  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.
  We study this problem from the perspective of approximability and provide
constant factor approximations as well as an inapproximability result. Prior to
this work, only the NP-hardness of the unweighted case and the polynomial
solvability of a certain special case were known.
