Вот один из способов сделать это, используя только DateTime :
use DateTime;
sub first_day_of_week
{
my ($year, $week) = @_;
# Week 1 is defined as the one containing January 4:
DateTime
->new( year => $year, month => 1, day => 4 )
->add( weeks => ($week - 1) )
->truncate( to => 'week' );
} # end first_day_of_week
# Find first day of second week of 2012 (2012-01-09):
my $d = first_day_of_week(2012, 2);
print "$d\n";