Some Scheduling Problems With Job Rejection And A Learning Effect. (4th January 2022) - Toksari, M Duran; Atalay, Berrin
Abstract: In this paper, we examined single and parallel machine scheduling problems with a learning effect and job rejection simultaneously. In real life, job processing times decrease when there is a learning effect. In some cases, producers cannot process all the jobs and pay the penalty cost for these jobs that they do not process. In our study, learning effect and job rejection are considered at the same time. We examined four different objective functions. Our objectives for single-machine scheduling problems are makespan and rejection cost minimization, total completion time and rejection cost minimization and total absolute deviation of completion times (TADC) and rejection cost minimization. Our objective for parallel machines is makespan and rejection cost minimization. The problems are solved by mathematical models, and four different algorithms are proposed for the problems. From these algorithms, the same results are obtained with single-machine makespan and rejection cost minimization, parallel machine makespan and rejection cost minimization and total completion time and rejection cost minimization. The accuracy for these models is obtained as 100%. The proposed algorithm for TADC and rejection cost minimization yielded close-to-optimal results. Mathematical model and algorithm results for 10 jobs, 20 jobs and 30 jobs are compared and the results are presented. The obtained solutions are obtained in polynomial time.