A simplified iterative approach, provided in pseudocode. Assumes supervisor is empty or null when hits CEO level. (Adjust while condition if not a good assumption.)

my $supervisor = $initial_employee_id;
while ($supervisor) (
  $row = select columns where eid = $supervisor;

  print out spreadsheet row for employee;

  $supervisor = $row{supervisor};
}
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Also, since the database only returns a single row, you should be able to use the selectrow_arrayref function to make your sql code a bit simpler. And as for your "how to use variable inside sql string" question, see 7548