Multitasking scheduling with alternate periods

In this paper, we consider the multitasking scheduling with alternate odd-period and even-period. For the minimization of makespan on one single machine, we present a 2-approximation algorithm for the general case and a 4 3 -approximation algorithm for a special case when jobs have identical release...

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Published in:Journal of combinatorial optimization Vol. 45; no. 3; p. 92
Main Authors: Huo, Yujia, Miao, Cuixia, Kong, Fanyu, Zhang, Yuzhong
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2023
Springer Nature B.V
Subjects:
Algorithms
Approximation
Combinatorics
Convex and Discrete Geometry
Dynamic programming
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Multitasking
Operations Research/Decision Theory
Optimization
Polynomials
Scheduling
Theory of Computation
Strongly NP-hard
Multitasking scheduling
Approximation algorithm
Pseudo-polynomial-time algorithm
ISSN:1382-6905, 1573-2886
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Abstract In this paper, we consider the multitasking scheduling with alternate odd-period and even-period. For the minimization of makespan on one single machine, we present a 2-approximation algorithm for the general case and a 4 3 -approximation algorithm for a special case when jobs have identical release dates. And we prove that the problem is strongly NP-hard when jobs have different release dates. For the minimization of makespan on identical parallel machines, we present a ( 5 2 - 1 m ) -approximation algorithm for the general case and a pseudo-polynomial time algorithm when the number of machines is constant. Furthermore, we prove that the single-machine scheduling of minimizing the lateness is strongly NP-hard.
AbstractList In this paper, we consider the multitasking scheduling with alternate odd-period and even-period. For the minimization of makespan on one single machine, we present a 2-approximation algorithm for the general case and a 43-approximation algorithm for a special case when jobs have identical release dates. And we prove that the problem is strongly NP-hard when jobs have different release dates. For the minimization of makespan on identical parallel machines, we present a (52-1m)-approximation algorithm for the general case and a pseudo-polynomial time algorithm when the number of machines is constant. Furthermore, we prove that the single-machine scheduling of minimizing the lateness is strongly NP-hard.
In this paper, we consider the multitasking scheduling with alternate odd-period and even-period. For the minimization of makespan on one single machine, we present a 2-approximation algorithm for the general case and a 4 3 -approximation algorithm for a special case when jobs have identical release dates. And we prove that the problem is strongly NP-hard when jobs have different release dates. For the minimization of makespan on identical parallel machines, we present a ( 5 2 - 1 m ) -approximation algorithm for the general case and a pseudo-polynomial time algorithm when the number of machines is constant. Furthermore, we prove that the single-machine scheduling of minimizing the lateness is strongly NP-hard.
ArticleNumber 92
Author Kong, Fanyu
Zhang, Yuzhong
Miao, Cuixia
Huo, Yujia
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  surname: Miao
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  organization: School of Mathematical Sciences, Qufu Normal University
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  fullname: Zhang, Yuzhong
  organization: Institute of Operations Research, Qufu Normal University
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Cites_doi 10.1016/j.cie.2009.04.014
10.1016/j.dam.2016.03.018
10.1080/00207543.2016.1208852
10.1007/BF00121681
10.1111/poms.12331
10.1007/s10878-020-00600-5
10.1007/s11590-015-0881-8
10.1109/ICSSSM.2018.8465050
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Copyright The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.
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SubjectTerms Algorithms
Approximation
Combinatorics
Convex and Discrete Geometry
Dynamic programming
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Multitasking
Operations Research/Decision Theory
Optimization
Polynomials
Scheduling
Theory of Computation
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