I found this interesting, so I began to hack a bit...

SORRY, I have to catch my plane (already late), so this goes without cleanup or further comment for now. I will come back to this node tomorrow...

our $oopser = 0; # protect from endless loops
$#empsh = 20; # prefill worktable

for my $sh (1 .. 21) { # 21 shifts are 7 days with 3 shifts
    for my $shid (1 .. 3) { # every shift has 3 mandtory workers
        # find a free worker
        my $emp = 0;
        $oopser = 0;
        while ($emp == 0) {
            $oopser++; die if $oopser > 100;
            $emp = int( 1 + rand(20) ); # take a random worker
            $emp = 0 if $empsh->[$emp][$sh]; # already assigned
        }
        $empsh[$emp][$sh] = "work ($shid)"; # work this shift (8 hours
+)
        $empsh[$emp][$sh+1] = 'free (+)';   # and have 2 shifts rest (
+16 hours)
        $empsh[$emp][$sh+2] = 'free (++)';  # (German law says 11 hour
+s between shifts)
        $shcount[$sh]++; # no of worker per shift
    }
    foreach my $emp (@empsh) { # all other workers are unassigned on t
+his shift
        $emp->[$sh] ||= ' - ';
    }
}

my %emplist = map { $_ => $_ } (1 .. 20); # workerlist, delete()able
$oopser = 0;
while (keys %emplist) { # check for remaining every worker (maybe add 
+"sort rand()"
    $oopser++; die if $oopser > 100;
    my @shnum = (); # no of shifts per worker
    for my $emp (keys %emplist) {
        foreach my $tag (@{ $empsh[$emp] }) {
            $shnum[$emp]++ if $tag =~ /^work/; # count his working shi
+fts
        }
        if ($shnum[$emp] == 5) { # worked 5 shifts?
            delete $emplist{$emp};
        } # (each worker has to work exactly 5 shifts a week)
    }
    EMP: foreach my $emp (keys %emplist) { # who has to work more?
        my $sh = 1;
        while ($empsh[$emp][$sh] ne ' - ') { # find a unassigned shift
+ for this worker
            if ($sh > 21) { # oops, none found?
                delete $emplist{$emp};
                print STDERR "$emp has underwork\n";
                next EMP; # re-run this program then
            }
            $sh++;
        }
        if ($shcount[$sh] >= 5) {
            # shift full
            $empsh[$emp][$sh] = 'free (shift full)';
        } elsif ($empsh[$emp][$sh+1] =~ /^work/) {
            # no 2 shifts rest possible
            $empsh[$emp][$sh] = 'free (-)';
        } elsif ($empsh[$emp][$sh+2] =~ /^work/) {
            # no 2 shifts rest possible
            $empsh[$emp][$sh] = 'free (--)';
        } else {
            # hehe, work here!
            $empsh[$emp][$sh] = 'work (backup)';
            $empsh[$emp][$sh+1] = 'free (+)';
            $empsh[$emp][$sh+2] = 'free (++)';
        }
    }
}

# now print
print "<table border><tr><td>***";
for my $sh (1 .. 21) {
    print "<th>-$sh-";
}
print "<td>";
for my $emp (1 .. 20) {
    print "<tr><th>", $emp;
    for my $sh (1 .. 21) {
        print "<td>", $empsh[$emp][$sh];
    }
}
print "</table>";
[download]

Yes, it's mess :-)

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