use Time::Piece;

my @vkeys;
my %ranges_dt;

# ==================================================
sub check_date_in_range
{
    my ($value, %h) = @_;
    my $cvalue = Time::Piece->strptime($value, '%m/%d/%Y-%H:%M:%S')->e
+poch;
    if (!@vkeys) {
        @vkeys = sort keys %h;
    }
    foreach my $k (@vkeys) {
        if (($cvalue >= $h{$k}{start}) && ($cvalue <= $h{$k}{end})) {
            return $k;
        }
    }
    return;
}

while (<DATA>) {
    chomp;
    if (s/^(\w+)://) {
        my $cat = $1;
        if ($cat eq "R") {
            my ($i, $s, $e) = split ',';
            $ranges_dt{$i}{start} = Time::Piece->strptime($s, '%Y-%m-%
+d %H:%M:%S')->epoch;
            $ranges_dt{$i}{end} = Time::Piece->strptime($e, '%Y-%m-%d 
+%H:%M:%S')->epoch;
        } else {
            my $rangeid = check_date_in_range($_, %ranges_dt);
            if (!defined $rangeid) {
                print "No range found for $_\n";
            } else {
                print "Found range: $rangeid\n";
            }
        }
    }
}
[download]

Another option would be not to store the timestamps in a hash and sort them every time a new one arrives, but use a data structure that can add a new element and quickly search for the closest members (binary search tree, for example).

($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
[download]