my $zip = Archive::Zip->new();
foreach $case (@items) {
  ...
  my $member = $zip->addDirectory( 'dirname/' );
  $member->desiredCompressionMethod();
  $member = $zip->addFile( "$file_to_zip", "$file_name" );               
}
die 'write error' unless $zip->writeToFileNamed( $zip_file_name ) == AZ_OK;