The most straight-forward solution I can think of is to generate all ways to assign each object with a container number. This will generate some assignments where some container does not receive any objects, so you will have to filter them out.

Using Algorithm::NestedLoops, that would look something like:

my $containers = ...
my $objects = ...

NestedLoops(
  [ (sub{ [0 .. $containers-1] }) x $objects ],
  sub {
    my @assignment = @_;

    my @bins;
    push @{ $bins[$assignment[$_]] }, $_ for 0 .. $objects-1;
    
    ## @bins now contains the groupings

    ## filter out if one of the bins is empty

  }
);
[download]

There is probably a more direct way to do this, so that you can cleverly iterate over just the assignments that use each bin. But I haven't discovered it yet in the short time that I've been thinking about your post.