Approximation schemes for scheduling on parallel machines

We discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The goal is to optimize objective functions that solely depend on the machine completion times. As a main result, we identify some conditions on the objective function, under which the resulting scheduling problems possess a polynomial-time approximation scheme. Our result contains, generalizes, improves, simplifies, and unifies many other results in this area in a natural way.