## 4 Discussion
#### 4.2.4. _R_elocation-Reallocation with the VAVMP Model to Service All Demands Using Both Algorithms  
Similar to scenario 1, the insufficient number of stations to minimize arrival time and the 59,080 demands remaining without service in this scenario means that we select new stations by relocation and reallocation. The number of existing stations in the region is 10. The purpose of relocation and reallocation to select 11 stations (10 existing stations, and 1 new station from 35 candidate stations) and then 12 and 13 stations. Checking the solution strength yields similar results as in the first scenario. Table 16 shows the accuracy obtained for different states. Table 17 shows the average of optimal values for 10 iterations.  
As the table shows, the increase in the number of stations leads to an improvement in the average value of the target function for 10 independent implementations of the model. The value is reduced because, with an increase in the number of stations, the demands can be allocated to their optimal stations. In Table 18, the accuracy value for allocation obtained from different states is shown for the two methods. The average percentage of all demands allocated with the two algorithms is shown in Table 19.  
In Table 20, a comparison of the average problem-solving time, in seconds, has been shown for the two methods.  
\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 & 0.0351 & 0.0398 \\
12 & 0.0727 & 0.0841 \\
13 & 0.1489 & 0.1855 \\ \hline \hline \end{tabular}
\end{table}
Table 16: The normalized standard deviation of solutions obtained using the VAVCOMP model with both algorithms.  
\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 & 105,982,411.3 & 106,227,122.4 \\
12 & 102,113,345.1 & 102,446,657.6 \\
13 & 100,142,011.0 & 100,815,312.2 \\ \hline \hline \end{tabular}
\end{table}
Table 17: Average of optimal values for 10 iterations of the model using both algorithms.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Number of Fire Stations**} & **Accuracy of Allocation Based on** & **Accuracy of Allocation Based on** \\  & **Tabu Search** & **Simulated Annealing** \\ \hline
11 & 88 & 84 \\
12 & 83.5 & 80 \\
13 & 81 & 76 \\ \hline \hline \end{tabular}
\end{table}
Table 18: Comparison of the accuracy of allocation results.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Number of Fire Stations**} & **Average Percentage of All** & **Average Percentage of All** \\  & **Demand Allocated Based on** & **Demand Allocated Based on** \\  & **Tabu Search** & **Simulated Annealing** \\ \hline
11 & 84.483 & 83.222 \\
12 & 96.959 & 95.435 \\
13 & 99.999 & 99.510 \\ \hline \hline \end{tabular}
\end{table}
Table 19: The average percentage of all demand allocated using both algorithms.  
Regarding the parameters studied, it can be said that the Tabu Search method has greater stability and strength than the Simulated Annealing method in the two scenarios. The Simulated Annealing algorithm produces a poorer result in solving the Median problem, while the solving time for the Median problem is higher than with the Tabu algorithm.