Approximation schemes for machine scheduling with resource (in-)dependent processing times

We consider two related scheduling problems: resource constrained scheduling on identical parallel machines and a generalization with resource dependent processing times. In both problems, jobs require a certain amount of an additional resource and have to be scheduled on machines minimizing the makespan, while at every point in time a given resource capacity is not exceeded. In the first variant of the problem the processing times and resource amounts are fixed, while in the second the former depends on the latter. We present asymptotic fully polynomial approximation schemes (AFPTAS) for the problems: For any e > 0 a schedule of length at most (1 + e) times the optimum plus an additive term of O(1/e2) is provided, and the running time is polynomially bounded in 1/e and the input length. Up to now only approximation algorithms with constant approximation ratios were known.