# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020174

## Parallel-machine scheduling in shared manufacturing

 1 School of Management and E-Business, Contemporary Business and Trade Research Center, Zhejiang Gongshang University, Hangzhou 310018, Zhejiang, P. R. China 2 Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Kowloon, Hong Kong

* Corresponding author: Yiwei Jiang

Received  May 2020 Revised  August 2020 Published  December 2020

Fund Project: This research was supported in part by the National Natural Science Foundation of China under grant numbers 11971434 and 11871327, Zhejiang Provincial Natural Science Foundation of China under grant number LY21G010002, and the Contemporary Business and Trade Research Center of Zhejiang Gongshang University, which is a key Research Institute of Social Sciences and Humanities of the Ministry of Education of China. Cheng was supported in part by The Hong Kong Polytechnic University under the Fung Yiu King - Wing Hang Bank Endowed Professorship in Business Administration

We consider parallel-machine scheduling in the context of shared manufacturing where each job has a machine set to which it can be assigned for processing. Such a set is called the processing set. In the shared manufacturing setting, a job can be assigned not only to certain machines for processing, but can also be processed on the remaining machines at a certain cost. Compared with traditional scheduling with job rejection, the scheduling model under study embraces the notion of sustainable manufacturing. Showing that the problem is NP-hard, we develop a fully polynomial-time approximation scheme to solve the problem when the number of machines is fixed.

Citation: Min Ji, Xinna Ye, Fangyao Qian, T.C.E. Cheng, Yiwei Jiang. Parallel-machine scheduling in shared manufacturing. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020174
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