An FPTAS for two performance measures for the relocation scheduling problem subject to fixed processing sequences
In this paper we consider a resource-constrained scheduling problem on two parallel dedicated machines with given fixed processing sequences of jobs assigned to each one of the machines. The problem is to determine the starting times of all jobs, subject to the resource constraint, in order to minim...
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| Published in | Optimization letters Vol. 16; no. 4; pp. 1181 - 1196 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.05.2022
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1862-4472 1862-4480 |
| DOI | 10.1007/s11590-021-01772-7 |
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| Abstract | In this paper we consider a resource-constrained scheduling problem on two parallel dedicated machines with given fixed processing sequences of jobs assigned to each one of the machines. The problem is to determine the starting times of all jobs, subject to the resource constraint, in order to minimize some given performance measure. Lin et al. (J Sched 19(2):153–163, 2016) showed that the problem is NP-hard in the ordinary sense under the performance measures of weighted total tardiness and weighted number of tardy jobs, and questioned the existence of approximation schemes. In this paper we answer their question in the affirmative by designing fully polynomial time approximation schemes. |
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| AbstractList | In this paper we consider a resource-constrained scheduling problem on two parallel dedicated machines with given fixed processing sequences of jobs assigned to each one of the machines. The problem is to determine the starting times of all jobs, subject to the resource constraint, in order to minimize some given performance measure. Lin et al. (J Sched 19(2):153–163, 2016) showed that the problem is NP-hard in the ordinary sense under the performance measures of weighted total tardiness and weighted number of tardy jobs, and questioned the existence of approximation schemes. In this paper we answer their question in the affirmative by designing fully polynomial time approximation schemes. |
| Author | Halman, Nir Vinetz, Uriel |
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| Cites_doi | 10.1016/j.disopt.2006.06.003 10.1007/s10951-015-0455-8 10.1287/moor.1090.0391 10.1080/00207168808803664 10.1007/s10951-009-0151-7 10.1137/130925153 10.1177/239980838601300101 |
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| Keywords | approximation sets and functions Dynamic programming FPTAS Relocation scheduling |
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| References | Amir, Kaplan (CR1) 1988; 25 Halman, Klabjan, Mostagir, Orlin, Simchi-Levi (CR3) 2009; 34 Kononov, Lin (CR5) 2006; 3 Halman, Klabjan, Li, Orlin, Simchi-Levi (CR2) 2014; 28 Kaplan (CR4) 1986; 13 Kononov, Lin (CR6) 2010; 13 Lin, Hwang, Kononov (CR7) 2016; 19 N Halman (1772_CR3) 2009; 34 EH Kaplan (1772_CR4) 1986; 13 A Amir (1772_CR1) 1988; 25 AV Kononov (1772_CR5) 2006; 3 AV Kononov (1772_CR6) 2010; 13 N Halman (1772_CR2) 2014; 28 BMT Lin (1772_CR7) 2016; 19 |
| References_xml | – volume: 3 start-page: 366 issue: 4 year: 2006 end-page: 381 ident: CR5 article-title: On relocation problems with multiple identical working crews publication-title: Discrete Optim. doi: 10.1016/j.disopt.2006.06.003 – volume: 19 start-page: 153 issue: 2 year: 2016 end-page: 163 ident: CR7 article-title: Relocation scheduling subject to fixed processing sequences publication-title: J. Sched. doi: 10.1007/s10951-015-0455-8 – volume: 34 start-page: 674 year: 2009 end-page: 685 ident: CR3 article-title: A fully polynomial time approximation scheme for single-item stochastic inventory control with discrete demand publication-title: Math. Oper. Res. doi: 10.1287/moor.1090.0391 – volume: 25 start-page: 101 issue: 2 year: 1988 end-page: 110 ident: CR1 article-title: Relocation problems are hard publication-title: Int. J. Comput. Math. doi: 10.1080/00207168808803664 – volume: 13 start-page: 123 issue: 2 year: 2010 end-page: 129 ident: CR6 article-title: Minimizing the total weighted completion time in the relocation problem publication-title: J. Sched. doi: 10.1007/s10951-009-0151-7 – volume: 28 start-page: 1725 year: 2014 end-page: 1796 ident: CR2 article-title: Fully polynomial time approximation schemes for stochastic dynamic programs publication-title: SIAM J. Discrete Math. doi: 10.1137/130925153 – volume: 13 start-page: 5 issue: 1 year: 1986 end-page: 19 ident: CR4 article-title: Relocation models for public housing redevelopment programs publication-title: Environ. Plan. B Plan. Des. doi: 10.1177/239980838601300101 – volume: 19 start-page: 153 issue: 2 year: 2016 ident: 1772_CR7 publication-title: J. Sched. doi: 10.1007/s10951-015-0455-8 – volume: 13 start-page: 5 issue: 1 year: 1986 ident: 1772_CR4 publication-title: Environ. Plan. B Plan. Des. doi: 10.1177/239980838601300101 – volume: 34 start-page: 674 year: 2009 ident: 1772_CR3 publication-title: Math. Oper. Res. doi: 10.1287/moor.1090.0391 – volume: 28 start-page: 1725 year: 2014 ident: 1772_CR2 publication-title: SIAM J. Discrete Math. doi: 10.1137/130925153 – volume: 25 start-page: 101 issue: 2 year: 1988 ident: 1772_CR1 publication-title: Int. J. Comput. Math. doi: 10.1080/00207168808803664 – volume: 13 start-page: 123 issue: 2 year: 2010 ident: 1772_CR6 publication-title: J. Sched. doi: 10.1007/s10951-009-0151-7 – volume: 3 start-page: 366 issue: 4 year: 2006 ident: 1772_CR5 publication-title: Discrete Optim. doi: 10.1016/j.disopt.2006.06.003 |
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| Title | An FPTAS for two performance measures for the relocation scheduling problem subject to fixed processing sequences |
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