Then add another bin (tape) and start filling it with leftovers. Repeat until no more bins (tapes) or leftovers.

That wouldn't optimize anything. I think we all agree that there is something that he wants to optimize.

That wouldn't optimize anything

What I mean is, it's still a knapsack problem but there are fewer items with each iteration. In pseudocode:

my @items = qw( loads of variable size items here );
while (@items) {
  push @tapes, remove_from(\@items);
}

sub remove_from {
  my $arrayref = shift;
  my $taperef = [];

  # Knapsack algorithm goes here
  # ...
  
  # Whatever we put in $taperef is removed from $arrayref
  # ...

  return $taperef;
}
[download]

How would this not optimize for number of tapes?

-- FloydATC

Time flies when you don't know what you're doing