use List::Util qw( sum );
my %cache;
my @keys = keys %$hash_ref;
foreach my $a_ (@{ $array_ref }) {
    my $i = 0;
    foreach my $b_ (split('-', $a_)) {
        $i += $cache{$b_} //= sum map { $_->{value} } @{ $foo->{$b_} }{@keys}; # Use the cached value or compute the sum
    }
    push @{ $bar->{$i} }, $a_;
}