Unrelated Parallel Machines Scheduling with a Truncated Job-dependent Learning Effect

The majority of this paper dealing with unrelated parallel machines scheduling problems with a truncated job-dependent learning effect, in which the actual processing time of a job is a function which depends not only on the jobdependent learning effect but also on a control parameter. The goal is to determine the jobs assigned to corresponding each machine and the corresponding optimal schedule to minimize the total machine load and the total completion time respectively. If the number of machines is a given constant, we propose efficient polynomial time algorithms respectively.