Research On Schedulingproblemswith Learning Effect Andcontrollable Processing Times

With increasingly competition of enterprises, many companies, especially someproduction-oriented companies have been seeking for better production model toenhance productivity and reduce production costs. So scheduling plays anincreasingly important role in business management, and its effective combinationwith business management has extensive application and practicality. In thescheduling field， many experts have studied varies models of learning effect, whichmeans that the processing time of a job scheduled in the later will be shortened withthe improvement of workers’ proficiency. In the paper, we propose a new learningeffect model based on other model: namely the actual processing time is the functionof its normal processing time, its position and compression variable. Then weconsider some scheduling problems in single machine and parallel machine under theproposed model.In the first section of this paper, we introduce some knowledge about scheduling,domestic and foreign research status, and its application etc. The second sectionconsiders the proposed learning effect model in a single machine. The objectives areto minimizing the makespan and control cost, the total completion time and controlcost and the total absolute differences in completion times and control cost, we showthat the problems can be solved in polynomial time respectively, and itscorresponding optimal algorithms and numerical examples are also given. The thirdsection considers parallel-machine scheduling problems. We proved that the problemsof minimizing the total machine load and control cost and minimizing totalcompletion time and control cost can be polynomial solved respectively, we also givealgorithms and numerical examples.