Moreover, for the latter we devise the best possible resource augmentation result regarding speed: a polynomial time algorithm which computes a solution with optimal cost at 1+epsilon speedup. Finally, we present an elegant QPTAS for the special case where the cost functions of the jobs fall into at most log(n) many classes. This algorithm allows the jobs even to have up to log(n) many distinct release dates. All proposed quasi-polynomial time algorithms require the input data to be quasi-polynomially bounded.