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Description
The 'occurrence' (=cardinality) constraint expresses a relation on the frequency with which a value occurs in a set of decision variables. The 'distribute' constraint generalizes this constraint by extending the cardinality relation to a list of values.
• occurrence.mos: simple example of the use of occurrence constraints
• distribute.mos: using 'distribute' or 'occurrence' constraints in the formulation of a personnel planning problem.
Further explanation of this example: 'Xpress Kalis Reference Manual'

Source Files

occurrence.mos

```(!****************************************************************
CP example problems
===================

file occurrence.mos
```````````````````
Cardinality (=occurrence) constraints.

(c) 2008 Artelys S.A. and Fair Isaac Corporation
Creation: 2005, rev. Mar. 2013
*****************************************************************!)
model "Cardinality"
uses "kalis"

setparam("KALIS_DEFAULT_LB", 0)

declarations
R = 1..6
S = 1..10
x: array(R) of cpvar
y: array(S) of cpvar
a,b,c: cpvar
Card: cpctr
Vlist: cpvarlist
end-declarations

forall(i in R) setname(x(i), "x"+i)
forall(i in 1..3) x(i) = 1
forall(i in 4..6) x(i) <= 10
setname(c, "c")
c <= 15

writeln("Initial domains:\n ", x, "  ", c)

! Explicit posting of an occurrence constraint
Card:= occurrence(1, x) = c
if cp_post(Card) then
writeln("With occurrence constraint:\n ", x, "  ", c)
else exit(1)
end-if

c = 6
writeln("Fixing occurrence to 6:\n ", x, "  ", c)

forall(i in S) do
setname(y(i), "y"+i)
i <= y(i); y(i) <= i*2
end-do
setname(a, "a"); setname(b,"b")

writeln("Initial domains:\n ", y, "  ", a, "  ", b)

! Occurrence constraint on an array of variables
occurrence(4, y) <= 2

! Occurrence constraint on a list of variables
Vlist += y(1); Vlist += y(2); Vlist += y(4)
occurrence(2, Vlist) = 0

! Occurrence constraint on a set of variables
occurrence(9, {y(6), y(7), y(9)}) >= 3

! Occurrences bounded by variables
occurrence(5, y) >= a
occurrence(8, {y(4), y(5), y(6), y(7), y(8)}) <= b
writeln("With all constraints:\n ", y, "  ", a, "  ", b)

if cp_find_next_sol then
writeln("A solution:\n ", y, "  ", a, "  ", b)
end-if

end-model

```   