perl -e '
@months=qw(JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC);
$date_in="NOV-07";
($month,$year)=$date_in=~/([A-Z]{3})-(\d{2})/;
for $index (0..@months){
   print "20$year/",++$index,"\n" if $month eq $months[$index];
}
'
[download]

The following should do the trick ...

sub dateconvert       # converts dates from MMM-YY  ->   20YY/MM
{
  my %mon = ( "Jan" => 1, "Feb" => 2, "Mar" => 3, "Apr" => 4, "May" =>
+ 5, "Jun" => 6, "Jul" => 7, "Aug" => 8, "Sep" => 9, "Oct" => 10, "Nov
+" => 11, "Dec" => 12 );
  $_[0] =~ /(\w\w\w)\-(\d\d)/;
  return sprintf("20%02d.%02d",$2,$mon{$1});
}
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You could prepend a day (e.g. 01) to help ParseDate() disambiguate the input format:

print UnixDate( ParseDate(   'NOV-07'), '%Y-%m-%d' ), "\n";
print UnixDate( ParseDate('01-NOV-07'), '%Y-%m-%d' ), "\n";

__END__
2010-11-07
2007-11-01
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Also, why do you specify '%Y-%m-%d' as the output format when what you say you want is '%Y/%m'?

In this case though, NOV-07 was too ambiguous for str2time. Adding 1- to make 1-NOV-07 fixed it.

#!/usr/bin/perl

use warnings;
use strict;

use Date::Format;
use Date::Parse;

my $thingy = q{NOV-07};

my $time = str2time(qq{1-$thingy});
my $date = time2str(q{%Y/%m}, $time);

print  $date;
[download]

2007/11
[download]

#!/usr/local/bin/perl
use strict;
use warnings;

my %monthsOrder;
@monthsOrder{qw(Jan Feb Mar Apr May Jun Jul Aug Sept oct Nov Dec)}=1..
+12;
#provide a list of dates to convert
my @dates = ('Nov-07', 'Aug-09', 'Jul-01', 'Feb-02');

foreach my $element (@dates){
        my ($month, $year)= $element=~/(\w+)-(\d+)/;
        print convertMonth($month, $year),"\n";
        }

sub convertMonth{
    my ($month, $year) = @_;
    for my $key(keys %monthsOrder){
        return "20$year/$monthsOrder{$key} " if $month eq $key;
        }
    }
[download]

2007/11
2009/8
2001/7
2002/2
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Here is a way to do it with Date::Manip, although as far as I can tell your string does not contain a valid 'date'--because it does not specify a day. So you have to alter your string first:

use strict;
use warnings;
use 5.010;

use Date::Manip::Date;

my $string = 'Nov-07';
$string .= ' 01';  #add day field to string
my $format = '%b-%y %d';

my $date = new Date::Manip::Date;
my $error = $date->parse_format($format, $string);

if ($error == 0) {  #everything worked correctly
    say $date->printf('%Y/%m');
}
else { 
    say "something went wrong";

    if ($error == 1) {
        say "format didn't match your string";
    }
    else {
        say "format is invalid--won't create a valid date: $error";
    }
}

--output:--
2007/11
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See here for details:

#!/usr/bin/perl

use strict;
use warnings;

use Date::Manip;

my $thingy = 'NOV-2007';
my $date = UnixDate( ParseDate( "1-$thingy" ), '%Y/%m' );

print "$date\n";
[download]