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The Scientific World Journal
Volume 2014 (2014), Article ID 471016, 7 pages
Research Article

Some Single-Machine Scheduling Problems with Learning Effects and Two Competing Agents

1Mathematics Department, Zhoukou Normal University, Zhoukou 466001, China
2College of Mechanical and Electrical, Harbin Institute of Technology, Harbin 150001, China
3College of Sciences, East China Institute of Technology, Nanchang 330013, China
4Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China

Received 29 April 2014; Accepted 10 May 2014; Published 25 May 2014

Academic Editor: Dar-Li Yang

Copyright © 2014 Hongjie Li 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 study considers a scheduling environment in which there are two agents and a set of jobs, each of which belongs to one of the two agents and its actual processing time is defined as a decreasing linear function of its starting time. Each of the two agents competes to process its respective jobs on a single machine and has its own scheduling objective to optimize. The objective is to assign the jobs so that the resulting schedule performs well with respect to the objectives of both agents. The objective functions addressed in this study include the maximum cost, the total weighted completion time, and the discounted total weighted completion time. We investigate three problems arising from different combinations of the objectives of the two agents. The computational complexity of the problems is discussed and solution algorithms where possible are presented.