Approximating Weighted Completion Time for Order Scheduling with Setup Times

Alexander Mäcker, Friedhelm Meyer auf der Heide, Simon Pukrop

Abstract: Consider a scheduling problem in which jobs need to be processed on a single machine. Each job has a weight and is composed of several operations belonging to different families. The machine needs to perform a setup between the processing of operations of different families. A job is completed when its latest operation completes and the goal is to minimize the total weighted completion time of all jobs.