New index priority rules for no-wait flow shops

We derive an index priority rule for an m-machine no-wait flow shop with the minimum makespan objective and specially-structured job processing times. Our rule generalizes the previously known rules for two special cases of the problem. We also derive an index priority rule for a two-machine no-wait flow shop with the minimum weighted total job completion time objective when all jobs have the same processing time on the first machine. We then show that additional index priority rules can be derived for the latter problem with other scheduling objectives. Finally, we discuss extensions to flow shops with blocking and no-wait job shops and open shops.