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


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