## 3 Methods
### Solving 2 EVRP-DF with Simulated Annealing
#### 3.2.4 SA Solution Representation  
The solution of 2 EVRP-DF is represented by a series of numbers consisting of the drop box facilities denoted by the set \(\{1,2,...,\,|\,M|\}\); \(-1\) dummy zeros represent vehicles returning to the depot to empty capacity, set \(\{|\,M|\,,\,...,\,|\,M|+|\,N|\}\) represents the customer, and \(-2\) dummy zeros represent the customer assignment separator to the drop box facility. Figure 3 illustrates the solution representation for 2 EVRP-DF.  
The procedure for finding a solution based on this representation is as follows. First, two lists are created to be introduced into a representation solution, namely a list of drop box facilities and a list of customers. The list of drop box facilities will contain the order of facilities visited by vehicles from the depot. In addition, there is a dummy node with a value of \(-1\), which indicates that the vehicle returns to the depot to empty its vehicle capacity then goes to the next drop box facility. The second list is the customer list. This second list describes the assignment of customers to go to the specified drop box facility. In this list there are also dummy nodes with a value of \(-2\), which are the separators between customers assignments in the second echelon.  
Figure 2: Flowchart of the SA optimization process.  
Figure 3 illustrates the representation of the solution. Take examples of data provided for solution representation in Tables 1 and 2. In the examples illustrated, each drop box facility has a capacity of 15, demand from customers is 5, and the capacity of vehicles carrying goods is 15. As previously mentioned, the list of solutions {2,5,1,\(-\)1,4,11,\(-\)2,6,\(-\)2,7,\(-\)2,8,9,10} is divided into two, namely the list of drop box facilities and the list of customers. The list of drop box facilities will contain {2,5,1,\(-\)1,4}. On the other hand, the customer list is {11,\(-\)2,6,\(-\)2,7,\(-\)2,8,9,10}. Based on an example list of drop box facilities and customers, the following solutions can be explained. The first facility visited by the vehicle is the drop box facility 2. Then the vehicle goes to the drop box 5 facility, and then to the drop box facility 1. Then, the vehicle returns to the depot to empty the vehicle and then goes to drop box 4 as the last route. Furthermore, based on the customer list, demand from customer 11 will be handled by the drop box 2 facility, demand from customer 6 will be handled by the drop box 5 facility, demand from customer 7 is handled by the drop box 1 facility, and demands from customers 8, 9, and 10 are handled by the drop box 4 facility. The drop box 3 facility is not visited by vehicles, because all customers have been served.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Node Facilities** & & & & \\
**\& Customers** & & & \\ \hline
0 & \(-\)6.2701 & 106.8376 & - & - \\
1 & \(-\)6.25631 & 106.8126 & 15 & - \\
2 & \(-\)6.25693 & 106.8518 & 15 & - \\
3 & \(-\)6.25465 & 106.8138 & 15 & - \\
4 & \(-\)6.28424 & 106.8118 & 15 & - \\
5 & \(-\)6.25153 & 106.8247 & 15 & - \\
6 & \(-\)6.24495 & 106.8287 & - & 5 \\
7 & \(-\)6.26012 & 106.8155 & - & 5 \\
8 & \(-\)6.2746 & 106.8212 & - & 5 \\
9 & \(-\)6.28718 & 106.8012 & - & 5 \\
10 & \(-\)6.27253 & 106.8207 & - & 5 \\
11 & \(-\)6.24853 & 106.8441 & - & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Example of location, capacity, and demand for 2 EVRP-DF.  
Figure 3: An example of solution representation for 2 EVRP-DF.