065: Optimal Financial Portfolio Design

language Essence 1.3

$ Optimal Financial Portfolio Design
$
$ Problem details available at http://www.csplib.org/Problems/prob065/
$
$ Essence model by Jean-Noël Monette
$
$ Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/

given v,b,r: int(1..) 
where r <= b

letting Nums be domain int(1..b)

letting rv be r*v
letting rvmodb be rv % b
letting floorrv be rv / b
letting ceilrv be rv / b + toInt(rv % b != 0)
letting num be (ceilrv*ceilrv*rvmodb+floorrv*floorrv*(b-rvmodb)-rv)
letting denom be v*(v-1)
letting lb_lambda be num / denom + toInt( num % denom !=0)


find opd : set (size v) of set (size r) of Nums

find lambda : int(lb_lambda..b)

minimising lambda

such that
    forAll {i, j} subsetEq opd .
        |i intersect j| <= lambda