Try this:

 perl -e ' $a="abc"; $b="aCd"; @m = $a=~ /([^$b])/i; print "@m\n"'

Array @m will be empty whenever $a can be built from the letters in $b !

update: This regex says that "aa" can be built from letters in "a". But it can be used as a filter, before applying a more complex algorithm.

This is an example on how to use it (I don't claim it is perfect :)

use strict;
my ($a,$b) = (shift, shift);
my @m = $a =~ /([^$b])/ig;
if ($#m < 0) {
    print "ok, can build '$a' using letters in '$b'\n";
    foreach my $letter (split // => $a) {
        unless ($b =~ s/$letter//) {
            print "but will need an extra '$letter'\n"
        };
    }
}
else {
    print "can't build '$a' because I don't have '",join("' and '", @m
+),"'\n";
}
[download]

update: use of /ig may make it slower, but it gives an estimate on how many characteres are missing