Working with dates can be tricky. There are many modules available, but for something this simple doing it the long way should be find. The stat function can be used to get the mtime of a file. The mtime is an epoch value (your file's age in seconds since January 1, 1970). This can be used to sort the list. If you are dealing with subdirectores, use the File::Find module.

[matt@test ~/testdir]$ stat -c %Y AMR.xml
1206990376
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#!/usr/bin/perl

use strict;
use POSIX qw(strftime);

my $dir = '/your/dir';

opendir DIR, $dir or die $!;
my @files = grep { /\.xml$/ && ! /^\./ } readdir DIR;
closedir DIR;

my %ds;

for my $file (@files) {
    my $mtime = (stat("/your/dir/$file"))[9];

    $ds{$file} = $mtime;
}

for my $sorted_file (sort { $ds{$a} <=> $ds{$b} } keys %ds) {
    my $file_date = strftime("%Y-%m-%d", localtime($ds{$sorted_file}))
+;
    my $file_time = strftime("%H:%M:%S", localtime($ds{$sorted_file}))
+;
    print qq[<option value="$sorted_file">$file_date $file_time</optio
+n>\n];
}
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