Scheduling on parallel dedicated machines with job rejection

We study scheduling problems on parallel dedicated machines. Thus, each job can be processed on one specific machine only. The option of job-rejection is considered, and the total permitted rejection cost of all the jobs is bounded. Six scheduling problems are solved: ( $ i $ i ) minimising makespan, ( $ ii $ ii ) minimising makespan with release-dates, ( $ iii $ iii ) minimising total completion time, ( $ iv $ iv ) minimising total weighted completion time, ( $ v $ v ) minimising total load, and ( $ vi $ vi ) minimising maximum tardiness. Pseudo-polynomial dynamic programming algorithms are introduced for all these NP-hard problems.