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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 970510, 10 pages
Research Article

Minimizing Total Weighted Completion Time on Single Machine with Past-Sequence-Dependent Setup Times and Exponential Time-Dependent and Position-Dependent Learning Effects

School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, China

Received 13 May 2009; Revised 29 August 2009; Accepted 17 September 2009

Academic Editor: Stevo Stević

Copyright © 2009 Kaibiao Sun and Hongxing Li. 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.


This paper addresses a single-machine problem in which the past-sequence-dependent (p-s-d) setup times and exponential time-dependent and position-dependent learning effects are considered. By the exponential time-dependent learning effect, it means that the processing time of a job is defined by an exponent function of the total actual processing time of the already processed jobs. The setup times are proportional to the length of the already processed jobs. The aim is to minimize the total weighted completion time, this is an NP-hard problem. Under certain conditions, it is shown that the classical WSPT rule is optimal for the problem.