Paper:

# Unrelated Parallel-Machine Scheduling with Maintenance Activities and Rejection Penalties for Minimizing Total Cost

## Xiaona Yang^{*,**,†}, Can Peng^{*}, Lei Jin^{*}, and Qiangyi Li^{***}

^{*}College of Economics and Management, Nanjing University of Aeronautics and Astronautics

29 Jiangjun Road, Jiangning District, Nanjing City, Jiangsu 211106, China

^{†}Corresponding author

^{**}Management School, Henan University of Science and Technology, Henan, China

^{***}College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China

During the production process, regular maintenance is necessary and important to maintain high efficiency, because machines inevitably fail with increasing use. However, certain tasks are often neglected due to time and budget constraints, and other factors. In this regard, we propose the unrelated parallel-machine scheduling problem with maintenance and rejection penalties, wherein the ultimate objective is to minimize total cost while identifying the optimal maintenance frequencies, optimal maintenance positions, set of rejected jobs, and optimal scheduled job sequence. Considering resource constraints, the maintenance cost is controlled by the upper bound of the total maintenance frequency. Based on these factors, the optimal polynomial-time solution and its computational complexity with a fixed number of machines are presented. As an illustrative example, it was determined that the scheduling method proposed in this report is effective and practical.

*Int. J. Automation Technol.*, Vol.13, No.6, pp. 787-795, 2019.

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