@article{802e0aabd06e485cbaa12fa5590ffbc5,
title = "Approximation algorithms for bi-objective parallel-machine scheduling in green manufacturing",
abstract = "We consider bi-objective parallel-machine scheduling in green manufacturing to minimize the makespan and total processing cost. Each machine has a different constant processing cost per unit time. For the objective of minimizing the makespan, given a total cost budget, we provide an approximation algorithm with a worst-case ratio of [Formula presented], which improves the previous bound of 2. For the objective of minimizing the total processing cost, subject to all the jobs must be completed before a given common deadline, we provide an approximation algorithm with a worst-case ratio of [Formula presented], where r is the ratio of the maximum to the minimum processing cost per unit time on a machine.",
keywords = "Approximation algorithm, Green manufacturing, Parallel-machine scheduling, Worst-case ratio",
author = "Yiwei Jiang and Xuelian Tang and Kai Li and Cheng, {T. C.E.} and Min Ji",
note = "Funding Information: We are thankful to two anonymous referees for their helpful comments and suggestions on an earlier version of our paper. This research was supported in part by the Zhejiang Provincial Natural Science Foundation of China under grant number LZ23G010001 , LY21G010002 ; National Natural Science Foundation of China under grant numbers 11971434 , 11871327 , 72271070 , and 71871076 ; Natural Science Foundation of Anhui Province under grant number 2208085J07 ; 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 . Funding Information: Acknowledgments: We are thankful to two anonymous referees for their helpful comments and suggestions on an earlier version of our paper. This research was supported in part by the National Natural Science Foundation of China under grant numbers 11971434 , 11871327 , 72271070 , and 71871076 ; Zhejiang Provincial Natural Science Foundation of China under grant number LY21G010002 ; Natural Science Foundation of Anhui Province, China under grant number 2208085J07 ; 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. Publisher Copyright: {\textcopyright} 2022 Elsevier Ltd",
year = "2023",
month = feb,
doi = "10.1016/j.cie.2022.108949",
language = "English",
volume = "176",
journal = "Computers and Industrial Engineering",
issn = "0360-8352",
publisher = "Elsevier Ltd",
}