Scheduling on parallel dedicated machines with job rejection - Mor, Baruch; Mosheiov, Gur (International journal of production research, 2024)
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.