Approximation schemes for parallel machine scheduling problems with controllable processing times

We consider the problem of scheduling n independent jobs on m identical machines that operate in parallel. Each job has a controllable processing time. The fact that the jobs have a controllable processing time means that it is allowed to compress (a part of) the processing time of the job, in return for compression cost. We present the first known polynomial time approximation schemes for the non-preemptive case of several identical parallel machines scheduling problems with controllable processing times. Moreover, we study the problem when preemption is allowed and describe efficient exact and approximation algorithms.