{"title":"具有作业拒绝的机器调度与DeJong学习效应","authors":"Jie Gao, Juan Zou, Xiaoxuan Cheng","doi":"10.3934/mfc.2022024","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>This paper mainly discusses machine scheduling problems with job rejection and DeJong's learning effect. The goal is to determine the job sequence of the accepted jobs so as to minimize the scheduling cost of the accepted jobs plus the total rejection penalty of the rejected jobs. The scheduling costs of the accepted jobs are the makespan and the total completion time. For the single-machine setting, we show that both of the objectives can be optimally solved in polynomial time. For the parallel-machine setting, we show that minimizing the total completion time of the accepted jobs plus the total rejection penalty of the rejected jobs is still polynomially solvable, whereas the other problem is <inline-formula><tex-math id=\"M1\">\\begin{document}$ NP $\\end{document}</tex-math></inline-formula>-hard, for which we provide a fully polynomial-time approximation scheme (FPTAS).</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Machine scheduling with job rejection and DeJong's learning effect\",\"authors\":\"Jie Gao, Juan Zou, Xiaoxuan Cheng\",\"doi\":\"10.3934/mfc.2022024\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p style='text-indent:20px;'>This paper mainly discusses machine scheduling problems with job rejection and DeJong's learning effect. The goal is to determine the job sequence of the accepted jobs so as to minimize the scheduling cost of the accepted jobs plus the total rejection penalty of the rejected jobs. The scheduling costs of the accepted jobs are the makespan and the total completion time. For the single-machine setting, we show that both of the objectives can be optimally solved in polynomial time. For the parallel-machine setting, we show that minimizing the total completion time of the accepted jobs plus the total rejection penalty of the rejected jobs is still polynomially solvable, whereas the other problem is <inline-formula><tex-math id=\\\"M1\\\">\\\\begin{document}$ NP $\\\\end{document}</tex-math></inline-formula>-hard, for which we provide a fully polynomial-time approximation scheme (FPTAS).</p>\",\"PeriodicalId\":93334,\"journal\":{\"name\":\"Mathematical foundations of computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical foundations of computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/mfc.2022024\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical foundations of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/mfc.2022024","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 1
摘要
This paper mainly discusses machine scheduling problems with job rejection and DeJong's learning effect. The goal is to determine the job sequence of the accepted jobs so as to minimize the scheduling cost of the accepted jobs plus the total rejection penalty of the rejected jobs. The scheduling costs of the accepted jobs are the makespan and the total completion time. For the single-machine setting, we show that both of the objectives can be optimally solved in polynomial time. For the parallel-machine setting, we show that minimizing the total completion time of the accepted jobs plus the total rejection penalty of the rejected jobs is still polynomially solvable, whereas the other problem is \begin{document}$ NP $\end{document}-hard, for which we provide a fully polynomial-time approximation scheme (FPTAS).
Machine scheduling with job rejection and DeJong's learning effect
This paper mainly discusses machine scheduling problems with job rejection and DeJong's learning effect. The goal is to determine the job sequence of the accepted jobs so as to minimize the scheduling cost of the accepted jobs plus the total rejection penalty of the rejected jobs. The scheduling costs of the accepted jobs are the makespan and the total completion time. For the single-machine setting, we show that both of the objectives can be optimally solved in polynomial time. For the parallel-machine setting, we show that minimizing the total completion time of the accepted jobs plus the total rejection penalty of the rejected jobs is still polynomially solvable, whereas the other problem is \begin{document}$ NP $\end{document}-hard, for which we provide a fully polynomial-time approximation scheme (FPTAS).