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 |
You Need a Professional Writer To Work On Your Paper?
