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Mathematical Problems in Engineering
Volume 2013, Article ID 218981, 8 pages
Research Article

Minimizing the Makespan for Scheduling Problems with General Deterioration Effects

1School of Economics and Management, Southeast University, Nanjing, Jiangsu 211189, China
2DeGroote School of Business, McMaster University, Hamilton, ON, Canada L8S 4M4
3School of Sciences, East China Institute of Technology, Fuzhou, Jiangxi 344000, China

Received 29 August 2013; Accepted 19 November 2013

Academic Editor: Yunqiang Yin

Copyright © 2013 Xianyu Yu 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 investigates the scheduling problems with general deterioration models. By the deterioration models, the actual processing time functions of jobs depend not only on the scheduled position in the job sequence but also on the total weighted normal processing times of the jobs already processed. In this paper, the objective is to minimize the makespan. For the single-machine scheduling problems with general deterioration effects, we show that the considered problems are polynomially solvable. For the flow shop scheduling problems with general deterioration effects, we also show that the problems can be optimally solved in polynomial time under the proposed conditions.