Complexity of server scheduling on parallel dedicated machines subject to fixed job sequences

We study server scheduling on parallel dedicated machines to minimize the makespan subject to given processing sequences. Before a job starts its processing on its designated machine, a loading operation must be performed, which is undertaken by a server shared by all the jobs. While the two-machine problem is polynomially solvable, we show that the problem becomes binaryNP-hard when the number of machines is three, and propose a pseudo-polynomial algorithm to solve the problem with a constant number of machines.