# A Multi-Strategy ALNS for the VRP with Flexible Time Windows and Delivery Locations
## 5 Results and Discussion
### Evaluation of Question Features
#### 5.3.1 The Effect of Customer Satisfaction  
To investigate the impact of customer satisfaction on the solution, the MSALNS was run on all instances with and without customer satisfaction. In each case, MSALNS is run 10 times on the instance. The satisfaction and delivery cost of the solution are shown in Table 4 and Figure 8.  
Table 4 shows the comparison experiment considering customer satisfaction and not considering customer satisfaction. We call the case where customer satisfaction is considered the VRP-CS and the case where customer satisfaction is not considered the VRPDO. The first column shows the instance we use; the second column shows the experimental \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Init.**} & \multicolumn{2}{c}{**VRP-CS**} & \multicolumn{2}{c}{**VRPDO**} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ \cline{2-7}  & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{1}}\) & \(\mathbf{GAP_{1}}\)(\%) & \(\mathbf{C_{2}}\) & \(\mathbf{GAP_{2}}\)(\%) \\ \hline C16L50 & 3065.67 & 4.95 & 2753.33 & **10.19\%** & 2.51 & **12.24\%** \\ C16L52 & 2486.33 & 5.28 & 2307.33 & **7.20\%** & 1.48 & **18.76\%** \\ C16L57 & 3282.00 & 3.62 & 2979.17 & **9.23\%** & 0.04 & **19.21\%** \\ C16L62 & 2491.17 & 5.19 & 2211.67 & **11.22\%** & 1.70 & **17.32\%** \\ C21L63 & 4258.17 & 7.31 & 4136.00 & **2.87\%** & 2.66 & **17.05\%** \\ C21L66 & 3570.17 & 6.28 & 3331.50 & **6.69\%** & 4.28 & **7.60\%** \\ C21L68 & 3198.00 & 6.31 & 2844.33 & **11.06\%** & 0.67 & **21.43\%** \\ C21L76 & 3161.83 & 5.76 & 3004.67 & **4.97\%** & 2.51 & **12.61\%** \\ C21L80 & 3842.67 & 6.91 & 3832.33 & **0.27\%** & 3.80 & **11.58\%** \\ C31L75 & 4741.83 & 9.09 & 4449.33 & **6.17\%** & 2.47 & **16.94\%** \\ C31L98 & 5290.50 & 9.14 & 5128.45 & **3.06\%** & 5.20 & **10.08\%** \\ C31L103 & 4632.50 & 4.49 & 4458.33 & **3.76\%** & -0.08 & **13.26\%** \\ C31L107 & 4000.33 & 10.72 & 3558.00 & **11.06\%** & 4.24 & **15.91\%** \\ C31L113 & 5269.00 & 7.65 & 5156.83 & **2.13\%** & 3.11 & **12.06\%** \\ C31L118 & 5012.67 & 10.38 & 4440.67 & **11.41\%** & 3.23 & **17.70\%** \\ C31L124 & 4862.50 & 10.20 & 4579.00 & **5.83\%** & 4.01 & **15.41\%** \\ C31L130 & 5479.00 & 11.11 & 5287.67 & **3.49\%** & 4.38 & **16.37\%** \\ C61L208 & 8301.00 & 18.82 & 7847.05 & **5.47\%** & 5.67 & **16.68\%** \\ C61L213 & 7880.67 & 20.50 & 7654.45 & **2.87\%** & 10.47 & **12.45\%** \\ C61L225 & 9804.67 & 15.08 & 9723.75 & **0.83\%** & 0.79 & **19.04\%** \\ C61L229 & 9528.17 & 16.79 & 9241.65 & **3.01\%** & 5.05 & **15.29\%** \\ C61L235 & 11,132.67 & 20.68 & 10,912.80 & **1.97\%** & 7.30 & **16.59\%** \\ C61L238 & 10,194.50 & 16.35 & 9604.65 & **5.79\%** & 3.60 & **16.70\%** \\ Average & 5455.91 & 10.11 & 5193.17 & **5.68\%** & 3.43 & **15.32\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of scenarios with and without customer satisfaction consideration. Figure 8: Results of different sub-objectives influenced by customer satisfaction. results in the VRP-CS case; \(C_{1}\) represents the corresponding delivery cost; and \(C_{2}\) represents the corresponding customer satisfaction. The third column shows the corresponding results of VRPDO and the corresponding parameter gap. We use \(Gap_{1}(\%)\) and \(Gap_{2}(\%)\) to represent the corresponding value gap, and the calculation formula for \(Gap\) is as follows:  
\[Gap=(C_{cs}-C_{\overline{cs}})/C_{cs}\times 100\% \tag{19}\]  
where \(C_{cs}\) indicates the parameters that take customer satisfaction into account, and \(C_{\overline{cs}}\) indicates the parameters that do not take customer satisfaction into account. For distribution cost, \(C_{cs}\) and \(C_{\overline{cs}}\) are both calculated using the corresponding \(C_{1}\). For customer satisfaction, we use \(C_{worst}\) to represent the situation where all customers are completely dissatisfied. \(C_{cs}\) and \(C_{\overline{cs}}\) are both calculated using the corresponding \(C_{2}-C_{worst}\).