Approximation schemes for parallel machine scheduling problems with controllable processing times

Abstract

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. Scope and purpose Most classical scheduling models assume fixed processing times for the jobs. However, in real-life applications the processing time of a job often depends on the amount of resources such as facilities, manpower, funds, etc. allocated to it, and so the processing time can be reduced when additional resources are given to the job. This speed up of the processing time of a job comes at a certain cost. A scheduling problem in which the processing times of the jobs can be reduced at some expense is called a scheduling problem with controllable processing times. We contribute by presenting new approximation algorithms for this kind of problems.