Research On Some Scheduling Problems With Learning Effect

Scheduling plays a more important role in business management especially enterpriseproduction and operation management. Management also needs a finer, digital theory tosupport, so the combination of scheduling and management greatly adapted to the needs ofmanagement development. Initially, researchers on learning effects often considered theimpact of a single factor, such as the location of the processing jobs, the jobs have beencompleted, and so on. With further research, some scholars began to consider new influencingfactors, some considered different factors simultaneous, others gave different factors withdifferent learning indices. These make the research of learning effect more perfect andpractical. Motivated by this observation, we propose a truncated position-weighted learningmodel based on sum-of-logarithm-processing-times and job position. Then, we consider somescheduling problems under the proposed model.The first chapter of this paper describes some scheduling knowledge related, thebackground and application etc. The second chapter considers the learning effect modelproposed in this paper. This paper shows that the single-machine scheduling problems tominimize the makespan, the sum of the th power of job completion times, the sum ofweighted completion times and the sum of weighted discounted completion times arepolynomially solvable under the proposed model. The third chapter considers single-machinescheduling problems with learning effect and release times. We provide several dominanceproperties and lower bounds for the problem of minimizing the makespan and two lowerbounds for the problem of minimizing the sum of completion times, so the branch-and-boundalgorithm can be used to solve them, and an example is given for the problem of minimizingthe sum of completion times to show how to use branch-and-bound algorithm. The fourthchapter considers single-machine scheduling problems with learning effect and due date. Thispaper shows that the problems to minimize the total tardiness are polynomially solvable. Thenwe consider a due-window problem for the special cases of the learning model and analgorithm developed to solve the problem.