A note on makespan minimization in proportionate flow shops

We consider two generalizations of the proportionate flow shop scheduling problem with the makespan objective. Each job has a processing requirement and each machine has a characteristic value. In our first (second) case we assume that the time a job occupies a machine is the maximum (minimum) of the processing requirement of the job and the characteristic value of the machine. We show that the first case is NP-hard in the ordinary sense for three machines. For the second case we show that the makespan is a constant that is independent of the sequence even if the number of machines is larger than three.