Abstract
This article aims to study the problems related to identical parallel-machine scheduling with setup, processing, and removal times under consideration of the learning effect. The objectives are to minimize the total completion time, total load, and total absolute deviation of job completion times (TADC) on all the machines. We show that these problems can be solved in time if the jobs satisfy an agreeable condition, i.e. implies that and for any two jobs Ji and Jj , , where n denotes the number of jobs, m denotes the number of machines, and Pi , si , and ri , respectively, denote the normal processing, setup, and removal times of job Ji . For the case where all jobs have a common learning factor for job processing, setup, and removal times, we prove that these problems can also be solved in time. In addition, we extend the problem under study to an unrelated parallel-machine environment and show that all the problems studied can be formulated as assignment problems and hence can be solved in time.
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