## 4 Discussion
#### 4.2.1 Implementation of the Tabu Search Algorithm  
To achieve optimal results, it is necessary to reset the parameters of this algorithm for the VAOCMP model. The most appropriate parameters for this algorithm are identified by sensitivity analysis as follows: 25 Tabu tenures, 70 generation, and 90 neighborhoods. Allocation results for 10 existing fire  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Number of Fire Stations**} & **Solving Time Based on Tabu** & **Solving Time Based on** \\  & **Search** & **Simulated Annealing** \\ \hline
26 & 632.315 & 749.219 \\
27 & 651.103 & 768.320 \\
28 & 695.514 & 800.107 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Comparison of the average problem-solving time in seconds.  
\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
26 & 0.0691 & 0.0745 \\
27 & 0.0913 & 0.1144 \\
28 & 0.1327 & 0.1599 \\ \hline \hline \end{tabular}
\end{table}
Table 10: 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**} & **Average of Optimal Values** & **Average of Optimal Values** \\  & **Based on Tabu Search** & **Based on Simulated Annealing** \\ \hline
26 & 391,081,355.14 & 400,233,479.26 \\
27 & 387,451,662.22 & 393,846,782.62 \\
28 & 384,991,646.11 & 389,329,631.14 \\ \hline \hline \end{tabular}
\end{table}
Table 10: 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
26 & 86 & 81 \\
27 & 81 & 78 \\
28 & 79 & 75 \\ \hline \hline \end{tabular}
\end{table}
Table 11: 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
26 & 84.332 & 82.540 \\
27 & 95.212 & 94.571 \\
28 & 99.720 & 98.885 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Comparison of the average problem-solving time in seconds.  
stations are shown in Figure 9 (unallocated demands have not been shown in the figure). The allocations for each station and unallocated demands are also shown in Table 14.  
To minimize the arrival time for fire engines to the location of an incident using the VAOCMP model with the Tabu Search algorithm, the value of the objective function falls, because, as expected, when a demand cannot be allocated to a station according to the capacity criterion, it must be allocated to the next adjacent station that has a distance of less than 5 min. However, in many cases, the time interval to the next station is more than 5 min. As a result, the demand cannot be allocated to any station. Therefore, the value of the objective function has fallen in this case compared to the VAOMP model. In this method, since each array of the OD Cost Matrix is ranked from the minimum to maximum value, a closer demand is assigned to each station, so that each station cannot exceed its capacity. At the same time, the surplus capacity of each station can be transferred to other stations.