The problem scenario is an evening party in the context of a
yachting rally. Certain boats are to be designated hosts, and the
crews of the remaining boats in turn visit the host boats for several
successive half-hour periods. The crew of a host boat remains on
board to act as hosts while the crew of a guest boat together visits
several hosts. Every boat can only host a limited number of guests at
a time (its capacity) and crew sizes are different. The table with
boat capacities and crew sizes can be found below; there were six time
periods. A guest boat cannot not revisit a host and guest crews
cannot meet more than once. The problem facing the rally organizer is
that of minimizing the number of host boats.
(Smith et. al 1996)
| boat number | capacity | crew size |
| 1 | 6 | 2 |
| 2 | 8 | 2 |
| 3 | 12 | 2 |
| 4 | 12 | 2 |
| 5 | 12 | 4 |
| 6 | 12 | 4 |
| 7 | 12 | 4 |
| 8 | 10 | 1 |
| 9 | 10 | 2 |
| 10 | 10 | 2 |
| 11 | 10 | 2 |
| 12 | 10 | 3 |
| 13 | 8 | 4 |
| 14 | 8 | 2 |
| 15 | 8 | 3 |
| 16 | 12 | 6 |
| 17 | 8 | 2 |
| 18 | 8 | 2 |
| 19 | 8 | 4 |
| 20 | 8 | 2 |
| 21 | 8 | 4 |
| 22 | 8 | 5 |
| 23 | 7 | 4 |
| 24 | 7 | 4 |
| 25 | 7 | 2 |
| 26 | 7 | 2 |
| 27 | 7 | 4 |
| 28 | 7 | 5 |
| 29 | 6 | 2 |
| 30 | 6 | 4 |
| 31 | 6 | 2 |
| 32 | 6 | 2 |
| 33 | 6 | 2 |
| 34 | 6 | 2 |
| 35 | 6 | 2 |
| 36 | 6 | 2 |
| 37 | 6 | 4 |
| 38 | 6 | 5 |
| 39 | 9 | 7 |
| 40 | 0 | 2 |
| 41 | 0 | 3 |
| 42 | 0 | 4 |