# Globally Optimal Facility Locations for Continuous-Space Facility Location Problems
## 4 Numerical Examples
### Comparison with Previous Methods
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number of Facilities** & **ID** & **K-Means Clustering Algorithm** & **[PERSON], [PERSON] [40]** & **[PERSON] [65]** & **The Proposed Method** \\ \hline \multirow{4}{*}{3} & 1 & (51.7, 13.0) & (20.6, 42.6) & (55, 43) & (55, 43) \\  & 2 & (30.6, 48.6) & (68.3, 74.4) & (21, 39) & (21, 39) \\  & 3 & (69.5, 66.1) & (58.8, 35.8) & (63, 79) & (63, 81) \\ \hline \multirow{4}{*}{4} & 1 & (56.9, 13.4) & (30.3, 73.3) & (21, 37) & (21, 37) \\  & 2 & (73.7, 66.1) & (71.3, 79.0) & (51, 43) & (51, 43) \\  & 3 & (16.2, 43.1) & (60.1, 38.2) & (63, 81) & (63, 83) \\  & 4 & (44.7, 54.5) & (17.7, 33.0) & (83, 43) & (83, 51) \\ \hline \multirow{4}{*}{5} & 1 & (36.9, 8.8) & (19.6, 65.6) & (51, 49) & (51, 43) \\  & 2 & (18.0, 48.6) & (18.5, 27.8) & (51, 9) & (45, 9) \\  & 3 & (75.7, 38.0) & (66.6, 81.2) & (71, 43) & (83, 51) \\  & 4 & (48.6, 47.5) & (77.4, 38.5) & (63, 81) & (59, 83) \\  & 5 & (48.6, 47.5) & (49.2, 39.7) & (21, 39) & (21, 39) \\ \hline \multirow{4}{*}{6} & 1 & (62.6, 84.5) & (47.2, 45.7) & (51, 47) & (51, 43) \\  & 2 & (83.5, 20.2) & (63.9, 52.2) & (45, 7) & (51, 9) \\ \cline{1-1}  & 3 & (17.9, 47.7) & (86.6, 45.0) & (17, 63) & (17, 63) \\ \cline{1-1}  & 4 & (35.3, 7.5) & (17.5, 44.8) & (63, 81) & (63, 81) \\ \cline{1-1}  & 5 & (50.0, 43.4) & (55.1, 9.5) & (21, 35) & (21, 33) \\ \cline{1-1}  & 6 & (71.8, 55.6) & (64.9, 85.0) & (83, 15) & (83, 51) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of facility locations using different methods for Instance 24. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number of Facilities** & **ID** & **K-Means Clustering Algorithm** & **Gao, Nayeem [40]** & **Gao [65]** & **The Proposed Method** \\ \hline \multirow{4}{*}{3} & 1 & (31.9, 77.1) & (74.5, 21.8) & (15, 69) & (39, 67) \\  & 2 & (81.0, 32.1) & (40.1, 76.9) & (75, 75) & (63, 79) \\  & 3 & (30.0, 19.5) & (23.6, 19.0) & (49, 19) & (69, 17) \\ \hline \multirow{4}{*}{4} & 1 & (70.5, 77.8) & (16.1, 74.5) & (25, 19) & (25, 19) \\  & 2 & (16.1, 74.5) & (69.5, 80.2) & (15, 69) & (15, 69) \\  & 3 & (24.3, 17.0) & (47.8, 17.5) & (63, 77) & (63, 77) \\  & 4 & (74.1, 21.2) & (90.6, 40.9) & (77, 17) & (77, 17) \\ \hline \multirow{4}{*}{5} & 1 & (26.8, 18.4) & (14.8, 21.1) & (77, 17) & (75, 17) \\  & 2 & (27.2, 83.6) & (49.7, 17.7) & (63, 77) & (63, 77) \\ \cline{1-1}  & 3 & (76.2, 20.3) & (71.4, 78.9) & (15, 69) & (15, 69) \\ \cline{1-1}  & 4 & (70.5, 77.8) & (80.0, 22.2) & (47, 21) & (91, 41) \\ \cline{1-1}  & 5 & (7.1, 67.0) & (16.3, 75.2) & (15, 19) & (25, 19) \\ \hline \multirow{4}{*}{6} & 1 & (15.1, 19.8) & (89.4, 36.3) & (15, 69) & (15, 69) \\  & 2 & (7.1, 67.0) & (71.5, 14.7) & (47, 21) & (47, 21) \\ \cline{1-1}  & 3 & (71.4, 78.9) & (16.1, 74.5) & (77, 17) & (77, 17) \\ \cline{1-1}  & 4 & (78.7, 20.1) & (89.6, 72.5) & (63, 77) & (77, 77) \\ \cline{1-1}  & 5 & (27.2, 83.6) & (26.8, 18.4) & (93, 41) & (15, 41) \\ \cline{1-1}  & 6 & (46.7, 20.5) & (61.2, 80.4) & (9, 19) & (25, 19) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of facility locations using different methods for Instance 25.