001: Car Sequencing

language ESSENCE' 1.0


given numcars : int(1..)

given numclasses : int(1..)
given numoptions : int(1..)

given optMax : matrix indexed by [ int(1..numoptions) ] of int(0..)
given windowSize : matrix indexed by [ int(1..numoptions) ] of int(0..)


given optionsRequired : matrix indexed by [ int(1..numclasses), int(1..numoptions) ] of bool 

given numberPerClass : matrix indexed by [ int(1..numclasses) ] of int(1..)


$ Decision variables

find seq: matrix indexed by [ int(1..numcars) ] of int(1..numclasses)

such that

forAll option : int(1..numoptions) . 
    forAll windowStart : int(1..numcars-windowSize[option]+1) . 
        (sum pos : int(windowStart..windowStart+windowSize[option]-1) . 
            seq[pos] in toSet([ class | class : int(1..numclasses), optionsRequired[class, option]]) 
        )<=optMax[option],

forAll option : int(1..numoptions) . 
    (sum pos : int(1..numcars) . 
        seq[pos] in toSet([ class | class : int(1..numclasses), optionsRequired[class, option]]) 
    )=
    (
        sum class : int(1..numclasses) . optionsRequired[class, option]*numberPerClass[class]
    ),

gcc(seq, [ i | i : int(1..numclasses)], numberPerClass)