A dynamic optimisation approach for a single machine scheduling problem with machine conditions and maintenance decisions

Abstract

In modern production systems, considering machine conditions is becoming essential to achieving an overall optimisation of the production schedule. This paper studies a single machine scheduling problem, where the actual processing times of jobs depend on their position in the production sequence and maintenance is considered. Moreover, the machine is subject to an uncertain condition variation. There is a trade-off between rejecting a maintenance action, resulting in longer processing times, and accepting a maintenance action, leading to higher processing efficiency for future jobs. The problem is formulated as a finite-horizon Markov Decision Process. The objective is to minimise the makespan. Optimality properties are analysed, based on which a dynamic optimisation approach is developed. Computational experiments demonstrate the effectiveness of the proposed approach.

Keywords:

• Single machine scheduling
• machine condition
• Markov decision process
• dynamic optimisation approach
• maintenance

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Project number: 51775347). We thank the referees for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Project number: 51775347).

Notes on contributors

Wenhui Yang

Wenhui Yang is currently a Ph.D. student in industrial engineering in the School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China. Her research interests include production system modelling and optimisation and intelligent decision-making algorithm design.

Lu Chen

Lu Chen is Professor in the School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China. She received her double Ph.D. degrees in industrial engineering from the School of Mechanical Engineering, Shanghai Jiao Tong University of China & University of Nantes of France, in 2006. Her research interests include modelling and optimisation of production and logistics systems, intelligent decision-making algorithm design and development and optimisation of container terminal logistics operations. In these areas, she has published in refereed journals and coordinated multiple academic and industrial research projects.

Stèphane Dauzère-Pèrés

Stéphane Dauzère-Pèrés is Professor at the Center of Microelectronics in Provence (CMP) of Mines Saint-Etienne in France and Adjunct Professor at BI Norwegian Business School in Norway. He received the Ph.D. degree from the Paul Sabatier University in Toulouse, France, in 1992. His research interests broadly include modeling and optimisation of operations at various decision levels (from real-time to strategic) in manufacturing and logistics, with a special emphasis on semiconductor manufacturing. He has published more than 70 papers in international journals.