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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 682738, 7 pages
Research Article

Due Date Single Machine Scheduling Problems with Nonlinear Deterioration and Learning Effects and Past Sequence Dependent Setup Times

Kırıkkale Vocational School, Kırıkkale University, 71451 Kırıkkale, Turkey

Received 26 February 2014; Revised 7 July 2014; Accepted 9 July 2014; Published 23 July 2014

Academic Editor: Sabri Arik

Copyright © 2014 Hüseyin Ceylan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present some problems against due dates with nonlinear learning and deterioration effects and past sequence dependent setup times. In this study, two effects (learning and deterioration) are used for the same processing time. The processing time of a job is shorter if it is scheduled later, rather than in the sequence. This phenomenon is known in the literature as a “learning effect.” On the other hand, in many realistic scheduling settings, a job processed later consumes more time than the same job processed earlier—this is known as scheduling with deteriorating jobs. In the past sequence dependent setup times approach, the setup time of a job is proportionate to the sum of processing times of the jobs already scheduled. In this study, we demonstrated that some problems with due dates remain polynomially solvable. However, for some other problems, we concentrated on finding polynomially solves under their special cases.