## 6 Experimental Tests
### Model Validation and Comparison Results  
To validate the developed model, two approaches are deployed. In the first approach, the solutions of hybrid covering location problem will be compared with the results of the conventional separate models for some of the test problems from Table 3. In order to do this, we compare the results of HCLP with the problem in which the location of the facilities would be selected by SCLP separately using the second term of the objective function (6) (minimizing the cost of facility location) subject to constraints (7), (8), (11), and (14). The solutions of the located facilities are used and fixed in the second problem to  
Figure 5: A schematic illustration of three-region and four-region test problems. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline _i=j_ & \begin{tabular}{c} **Demand** \\ **Scenario** \\ \end{tabular}  & \begin{tabular}{c} **\(t\)** \\ \end{tabular}  & \begin{tabular}{c} **\(\tau\)** \\ \end{tabular}  & \begin{tabular}{c} **\(l\)** \\ \end{tabular}  & \begin{tabular}{c} **\(k\)** \\ \end{tabular}  & \begin{tabular}{c} **\(q_{l}\)** \\ \end{tabular}  & \begin{tabular}{c} **\(\sigma_{l}\)** \\ \end{tabular}  & \begin{tabular}{c} **\(h_{i}\)** \\ \end{tabular}  & \begin{tabular}{c} **\(f_{i}\)** \\ \end{tabular}  & \begin{tabular}{c} **Obj** \\ \end{tabular}  & \ \begin{tabular}{c} **\(\text{\bf Coverage \%}\)** \\ \end{tabular}  & \begin{tabular}{c} **Time** \\ \end{tabular}  \\ \hline \multirow{2}{*}{50} & Low & 3 & 2 & 2 & 2 & U (4,7) & U (150, 250) & U (500, 1000) & U (400, 800) & 3042.1 & 86\% & 4 \\  & High & 3 & 2 & 2 & U (4,7) & U (150, 250) & U (500, 1000) & U (400, 800) & 4359.5 & 65\% & 3 \\ \hline \multirow{2}{*}{100} & Low & 3 & 3 & 2 & 3 & U (7, 10) & U (200, 250) & U (1000, 1500) & U (400, 800) & 17,251.2 & 84\% & 213 \\  & High & 3 & 3 & 2 & 3 & U (7, 10) & U (200, 250) & U (1000, 1500) & U (400, 800) & 21,936.2 & 62\% & 249 \\ \hline \multirow{2}{*}{150} & Low & 3 & 3 & 3 & U (10, 15) & U (200, 250) & U (1500, 2000) & U (400, 800) & 41,056.5 & 86\% & 1013 \\  & High & 3 & 3 & 3 & 3 & U (10, 15) & U (200, 250) & U (1500, 2000) & U (400, 800) & 50,697.4 & 62\% & 1073 \\ \hline \multirow{2}{*}{200} & Low & 3 & 4 & 4 & 3 & U (15, 20) & U (300, 350) & U (1000, 1500) & U (400, 800) & 25,134.5 & 30\% & 1029 \\  & High & 3 & 4 & 3 & U (15, 20) & U (300, 350) & U (1000, 1500) & U (400, 800) & 26,74.6 & 22\% & 1072 \\ \hline \multirow{2}{*}{250} & Low & 3 & 4 & 4 & 3 & U (20, 30) & U (300, 350) & U (1000, 1500) & U (400, 800) & 24,545.6 & 21.9\% & 2169 \\  & High & 3 & 4 & 4 & 3 & U (20, 30) & U (300, 350) & U (1000, 1500) & U (400, 800) & 27,159.4 & 14.1\% & 1479 \\  & Low & 3 & 4 & 4 & 3 & U (20, 30) & U (300, 350) & U (1500, 2000) & U (400, 800) & 28,235 & 24\% & 1203 \\  & High & 3 & 4 & 4 & 3 & U (20, 30) & U (300, 350) & U (1000, 2000) & U (400, 800) & 31,482.5 & 16\% & 1355 \\  & Low & 3 & 4 & 4 & 3 & U (20, 30) & U (300, 350) & U (2000, 3000) & U (400, 800) & 28,235 & 24\% & 1169 assign the modules and allocate the demand points using the first term of the objective function (6) (maximizing the total covered demands) subject to constraints (9)-(13). The computational results are illustrated in Table 5, in which the columns under \"Hybrid\" and \"Con.\" include the results of the hybrid covering location problem and the described conventional procedure, respectively. Rows of \"Obj\" show the objective value of income minus fixed cost of facility locations for both methods. Furthermore, the last row of Table 5 shows the results for the total number of the assigned modules in all time periods out of the predefined amounts of available modules. For example, the value 58/66 means that the problem used 58 modules out of 66 available modules. The higher is this proportion, the problem used the available resources in a better way.