use File::Spec::Functions qw( catfile );

sub get_files_in_dir {
   my ($dir_name) = @_;
   opendir(my $dh, $dir_name)
      or die("Unable to open dir \"$dir_name\": $!\n");
   return map catfile($dir_name, $_),
          grep -f,
          grep !/^\.\.?\z/,
          readdir($dh);
}

my $dir_name = '...';

# Get list of files.
my @files = get_files_in_dir($dir_name);

# Group files by customer.
my %files_by_cust;
foreach (@files) {
   my ($cust_id) = /^customer(\d+)\./
      or next;

   push @{ $files_by_cust{$cust_id} }, $_;
}

# Process each customer's files.
foreach my $cust_id (keys %files_by_cust) {
   # List of files is in @{ $files_by_cust{$cust_id} }.
   # ...
}
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Updated: Added omitted call to opendir.