## The Progressive Party Problem: Specification

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