Single machine controllable scheduling with bounded makespan
In a controllable scheduling environment, the processing time of a job can be shortened by allocating extra resource at a cost, or the job can be declined for processing by paying a penalty. We investigate the single machine controllable scheduling to minimize the sum of the total resource consumpti...
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| Vydáno v: | Theoretical computer science Ročník 1060; s. 115642 |
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Elsevier B.V
18.01.2026
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| ISSN: | 0304-3975 |
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| Abstract | In a controllable scheduling environment, the processing time of a job can be shortened by allocating extra resource at a cost, or the job can be declined for processing by paying a penalty. We investigate the single machine controllable scheduling to minimize the sum of the total resource consumption cost, the total job rejection cost, and the makespan of the accepted jobs, where the makespan is upper bounded and the job processing time is a decreasing linear function in the amount of allocated resource. We first show that the studied problem is polynomial solvable if the makespan is unbounded, but otherwise is NP-hard, and characterize important structural properties for the optimal solution; we then take advantage of the structural properties to design several algorithms for the problem, including a pseudo-polynomial time dynamic programming exact algorithm, an O(n2)-time n-approximation algorithm where n is the number of jobs, and building on top of the dynamic programming exact algorithm, the n-approximation algorithm and the bound improvement procedure, two fully polynomial time approximation schemes. |
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| AbstractList | In a controllable scheduling environment, the processing time of a job can be shortened by allocating extra resource at a cost, or the job can be declined for processing by paying a penalty. We investigate the single machine controllable scheduling to minimize the sum of the total resource consumption cost, the total job rejection cost, and the makespan of the accepted jobs, where the makespan is upper bounded and the job processing time is a decreasing linear function in the amount of allocated resource. We first show that the studied problem is polynomial solvable if the makespan is unbounded, but otherwise is NP-hard, and characterize important structural properties for the optimal solution; we then take advantage of the structural properties to design several algorithms for the problem, including a pseudo-polynomial time dynamic programming exact algorithm, an O(n2)-time n-approximation algorithm where n is the number of jobs, and building on top of the dynamic programming exact algorithm, the n-approximation algorithm and the bound improvement procedure, two fully polynomial time approximation schemes. |
| ArticleNumber | 115642 |
| Author | Lin, Guohui Guo, Yanjie Luo, Wenchang |
| Author_xml | – sequence: 1 givenname: Yanjie orcidid: 0009-0004-5471-9819 surname: Guo fullname: Guo, Yanjie email: guoyanjier@163.com organization: School of Mathematics and Statistics, Ningbo University, Ningbo, China – sequence: 2 givenname: Wenchang orcidid: 0000-0002-0335-3253 surname: Luo fullname: Luo, Wenchang email: luowenchang@163.com organization: School of Mathematics and Statistics, Ningbo University, Ningbo, China – sequence: 3 givenname: Guohui orcidid: 0000-0003-4283-3396 surname: Lin fullname: Lin, Guohui email: guohui@ualberta.ca organization: Department of Computing Science, University of Alberta, Edmonton, Canada |
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| Cites_doi | 10.1016/0166-218X(90)90105-L 10.1080/00207543.2024.2314714 10.1007/s10951-015-0417-1 10.1016/j.ijpe.2017.12.025 10.1016/0167-6377(95)91591-Z 10.1007/s10951-022-00723-z 10.1016/j.ijpe.2015.12.014 10.1080/00207543.2015.1136081 10.1080/05695558008974515 10.1007/s10878-021-00842-x 10.1504/IJOR.2019.098312 10.1007/s10878-020-00649-2 10.1007/s10951-012-0303-z 10.1016/j.ejor.2021.03.034 10.1016/j.ijpe.2013.12.021 10.1007/s10107-005-0641-0 10.1016/S0167-6377(99)00066-8 10.1007/s10951-022-00745-7 10.1016/0377-2217(90)90376-M 10.1007/s10479-018-2866-3 10.1016/j.dam.2007.02.003 10.1016/S0196-6774(03)00078-6 10.1016/j.ejor.2023.11.002 10.1016/S0167-5060(08)70356-X 10.1137/S0895480196300522 10.1016/j.ejor.2008.10.006 |
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| Keywords | Controllable scheduling Makespan Approximation algorithm Single machine scheduling Job rejection |
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| SubjectTerms | Approximation algorithm Controllable scheduling Job rejection Makespan Single machine scheduling |
| Title | Single machine controllable scheduling with bounded makespan |
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