Splitting versus setup trade-offs for scheduling to minimize weighted completion time

We study scheduling problems when jobs can be split and a setup is required before processing each part, to minimize the weighted sum of completion times. Using a simple splitting strategy and a reduction to an orders scheduling problem we derive a 2-approximation algorithm for the case with uniform weights and setups, improving upon previous work. We extend this idea to the general identical machine case and conclude by designing a constant factor approximation algorithm when machines are unrelated.