A note: on the two-stage flowshop with dedicated machines to minimize total load

We study scheduling problems on a two-stage flowshop, where stage 1 consists of a single (critical) machine and there are a number of parallel dedicated machines in stage 2. The scheduling measure considered is minimum total load. Related measures such as total weighted load, total completion time and total weighted completion time, are also studied. Under a common assumption for this machine setting (of block processing on the critical machine), all these problems are shown to have a polynomial time solution. The general setting in which jobs are not processed in blocks on the critical machine is also discussed. A heuristic is proposed, analyzed and tested.