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The Scientific World Journal
Volume 2014, Article ID 620150, 9 pages
Research Article

Single Machine Scheduling and Due Date Assignment with Past-Sequence-Dependent Setup Time and Position-Dependent Processing Time

1College of Mathematics and Systems Sciences, Shenyang Normal University, Shenyang, Liaoning 110034, China
2Department of Industrial Management, Nan Kai University of Technology, Nantou 542, Taiwan

Received 23 July 2014; Accepted 14 August 2014; Published 27 August 2014

Academic Editor: Dehua Xu

Copyright © 2014 Chuan-Li Zhao et al. 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 considers single machine scheduling and due date assignment with setup time. The setup time is proportional to the length of the already processed jobs; that is, the setup time is past-sequence-dependent (p-s-d). It is assumed that a job's processing time depends on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs, and the cost of due date assignment. We analyze these problems with two different due date assignment methods. We first consider the model with job-dependent position effects. For each case, by converting the problem to a series of assignment problems, we proved that the problems can be solved in time. For the model with job-independent position effects, we proved that the problems can be solved in time by providing a dynamic programming algorithm.