I am using this.  $loadrel{$load} .="$dept"; I am getting null as output. $loadrel is not getting set to any value..

Sorry, but that is inadequate. In your code snippet $load and $dept are never defined, so of course they are undef.

Instead of describing how you understand $dept and $load and %loadrel get defined , you need to show code that demonstrates that ( How do I post a question effectively?, Short, Self Contained, Correct (Compilable), Example)

For example

#!/usr/bin/perl --
use strict; use warnings;
use Data::Dumper;
my %loadrel;
for my $load ( qw/ a b c /){
    for my $dept ( qw/ 1 2 3 / ){
        $loadrel{$load} .= " $dept ";
    }
}
print Dumper( \%loadrel );
__END__

$VAR1 = {
          'c' => ' 1  2  3 ',
          'a' => ' 1  2  3 ',
          'b' => ' 1  2  3 '
        };
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