## 4 Discussion
#### 4.1.4 Relocation-Reallocation with the VAOMP Model to Service All Demands Using Both Algorithms  
Considering that the number of stations to minimize response time yields 52,840 demands with no service, several new stations will be selected using relocation and reallocation. This means that existing stations stay constant, and some new stations are selected from among the candidate stations produced by location analysis. The number of stations in the area is 10. The purpose of relocation-reallocation is \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**No. Stations** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline Number of allocations & 25,760 & 18,200 & 35,840 & 33,240 & 21,960 & 17,520 & 51,240 & 17,760 & 9880 & 52,360 \\ Runtime (sec) & & & & & & 466.285 & & & & \\ Optimal value & & & & & 143,478,895.2 & & & & & \\ Number of demands & & & & & & 336,600 & & & & \\ Number of & & & & & & 52,840 & & & & \\ unallocated demands & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The number of allocations for each station, runtime, and the optimal value of the function using the Simulated Annealing algorithm. Figure 5: The allocation of each station using the Simulated Annealing algorithm. to select 11 stations (10 existing stations, and 1 new station from 35 candidate stations), 12 stations, and then 13 stations. Figure 6 shows the location of the candidate stations. Since, with metaheuristic algorithms, each execution of the algorithm has a different solution from the others, it is necessary to use a repeatability test to evaluate the robustness of solutions. In this way, the results obtained from a certain number of successive performances with the same parameters are compared in terms of convergence. If the solutions obtained do not differ significantly, we can say that the algorithm is robust in solving the problems. To investigate the robustness of the methods developed and the average time of problem-solving for each, experiments were designed involving different numbers of fire stations, namely, 11, 12, and 13 stations, respectively. Each of these modes was solved 10 times with the two algorithms. Then, the normalized standard deviation of solutions obtained for the target function for both methods was calculated for each set of experiments. The accuracy obtained for the different modes has been shown in Table 3. Table 4 shows the average of the optimal values with 10 independent implementation of the model. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Number of Fire Stations**} & **Normalized Standard Deviation** & **Normalized Standard Deviation** \\  & **Solutions of Obtained Based on** & **of Solutions Obtained Based on** \\  & **Tabu Search** & **Simulated Annealing** \\ \hline
11 & 0.0277 & 0.0288 \\
12 & 0.0498 & 0.0618 \\
13 & 0.0903 & 0.1041 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The normalized standard deviation of solutions obtained using the VAOMP model with both algorithms. Figure 6: Location of candidate stations. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Number of Fire Stations**} & **Average of Optimal Values** & **Average of Optimal Values** \\  & **Based on Tabu Search** & **Based on Simulated Annealing** \\ \hline
11 & 110,336,112.9 & 110,905,133.8 \\
12 & 106,997,363.5 & 107,456,433.3 \\
13 & 104,312,426.7 & 104,614,621.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average of optimal values for 10 iterations of the model using both algorithms. As Table 4 shows, the increase in the number of stations generates complexity in the problem. As a result, the average value of the target functions when the model is implemented on 10 occasions independently has fallen, because, by increasing the number of stations, the demands can be allocated to their optimal stations.