Job Shop Scheduling Problems withControllable Processing

Most scheduling models assume that the jobs have xed processing times. 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 its processing time can be reduced when additional resources are assigned to the job. 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. In this paper we study the job shop scheduling problem under the assumption that the jobs have controllable processing times. We consider two models of controllable processing times: continuous and discrete. For both models we present polynomial time approximation schemes when the number of machines and the number of operations per job are xed.