We propose a polynomial time approximation scheme for schedu\-ling
a set of dedicated tasks on a constant number $m$ of processors in
order to minimize the sum of completion times $Pm| \mbox{fix}_j
|\sum C_j$. In addition we give a polynomial time approximation
scheme for the weighted preemptive problem with release dates,
$Pm| \mbox{fix}_j,pmtn,r_j |\sum w_j C_j$.