  In this paper, we will find a pseudopolynomial algorithm to solve $Qm \mid
\mid L_{\max}$ and then we will prove that it is impossible to get any
constant-factor approximation in polynomial time, and thus also impossible to
have a PTAS for this problem. We will also show that the the problem when we
don't assume a fixed number of machines, $P \mid \mid L_{\max}$, is strongly
NP-hard.
