013: Progressive Party Problem

language Essence 1.3
$ prob013.essence: Progressive Party Problem
$ Problem details available at http://www.csplib.org/Problems/prob013/

given n_boats, n_periods : int(1..)

letting Boat be domain int(1..n_boats)

given capacity, crew : function (total) Boat --> int(1..)

find hosts : set (minSize 1) of Boat,
     sched : set (size n_periods) of partition from Boat

minimising |hosts|

$ Hosts remain the same throughout the schedule
such that
    forAll p in sched . |parts(p)| = |hosts| /\
    forAll part in parts(p) . |part intersect hosts| = 1

$ Hosts have the capacity to support the visiting crews
such that forAll p in sched . forAll h in hosts .
    (sum b in party(h,p) . crew(b)) <= capacity(h)

such that allDiff([ (i, j)
                  | p <- sched
                  , part <- p
                  , {i,j} <- powerSet(part)
                  ])