Stuff is left behind.

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

The first few bins would probably be most optimally filled for most datasets but if the goal is to use the least amount of tapes this should work... or am I missing something?

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;
}
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How would this not optimize for number of tapes?

-- FloydATC

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

Except that the original problem description does not include the size of the tapes, which means it doesn't clearly map to either of your suggestions. Thus my attempt to gather more data.