf{-31.66\%}\) & 1.25 & **19.88\%** \\ C16L57 & 3326.24 & 3282.00 & 3.62 & 3643.13 & \(\mathbf{-9.53\%}\) & 3514.83 & \(\mathbf{-7.09\%}\) & 0.42 & **17.19\%** \\ C16L62 & 2473.99 & 2491.17 & 5.19 & 2829.65 & \(\mathbf{-14.38\%}\) & 2757.50 & \(\mathbf{-10.69\%}\) & 1.39 & **18.81\%** \\ C21L63 & 4265.30 & 4258.17 & 7.31 & 5082.68 & \(\mathbf{-19.16\%}\) & 4965.33 & \(\mathbf{-16.61\%}\) & 4.14 & \(\mathbf{11.63\%}\) \\ C21L66 & 3554.53 & 3570.17 & 6.28 & 4573.97 & \(\mathbf{-28.68\%}\) & 4442.17 & \(\mathbf{-24.42\%}\) & 1.41 & \(\mathbf{18.53\%}\) \\ C21L68 & 3175.22 & 3198.00 & 6.31 & 3362.40 & \(\mathbf{-5.89\%}\) & 3308.50 & \(\mathbf{-3.46\%}\) & 3.47 & \(\mathbf{10.77\%}\) \\ C21L76 & 3156.54 & 3161.83 & 5.76 & 3688.18 & \(\mathbf{-16.84\%}\) & 3591.33 & \(\mathbf{-13.58\%}\) & 2.66 & \(\mathbf{12.05\%}\) \\ C21L80 & 3827.82 & 3842.67 & 6.91 & 4349.50 & \(\mathbf{-13.63\%}\) & 4301.17 & \(\mathbf{-11.93\%}\) & 5.09 & **6.78\%** \\ C31L75 & 4719.97 & 4741.83 & 9.09 & 4755.24 & \(\mathbf{-0.75\%}\) & 4689.33 & 1.11\% & 5.21 & **9.94\%** \\ C31L98 & 5267.68 & 5290.50 & 9.14 & 5954.67 & \(\mathbf{-13.04\%}\) & 5882.67 & \(\mathbf{-11.19\%}\) & 6.74 & **6.14\%** \\ C31L103 & 4699.35 & 4632.50 & 4.49 & 4932.78 & \(\mathbf{-4.97\%}\) & 4784.33 & \(\mathbf{-3.28\%}\) & 2.25 & 6.51\% \\ C31L107 & 3932.55 & 4000.33 & 10.72 & 4656.88 & \(\mathbf{-18.42\%}\) & 4561.00 & \(\mathbf{-14.02\%}\) & 4.71 & **14.77\%** \\ C31L13 & 5292.73 & 5269.00 & 7.65 & 5408.30 & \(\mathbf{-2.18\%}\) & 5256.67 & 0.23\% & 2.09 & **14.77\%** \\ C31L118 & 4968.49 & 5012.67 & 10.38 & 5957.43 & \(\mathbf{-19.90\%}\) & 5798.50 & \(\mathbf{-15.68\%}\) & 2.89 & **18.55\%** \\ C31L124 & 4821.78 & 4862.50 & 10.20 & 4941.24 & \(\mathbf{-2.48\%}\) & 4874.67 & \(\mathbf{-0.25\%}\) & 6.67 & **8.79\%** \\ C31L130 & 5460.13 & 5479.00 & 11.11 & 6422.31 & \(\mathbf{-17.62\%}\) & 6352.17 & \(\mathbf{-15.94\%}\) & 8.66 & **5.96\%** \\ C61L208 & 8197.94 & 8301.00 & 18.82 & 9401.59 & \(\mathbf{-14.68\%}\) & 9244.17 & \(\mathbf{-11.36\%}\) & 11.30 & **9.55\%** \\ C61L213 & 7734.12 & 7880.67 & 20.50 & 9916.88 & \(\mathbf{-28.22\%}\) & 9790.00 & \(\mathbf{-24.23\%}\) & 12.82 & **9.53\%** \\ C61L225 & 9819.67 & 9804.67 & 15.08 & 11,302.84 & \(\mathbf{-15.10\%}\) & 10,965.50 & \(\mathbf{-11.84\%}\) & 3.30 & \(\mathbf{15.69\%}\) \\ C61L229 & 9499.02 & 9528.17 & 16.79 & 10,614.42 & \(\mathbf{-11.74\%}\) & 10,373.83 & \(\mathbf{-8.88\%}\) & 7.80 & **11.70\%** \\ C61L235 & 11,069.1 & 11,132.67 & 20.68 & 12,813.19 & \(\mathbf{-15.76\%}\) & 12,594.17 & \(\mathbf{-13.13\%}\) & 10.72 & \(\mathbf{12.35\%}\) \\ C61L238 & 10,194.2 & 10,194.50 & 16.35 & 11,987.35 & \(\mathbf{-17.59\%}\) & 11,771.17 & \(\mathbf{-15.47\%}\) & 10.02 & \(\mathbf{8.28\%}\) \\ _Average_ & 5434.52 & 1091.18 & 2.02 & 6218.49 & \(\mathbf{-14.22\%}\) & 6089.22 & \(\mathbf{-11.30\%}\) & 5.07 & \(\mathbf{12.37\%}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of using optional delivery locations and single delivery locations.