## 4 Computational Results and Discussions
### Comparison between the Exact Solution and SA  
This sub-section describes the comparison of the results between the exact solution approach using an approximation approach of the proposed simulated annealing. The experiments are conducted on 20 samples which consist of data based on Tables 1 and 2. However, each sample has different minimum and maximum percentages permitted for cultivation in each area, in which the example has been shown previously in Table 3. This experiment aims to test the quality of the solution provided by the exact solution approach compared with SA. The exact solution approach was applied using AMPL, a commercial software package. The solution provided by AMPL was regarded as the optimal solution. However, the exact solution has some limitations. To solve larger size or more complex problems, AMPL may take a longer time to find the answers. Sometimes, it could not even find one. Therefore, in this case, metaheuristics are preferred. In addition, the AMPL software package maybe not be feasible for some decision-makers due to investment costs that need to be applied if the application is going to be used for commercial purposes.  
Table 6 shows that SA can find the exact solution generated by AMPL. However, it may take a longer time to solve the problem. This is suspected because the size of instances available to use for the experiment is still considerably small. In more detail, AMPL can report the optimal solution on an average of 2.40 s. Meanwhile, SA requires an average of 6.95 s to report the optimal solution. Despite SA reportedly taking a long time to generate the solution, this study still encourages the use of SA for further experiments. First, the time difference to solve the problem is still considered reasonable. Second, it is due to the consideration of practical delivery of the DSS to the stakeholder that the use of AMPL will require the decision-maker to have another investment in the software to be able to use it for a commercial purpose.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Month**} & \multicolumn{6}{c}{**Expected Water Amounts/Month (m\({}^{3}\))**} \\ \cline{2-9}  & **Mac Thor 2** & **Ban Nong** & **[PERSON] 3** & **Mac Thor Ban** & **Na Pae** & **Mae Thor** & **Total Water** \\  & **(Den Ai Tai)** & **Khaem** & **(Na Berk)** & **Huay Nueng** & **Na Pae** & **Tung Luang** & **Amount** \\ \hline
1 & 2,068,420 & 1,569,740 & 1,561,980 & 3,739,060 & 333,741 & 3,331,580 & 12,604,521 \\ \hline
2 & 1,770,630 & 1,343,750 & 1,337,110 & 3,200,760 & 285,693 & 2,851,950 & 10,789,893 \\ \hline
3 & 2,237,350 & 1,697,950 & 1,689,550 & 4,044,430 & 360,998 & 3,603,680 & 13,633,958 \\ \hline
4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline
5 & 1,087,880 & 825,605 & 821,523 & 1,966,550 & 175,530 & 1,752,240 & 6,629,328 \\ \hline
6 & 822,623 & 624,298 & 621,211 & 1,487,050 & 132,731 & 1,324,990 & 5,012,903 \\ \hline
7 & 865,459 & 656,807 & 653,559 & 1,564,480 & 139,643 & 1,393,990 & 5,273,938 \\ \hline
8 & 2,482,100 & 1,883,690 & 1,874,380 & 4,486,870 & 400,489 & 3,997,900 & 15,125,429 \\ \hline
9 & 1,373,340 & 1,042,240 & 1,037,090 & 2,482,570 & 221,589 & 2,212,030 & 8,368,859 \\ \hline
10 & 2,191,230 & 1,662,950 & 1,654,730 & 3,961,060 & 353,556 & 3,529,400 & 13,352,926 \\ \hline
11 & 684,098 & 519,170 & 516,603 & 1,236,640 & 110,380 & 1,101,870 & 4,168,761 \\ \hline
12 & 647,443 & 491,352 & 488,922 & 1,170,380 & 104,465 & 1,042,830 & 3,945,392 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Expected water amounts of each area in each month.