038: Steel Mill Slab Design

language ESSENCE 1.2.0
$ prob038.essence: Steel Mill Slab Design Problem
$ Problem details available at http://www.csplib.org/Problems/prob038/
$ 07 September 2007

given n_colours, n_orders, col_per_slab, n_orderSize : int(1..)
given nbSizes : int(1..)
letting sizes be domain int(1..nbSizes)

letting Colour be domain int(1..n_colours),
        Order be domain int(1..n_orders)

given ordSize : function (total) Order --> int(1..n_orderSize),
      ordCol : function (total) Order --> Colour

find cut : function set of Order --> sizes

minimising sum (_,os) in toSet(cut) . os

such that
    forAll os1, os2 in defined(cut), os1 != os2 . |os1 intersect os2| = 0,
    forAll o : Order . exists os in defined(cut) . o in os,
    forAll os in defined(cut) . (sum o in os . ordSize(o)) <= cut(os),
    forAll (os,cut_os) in toSet(cut) . (sum o in os . ordSize(o)) <= cut_os,
    forAll os in defined(cut) . (sum o in os . ordCol(o) ) <= col_per_slab