Any reference is appreciated.
There are $n$ jobs and $m$ machines, machines has speeds and jobs have processing times. It takes $p_j/s_i$ units of time for machine $i$ with speed $s_i$ to process job $j$ with processing requirement $p_j$. The objective is to find a non-preemptive schedule to minimize the makespan of the schedule.
Chandra Chekuri and Michael Bender studied it under constraint: "precedence constraints between jobs are given in the form of a partial order" at CB.
I am looking for reference of the problem without precedence constraints. Shmoys, Wein, and Williamson SWH showed a 2-approximation algorithm.
Is there any other result?