## 3 Materials and Methods
### Proposed Adaptive Large Neighborhood Search
#### 3.2.1 Initial Solution
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Customer** & \multirow{2}{*}{**Location**} & **Earliest Start** & **Latest Start** & \multirow{2}{*}{**Service**} & \multirow{2}{*}{**Request**} \\
**ID** & & **Time to** & & **Time to** & \\  & & **Service** & & **Service** & \\ \hline
75 & 39.747233–30.47377 & 424 & 487 & 120 & 38 \\
42B & 39.75233–30.48119 & 649 & 729 & 120 & 95 \\
32 & 39.752487–30.488123 & 1322 & 1378 & 180 & 76 \\
31 & 39.752941–30.483072 & 1372 & 1448 & 120 & 57 \\
115 & 39.752373–30.490197 & 1459 & 1531 & 180 & 76 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RC05 test problem. It is seen that the proposed hybrid ALNS algorithm gives optimal solutions for up to 40 customers. For problems with 40 customers, ALNS deviates from the optimal results by 3.22%, 3.33%, and 2.38%, respectively. In test problems with 60 customers, ALNS outperforms in reasonable times, achieving distance savings of up to 6.76%. As the problem size increases, the running time of CPLEX increases significantly, while ALNS finds solutions in as little as 70 s, even for problems with 60 customers. The success of the hybrid ALNS algorithm is proven. ### Trade-Offs Between Cost-Oriented and Customer-Oriented Solutions

An example route representation of the C20 problem from the obtained results is given in Figure 4.

In this study, customer-oriented and cost-oriented scenarios were created in terms of last-mile delivery. In the cost-oriented scenario, the logistics provider tries to minimize the cost by minimizing the total distance without taking into account when the customer wants the product. Classical ALNS solves the problems with operators known in the literature for the cost-oriented scenario. In the second scenario, the customer-satisfaction-oriented scenario, the aim is to optimize the route to provide customer time windows, taking into account customer satisfaction rather than cost. In this context, the number of vehicles is expected to increase. In Table 5, the results of our proposed hybrid ALNS for both scenarios are given, and the results are compared in terms of distance and tardiness. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instances**} & \multicolumn{4}{c}{**CPLEX**} & \multicolumn{4}{c}{**Proposed Hybrid ALNS**} \\ \cline{2-10}  & **\# of** & **Total** & **Total** & **Runtime** & **\# of** & **Total** & **Total** & **Runtime** & **\#\%** \\  & **Route** & **Distance (m)** & **Tardiness (s)** & **(s)** & **Route** & **Distance (m)** & **Tardiness (s)** & **(s)** & \\ \hline C05 & 2 & 5005.43 & 0 & 0.05 & 2 & 5005.43 & 0 & 0.198 & 0 \\ R05 & 3 & 5726.1 & 0 & 0.12 & 3 & 5726.1 & 0 & 0.201 & 0 \\ RC05 & 4 & 7093.17 & 0 & 0.05 & 4 & 7093.17 & 0 & 0.252 & 0 \\ C10 & 3 & 7530.96 & 0 & 0.23 & 3 & 7530.96 & 0 & 0.265 & 0 \\ R10 & 3 & 6823.93 & 0 & 0.06 & 3 & 6823.93 & 0 & 0.288 & 0 \\ RC10 & 3 & 7349.86 & 0 & 0.19 & 3 & 7349.86 & 0 & 0.272 & 0 \\ C20 & 6 & 12,736.51 & 0 & 0.44 & 6 & 12,736.51 & 0 & 3.123 & 0 \\ R20 & 6 & 14,023.35 & 0 & 4.51 & 6 & 14,023.35 & 0 & 3.035 & 0 \\ RC20 & 6 & 12,447.92 & 0 & 0.36 & 6 & 12,447.92 & 0 & 2.708 & 0 \\ C40 & 11 & 21,145.80 & 0 & 3.41 & 11 & 21,828.27 & 0 & 17.160 & 3.22\% \\ R40 & 11 & 26,316.81 & 0 & 75.09 & 11 & 27,193.94 & 0 & 16.397 & 3.33\% \\ RC40 & 11 & 23,372.91 & 0 & 19.31 & 10 & 23,931.24 & 0 & 17.838 & 2.38\% \\ C60 & 13 & 28,711.04\({}^{*}\) & 0 & 10,800 & 12 & 26,769.65 & 0 & 71.939 & \(-\)6.76\% \\ R60 & 12 & 29,396.37 \({}^{*}\) & 0 & 10,800 & 12 & 27,550.95 & 0 & 77.537 & \(-\)6.27\% \\ RC60 & 12 & 30,000.09\({}^{*}\) & 0 & 10,800 & 12 & 28,464.34 & 0 & 71.303 & \(-\)5.11\% \\ \hline \hline \end{tabular}

* It is not the optimal solution. In large-scale problems, the mathematical model could not provide solutions in a reasonable time. The results were obtained by CPLEX in a three-hour time limit.

\end{table} 
Table 4: CPLEX vs. ALNS results for min. total distance with time windows in small instances. Figure 4: Solution representation of the test problem C20.