Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date
•Fully polynomial time approximation scheme for early work maximization is proposed.•The new FPTAS dominates PTAS for the two-machine case known from the literature.•Complexity of parallel machine scheduling problems with common due date is studied.•Theoretical studies are completed with computation...
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| Vydáno v: | European journal of operational research Ročník 284; číslo 1; s. 67 - 74 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.07.2020
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | •Fully polynomial time approximation scheme for early work maximization is proposed.•The new FPTAS dominates PTAS for the two-machine case known from the literature.•Complexity of parallel machine scheduling problems with common due date is studied.•Theoretical studies are completed with computational experiments.
We study the scheduling problem on parallel identical machines in order to maximize the total early work, i.e. the parts of non-preemptive jobs executed before a common due date, and investigate mainly the model with a fixed number of machines, for which a dynamic programming approach and a fully polynomial time approximation scheme (FPTAS) are proposed. The proposal of these methods allowed us to establish the complexity and approximability status of this problem more exactly. Moreover, since our FPTAS can be also applied for the two-machine case, we improve considerably the result known in the literature for this model, in which a polynomial time approximation scheme (PTAS) was given. The new FPTAS has not only the best computational complexity, but also the much better approximation ratio than the PTAS. Finally, the theoretical studies are completed with computational experiments, performed for dynamic programming, PTAS and FPTAS, showing the high efficiencies of FPTAS both in terms of time consumption and solution quality. |
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| AbstractList | •Fully polynomial time approximation scheme for early work maximization is proposed.•The new FPTAS dominates PTAS for the two-machine case known from the literature.•Complexity of parallel machine scheduling problems with common due date is studied.•Theoretical studies are completed with computational experiments.
We study the scheduling problem on parallel identical machines in order to maximize the total early work, i.e. the parts of non-preemptive jobs executed before a common due date, and investigate mainly the model with a fixed number of machines, for which a dynamic programming approach and a fully polynomial time approximation scheme (FPTAS) are proposed. The proposal of these methods allowed us to establish the complexity and approximability status of this problem more exactly. Moreover, since our FPTAS can be also applied for the two-machine case, we improve considerably the result known in the literature for this model, in which a polynomial time approximation scheme (PTAS) was given. The new FPTAS has not only the best computational complexity, but also the much better approximation ratio than the PTAS. Finally, the theoretical studies are completed with computational experiments, performed for dynamic programming, PTAS and FPTAS, showing the high efficiencies of FPTAS both in terms of time consumption and solution quality. |
| Author | Liang, Yage Wang, Wen Chen, Xin Błażewicz, Jacek Sterna, Małgorzata |
| Author_xml | – sequence: 1 givenname: Xin surname: Chen fullname: Chen, Xin email: chenxin.lut@hotmail.com organization: School of Electronics and Information Engineering, Liaoning University of Technology, Shiying 169, Jinzhou 121001, China – sequence: 2 givenname: Yage surname: Liang fullname: Liang, Yage email: liangyage@mail.dlut.edu.cn organization: School of Software, Dalian University of Technology, Tuqiang 321, Dalian 116023, China – sequence: 3 givenname: Małgorzata surname: Sterna fullname: Sterna, Małgorzata email: malgorzata.sterna@cs.put.poznan.pl organization: Institute of Computing Science, Poznan University of Technology, Piotrowo 2, Poznan 60–965, Poland – sequence: 4 givenname: Wen surname: Wang fullname: Wang, Wen email: wangwen.lut@outlook.com organization: School of Electronics and Information Engineering, Liaoning University of Technology, Shiying 169, Jinzhou 121001, China – sequence: 5 givenname: Jacek surname: Błażewicz fullname: Błażewicz, Jacek email: jblazewicz@cs.put.poznan.pl organization: Institute of Computing Science, Poznan University of Technology, Piotrowo 2, Poznan 60–965, Poland |
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| Keywords | Fully polynomial time approximation scheme Late work Scheduling Early work Parallel identical machines |
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