use warnings;
use strict;

my %report = map { $_->[2] => $_->[0] }
            sort {
                   $a->[1] <=> $b->[1] 
                         || 
                   $b->[2] <=> $a->[2]
                 }
            map { [ $_, /^(\d+?)\/.+\/(\d+?)\./ ] } <DATA>;

print $report{$_}, $/ for reverse keys %report;

__DATA__
20120824/ABC/input/daily/11337111.xml
20120710/ABC/input/daily/11337101.xml
20120330/ABC/input/daily/11337111.xml
20130614/ABC/input/daily/11337890.xml
20130120/ABC/input/daily/11337111.xml
20120206/ABC/input/daily/11337111.xml
20121005/ABC/input/daily/11337890.xml
20130110/ABC/input/daily/11337111.xml
20120923/ABC/input/daily/11337111.xml
20130416/ABC/input/daily/11337101.xml
20120404/ABC/input/daily/11337111.xml
20130211/ABC/input/daily/11337111.xml