my @infiles = &GetINDirFiles($inpath);  
# instead of having an array with the outfiles use a hash for faster lookup
# also remove suffix at this stage already, no need to do it again and again in the loop
# you need to escape your suffix variable in \Q...\E for special characters such as the dot
# only remove the suffix at the end, no need for (.*)
my %outfiles = map { s/\Q$outsuffix\E$//; $_ => 1 } &GetOUTDirFiles($outpath);

my $index = 0; # index used to get string position in array
foreach my $infile (@infiles) {
		# see above re the replacement
		$infile =~ s/\Q$insuffix\E$//;      # remove suffix to do comparation # Added by me
		# instead of loop through array of outfiles do hash lookup
		push (@delindex, $index) if exists $outfiles{$infile};
		$index += 1;
}

##</code><code>##

my %outfiles = map { /(.*)\Q$outsuffix\E$/; $1 => 1 } &GetOUTDirFiles($outpath);
my @infiles = grep { /(.*)\Q$insuffix\E$/; not exists $outfiles{$1} } &GetINDirFiles($inpath);  
print "@infiles\n";

##</code><code>##

use strict;
use warnings;

sub GetINDirFiles {
        my ($path) = @_;
        opendir my $dir, $path or die $!;
        return grep {!/\_ACK_/} readdir $dir;
}

sub GetOUTDirFiles {
        my ($path) = @_;
        opendir my $dir, $path or die $!;
        return grep {/\_ACK.xml$/} readdir $dir;
}

# Main
my $inpath = "./IN";      
my $outpath = "./OUT";
my $outsuffix = "_ACK.xml";
my $insuffix = ".xml";     
my $timethreshold = 900;       # set time threshold in seconds (900 seconds equal 15 minutes)

my %outfiles = map { /(.*)\Q$outsuffix\E$/; $1 => 1 } &GetOUTDirFiles($outpath);
my @infiles = grep { /(.*)\Q$insuffix\E$/; $1 and not exists $outfiles{$1} } &GetINDirFiles($inpath);  

my $currenttime = time;        # get current time from system (epoch time)
@infiles = grep { -f "$inpath/$_" and ( $currenttime - (stat "$inpath/$_" )[9] ) > $timethreshold } @infiles;

# now you have all input files w/o corresponding output file that are older than 15 minutes
for (@infiles) {
		print "File $_ in $inpath directory was created ". ( $currenttime - (stat "$inpath/$_" )[9] )/60.0 ."minutes ago.\n";
		# put your action here
}