#!/usr/bin/perl -w
use strict;
use warnings;

use File::Basename;
use Archive::Zip qw( :ERROR_CODES :CONSTANTS );

my $procdate = sprintf "%02d%02d%02d%02d%02d%02d", (localtime)[4]+1, (
+localtime)[3], substr((localtime)[5]+1900,2,2),(localtime)[2], (local
+time)[1], (localtime)[0];

my @dipfile = glob('C:/ReportExtract/Director/*.xml');

##### Zip each file into a zip file for archiving  #####
my $targetdir = File::Spec->catdir('C:/ReportExtract/Director/');
my $targetzip = File::Spec->catdir($targetdir, basename($procdate) . "
+.zip"); #Need basename.     
my $zip = Archive::Zip->new();

my $zipdir = $zip->addDirectory($targetdir);
    

foreach my $xml_file (@dipfile) {
      
    my $temp = File::Basename::fileparse($xml_file); #Trying it with o
+nly the basename.
    $zipdir = $zip->addFile($temp);    
};

    unless ( $zip->writeToFileNamed($targetzip) eq "AZ_OK" ) {die 'rea
+d error';}
[download]

I think $zip->addFile() needs the complete path, not just the filename. So try this:

# outside of loop:
$dir = "C:/ReportExtract/Director";

# ...

# inside your foreach loop:
if (-e "$dir/$temp" ) {
  unless ( $zip->addFile("$dir/$temp") ) {
    print "Error: failed to add $dir/$temp to archive.\n";
  }
} else {
  print "Error: $dir/$temp does not exist!\n";
}
[download]

This also adds error checking, so you can see if it's doing the right thing as it runs.