## 3 Results
### Definition of Critical Values for Objective Effects  
The density of road networks, population density, economic density, and post-disaster response capability are all benefit type indicators, with higher values indicating better effects. According to Table 4, the basic data for the optimization scheme pertaining to the site selection of region- and city-level emergency supply reserve warehouses in Xinjiang are used to compute the density of road networks, economic density, population density, and post-disaster response capability across 14 regions, prefectures, and cities, as presented in Table 5. The minimum value of each indicator is selected as the critical value for  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**District and County**} & \multirow{2}{*}{**Density of Road Networks**} & \multirow{2}{*}{**Population Density**} & \multirow{2}{*}{**Economic Density**} & \multirow{2}{*}{**Post-disaster Response**} \\  & & **(km/km2)** & & **(CNY 100 Million/km2)** & \\ \hline
59 & Qiemo County & 0.0077 & 0.4990 & 0.0003 & 8.1605 \\
60 & Yanqi Hui Autonomous County & 0.0694 & 50.6542 & 0.0273 & 6.7826 \\
61 & Heijing County & 0.0285 & 4.2263 & 0.0026 & 5.1806 \\
62 & Hovak County & 0.0337 & 4.6460 & 0.0030 & 5.5987 \\
63 & Bohu County & 0.0261 & 13.4582 & 0.0072 & 7.3310 \\
64 & Aksu City & 0.0175 & 49.3352 & 0.0173 & 2.5122 \\
65 & Kuga City & 0.0417 & 36.4450 & 0.0199 & 4.5858 \\
66 & Wensu County & 0.0336 & 18.4477 & 0.0059 & 3.3007 \\
67 & Shaya County & 0.0111 & 8.7189 & 0.0027 & 4.2475 \\
68 & Xinhe County & 0.0464 & 33.2502 & 0.0104 & 6.1757 \\
69 & Baicheng County & 0.0230 & 14.4884 & 0.0059 & 5.5817 \\
70 & Udurpan County & 0.0274 & 22.4820 & 0.0056 & 3.6970 \\
71 & Awat County & 0.0190 & 18.4826 & 0.0048 & 3.8230 \\
72 & Kalpin County & 0.0296 & 5.6157 & 0.0016 & 7.5071 \\
73 & Artush City & 0.0375 & 18.4194 & 0.0044 & 8.2217 \\
74 & Akto County & 0.0183 & 9.1421 & 0.0019 & 5.3583 \\
75 & Akqi County & 0.0309 & 3.8236 & 0.0013 & 6.7615 \\
76 & Ulugat County & 0.0284 & 3.1661 & 0.0019 & 9.2100 \\
77 & Kashgar City & 0.0941 & 766.7744 & 0.2334 & 7.2611 \\
78 & Shuu County & 0.0319 & 94.7116 & 0.0180 & 5.0530 \\
79 & Shule County & 0.0558 & 160.9751 & 0.0336 & 7.5602 \\
80 & Yensigar County & 0.0520 & 79.1287 & 0.0135 & 4.3956 \\
81 & Poskam County & 0.0825 & 209.4737 & 0.0466 & 8.0031 \\
82 & Yarkant County & 0.0423 & 94.5424 & 0.0151 & 3.4596 \\
83 & Kargilik County & 0.0199 & 18.0094 & 0.0038 & 6.8115 \\
84 & Makit County & 0.0168 & 20.2781 & 0.0057 & 6.9863 \\
85 & Yopurga County & 0.0302 & 51.0592 & 0.0112 & 4.9178 \\
86 & Payzavat County & 0.0392 & 63.9548 & 0.0106 & 2.5799 \\
87 & Maralbexi County & 0.0277 & 19.6861 & 0.0040 & 4.6594 \\
88 & Tashkurgan Jajik Autonomous & 0.0138 & 1.6505 & 0.0007 & 5.1570 \\
89 & Hotan City & 0.0990 & 1065.9490 & 0.2431 & 4.3012 \\
90 & Hotan County & 0.0128 & 8.2387 & 0.0011 & 2.9305 \\
91 & Karakax County & 0.0132 & 22.1209 & 0.0031 & 5.5664 \\
92 & Pishan County & 0.0161 & 7.0474 & 0.0010 & 4.4003 \\
93 & Lop County & 0.0118 & 20.1751 & 0.0030 & 4.1094 \\
94 & Qira County & 0.0082 & 4.9604 & 0.0008 & 4.5947 \\
95 & Keriya County & 0.0092 & 6.5523 & 0.0010 & 5.7112 \\
96 & Niya County & 0.0056 & 0.7501 & 0.0003 & 7.0811 \\ \hline \hline \end{tabular}
\end{table}
Table 3: _Cont._objective effect in optimizing the site selection for 96 district- and county-level emergency supply reserve warehouses. Specifically, the density of road networks \(u_{ij}^{(1)}=0.0145\), population density \(u_{ij}^{(2)}=3.2011\), economic density \(u_{ij}^{(3)}=0.0016\), and post-disaster response capability \(u_{ij}^{(4)}=4.1012\).