Single-machine group scheduling problems with deteriorating and learning effect

Abstract

The concepts of deteriorating jobs and learning effects have been individually studied in many scheduling problems. However, most studies considering the deteriorating and learning effects ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as ‘group technology’ in the literature. In this paper, a new group scheduling model with deteriorating and learning effects is proposed, where learning effect depends not only on job position, but also on the position of the corresponding job group; deteriorating effect depends on its starting time of the job. This paper shows that the makespan and the total completion time problems remain polynomial optimal solvable under the proposed model. In addition, a polynomial optimal solution is also presented to minimise the maximum lateness problem under certain agreeable restriction.

Keywords:

• scheduling
• single-machine
• deteriorating and learning effects
• group technology

Acknowledgements

We are grateful to the editor and anonymous referees for their constructive comments on an earlier version of our paper.

Additional information

Funding

This work was partly supported by National Natural Science Foundation of China [grant number 11401065], [grant number 61302180], [grant number 71272085]; the China Postdoctoral Science Foundation funded project [grant number 2013M540698], [grant number 2014T70854]; the Foundation of Chongqing Education Commission [grant number KJ130606]; the Chongqing Municipal Science and Technology Commission of Natural Science Fund Projects [grant number cstc2014jcyjA00003]; and the Key Foundation of Chongqing Normal University [grant number 2011XLZ05].

Notes on contributors

Zhang Xingong

Xingong Zhang is an associate professor at Chongqing Normal University. He received his MS degree in mathematics from Zhengzhou University, China, in 2008 and PhD from University of Shanghai for Science and Technology, China, in 2011. At present, his publications include articles in international journals such as Information Science, Applied Mathematics and Computation, Mathematical and Computer Modeling, Annals of Operations Research, Asia-Pacific Journal of Operational Research, International Journal of Advanced Manufacture Technology, and International Journal of Combinatorics. His current research interests are computational complexity, approximation algorithm and scheduling problems. He has supervised five MS students in these areas.

Wang Yong

Yong Wang is currently a professor at School of Economics and Business Administration, Chongqing University, China. He received his PhD degree in management science from Chongqing University, China, in 1999. His research interests include logistics and supply chain management, optimisation theory and applications, etc. He has published papers in many journals, including Operations Research, International Journal of Production Research, International Journal of Production Economics, Mathematical Problems in Engineering, etc.

Bai Shikun

Shikun Bai is an associate professor at Chongqing Normal University. He received his BS degree and MS degree in mathematics from Chongqing Normal University, China, in 1993 and 2007, respectively. His current research interests are computational complexity, and scheduling problems.