Min hubs given max milage
distnaces
Miles between Locations | ||||||||
Y | 11 | 9 | 7.5 | 3.5 | 4 | 1 | ||
X | 12 | 13.5 | 11 | 12.5 | 17.5 | 17 | ||
Loc | X | Y | A | B | C | D | E | F |
A | 12 | 11 | 0.0 | 2.5 | 3.6 | 7.5 | 8.9 | 11.2 |
B | 13.5 | 9 | 2.5 | 0.0 | 2.9 | 5.6 | 6.4 | 8.7 |
C | 11 | 7.5 | 3.6 | 2.9 | 0.0 | 4.3 | 7.4 | 8.8 |
D | 12.5 | 3.5 | 7.5 | 5.6 | 4.3 | 0.0 | 5.0 | 5.1 |
E | 17.5 | 4 | 8.9 | 6.4 | 7.4 | 5.0 | 0.0 | 3.0 |
F | 17 | 1 | 11.2 | 8.7 | 8.8 | 5.1 | 3.0 | 0.0 |
Adjacency natrix
Two locations with < = | 4 | miles are considered adjacent. | ||||
1 means adjacent and can be served by the same hub | ||||||
Serve each location with least # of total hubs | ||||||
A | B | C | D | E | F | |
A | 1 | 1 | 1 | 0 | 0 | 0 |
B | 1 | 1 | 1 | 0 | 0 | 0 |
C | 1 | 1 | 1 | 0 | 0 | 0 |
D | 0 | 0 | 0 | 1 | 0 | 0 |
E | 0 | 0 | 0 | 0 | 1 | 1 |
F | 0 | 0 | 0 | 0 | 1 | 1 |
min # of hubs
Finding minimum number of hubs to serve each area | Mnimum | |||||||
Number of hubs serving each area must be >= 1 | # of hubs | |||||||
Solution | 1 | 0 | 0 | 1 | 1 | 0 | 3 | |
# of hubs | ||||||||
Area | A | B | C | D | E | F | Serving | |
A | 1 | 1 | 1 | 0 | 0 | 0 | 1 | |
B | 1 | 1 | 1 | 0 | 0 | 0 | 1 | |
C | 1 | 1 | 1 | 0 | 0 | 0 | 1 | |
D | 0 | 0 | 0 | 1 | 0 | 0 | 1 | |
E | 0 | 0 | 0 | 0 | 1 | 1 | 1 | |
F | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
Analysis
Hub | Location | Serving | ||
1 | A | A | 0.0 | |
B | 2.5 | |||
C | 3.6 | |||
2 | D | D | 0.0 | |
3 | E | E | 0.0 | |
F | 3.0 | |||
Total Distance | 9.2 | |||
Max distance | 3.6 |