Planning jobs as partition problem
I found the solution of the solution of this algorithm in this book: Handbook of Scheduling: Algorithms, Models, and Performance Analysis . 


In Theorem 3.4, they show an optimal algorithm for the preemptive case.
The largest processing time first algorithm has worst case bound of $\frac{4}{3} − \frac{1}{3k} $ if $t_i=0, \forall i$ for non-preemptive case


I will apply this largest processing time first to the general case and see how it works in practice.