## 6 Experimental Tests
### Model Validation and Comparison Results
The results of this conducted comparison show that using the integrated location decisions of SCLP and MCLP in a united model can improve the objective value, and this fact can be interpreted as the quality of provided services. It is important to note that the less value of facility cost in the conventional approach cannot be an advantage, as far as the total objective value is not better than hybrid approach, and these values are calculated and included in the table to have the evaluation of cost differences in both approaches. The results of Table 5 make it apparent that the hybrid approach has significant superiority to the conventional approach regarding objective value, coverage percentage, and exploiting the available modules. The same problems of the previous section in Tables 3 and 4 are solved for problems MCLP-MCLP, MCLP-SCLP, and SCLP-SCLP. It is important to note that we have first solved HCLP and obtained the total number of facilities that is determined to be opened and then used these numbers and run the experiments for the problems that need to have the number of facilities to be located, i.e., MCLP-MCLP and MCLP-SCLP. To be able to compare the models, two criteria were investigated. The first one that is in alignment with the optimization criteria as equity or fairness [58] that we interpret here as the percentage of coverage provided for demand points calculated as the total amount of covered demand divided by the total amount of demands, as explained earlier. The next investigated optimization criterion is the efficiency of models as the elapsed time to obtain the results. The columns under \"Z\" and \"Y\" contain the average number of facilities in all strategic periods and the average number of the assigned modules in all tactical periods, respectively. Tables 6 and 7 contain the results of these evaluations. To complete the tables and solve the problems of MCLP-MCLP and MCLP-SCLP, there was needed to have the number of facilities to be located. For this purpose, firstly, the problem HCLP was solved, and its solutions of the located facilities in the last strategic period (\(|T|\)) were used in MCLP-MCLP and MCLP-SCLP with two different values: one with the higher number (to provide even more facilities) and the other one with the optimal solution of HCLP. Solving problems for the values of \(p_{|T|}\) smaller than the values in Tables 6 and 7 would not result in better solutions. According to the results of the coverage percentage for HCLP, MCLP-MCLP, and MCLP-SCLP, HCLP could provide the highest coverage percentage almost for all test problems, with an optimum number of facilities. Only in three cases with the number of facilities more than the optimal number, the coverage percentage was better (one case of MCLP-MCLP and two cases of MCLP-SCLP). Notice that we excluded SCLP-SCLP from these comparisons, because we believe that \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**50 High**} & \multicolumn{2}{c}{**100 High**} & \multicolumn{2}{c}{**150 High**} & \multicolumn{2}{c}{**200 High**} \\ \cline{2-9}  & **Hybrid** & **Con.** & **Hybrid** & **Con.** & **Hybrid** & **Con.** & **Hybrid** & **Con.** \\ \hline Obj & **4359** & 1276 & **21,936** & 10,956 & **50,697** & 10,126 & **26,740** & 9689 \\ Facility cost & 5258 & 2470 & 5025 & 2559 & 11,230 & 2470 & 11,712 & 2409 \\ Coverage \% & **65.7\%** & 25.6\% & **61.9\%** & 31\% & **62\%** & 12.8\% & **22\%** & 0.7\% \\ Total modules & **58/66** & 28/66 & **120/126** & 72/126 & **304/306** & 108/306 & **216/621** & 144/621 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Computational results for comparing the performances of hybrid and conventional approaches. The bold is necessary as it shows the performance of the better method. the solution, which sets all the demand points to be a facility, is not a practical solution. Among the three variants of MCLP-MCLP, MCLP-SCLP, and SCLP-SCLP, it was expected that SCLP-SCLP can provide the best coverage, as it does not have any budgetary limitations.