First, don't confuse things by using '/' as your "quote like characters" for the regular expression. A regexp can look like this: m//, or you can use a wide variety of other characters, such as m{} or m!!. The reason this is helpful is that if your regexp has any literal '/' in it, you end up having to escape it with a preceding backslash. This leads to the leaning-toothpicks effect: (example) m/\\|\// matches '\' or '/', and does so in a visually confusing way.

Now that we've got that annoyance out of the way, we can use visually clear code. Your objective now is simply to make that trailing slash optional. The character inside of a regexp that means 'optional' is the question mark. So it could look like this:

m{$location/?$}
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Now on the other hand, if the expression held in $location actually ends in a slash too, then you're going to need to prepare your regexp with a little more care. Here I'm going to examine $location to see if it ends in a slash, and if it does, append a question mark. Then I'll use that new string as my regular expression.

my $file = 'some_filename';
my $location = 'some_filename/';

$location =~ s{/$}{/?};  # If a trailing / is found, append a ? to it.

if( $file ~= m{$location$} ) { # Do your stuff }
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