An FPTAS for the parallel two-stage flowshop problem
We consider the NP-hard m-parallel two-stage flowshop problem, abbreviated as the (m,2)-PFS problem, where we need to schedule n jobs to m parallel identical two-stage flowshops in order to minimize the makespan, i.e. the maximum completion time of all the jobs on the m flowshops. The (m,2)-PFS prob...
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| Published in: | Theoretical computer science Vol. 657; pp. 64 - 72 |
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02.01.2017
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| Abstract | We consider the NP-hard m-parallel two-stage flowshop problem, abbreviated as the (m,2)-PFS problem, where we need to schedule n jobs to m parallel identical two-stage flowshops in order to minimize the makespan, i.e. the maximum completion time of all the jobs on the m flowshops. The (m,2)-PFS problem can be decomposed into two subproblems: to assign the n jobs to the m parallel flowshops, and for each flowshop to schedule the jobs assigned to the flowshop. We first present a pseudo-polynomial time dynamic programming algorithm to solve the (m,2)-PFS problem optimally, for any fixed m, based on an earlier idea for solving the (2,2)-PFS problem. Using the dynamic programming algorithm as a subroutine, we design a fully polynomial-time approximation scheme (FPTAS) for the (m,2)-PFS problem. |
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| AbstractList | We consider the NP-hard m-parallel two-stage flowshop problem, abbreviated as the (m,2)-PFS problem, where we need to schedule n jobs to m parallel identical two-stage flowshops in order to minimize the makespan, i.e. the maximum completion time of all the jobs on the m flowshops. The (m,2)-PFS problem can be decomposed into two subproblems: to assign the n jobs to the m parallel flowshops, and for each flowshop to schedule the jobs assigned to the flowshop. We first present a pseudo-polynomial time dynamic programming algorithm to solve the (m,2)-PFS problem optimally, for any fixed m, based on an earlier idea for solving the (2,2)-PFS problem. Using the dynamic programming algorithm as a subroutine, we design a fully polynomial-time approximation scheme (FPTAS) for the (m,2)-PFS problem. |
| Author | Tong, Weitian Hu, Jueliang Lin, Guohui Dong, Jianming Wang, Xueshi Xu, Yinfeng Luo, Taibo |
| Author_xml | – sequence: 1 givenname: Jianming surname: Dong fullname: Dong, Jianming organization: Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China – sequence: 2 givenname: Weitian surname: Tong fullname: Tong, Weitian organization: Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada – sequence: 3 givenname: Taibo surname: Luo fullname: Luo, Taibo organization: Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada – sequence: 4 givenname: Xueshi surname: Wang fullname: Wang, Xueshi organization: Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China – sequence: 5 givenname: Jueliang surname: Hu fullname: Hu, Jueliang organization: Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China – sequence: 6 givenname: Yinfeng surname: Xu fullname: Xu, Yinfeng organization: Business School, Sichuan University, Chengdu, Sichuan 610065, China – sequence: 7 givenname: Guohui surname: Lin fullname: Lin, Guohui email: guohui@ualberta.ca organization: Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China |
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| Keywords | Multiprocessor scheduling Fully polynomial-time approximation scheme Makespan Dynamic programming Two-stage flowshop scheduling |
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| References | Chen (br0010) 1995; 46 Conway, Maxwell, Miller (br0030) 1967 Jansen, Sviridenko (br0140) 2000; vol. 1770 Williamson, Hall, Hoogeveen, Hurkens, Lenstra, Sevastj́anov, Shmoys (br0220) 1997; 45 Garey, Johnson (br0040) 1979 Johnson (br0150) 1954; 1 Gupta, Hariri, Potts (br0080) 1997; 69 Chen, Glass, Potts, Strusevich (br0020) 1996; 44 Hochbaum, Shmoys (br0120) 1987; 34 Hall (br0100) 1998; 82 Gonzalez, Sahni (br0060) 1978; 26 Gupta (br0070) 1988; 39 Hoogeveen, Lenstra, Veltman (br0130) 1996; 89 Gupta, Tunc (br0090) 1991; 29 Sahni (br0180) 1976; 23 Zhang, van de Velde (br0230) 2012; 216 Vairaktarakis, Elhafsi (br0200) 2000; 32 Garey, Johnson, Sethi (br0050) 1976; 1 Schuurman, Woeginger (br0190) 2000; 237 Lee, Vairaktarakis (br0160) 1994; 16 He, Kusiak, Artiba (br0110) 1996; 28 Wang (br0210) 2005; 22 Ruiz, Vázquez-Rodríguez (br0170) 2010; 205 Lee (10.1016/j.tcs.2016.04.046_br0160) 1994; 16 Vairaktarakis (10.1016/j.tcs.2016.04.046_br0200) 2000; 32 Garey (10.1016/j.tcs.2016.04.046_br0050) 1976; 1 Gupta (10.1016/j.tcs.2016.04.046_br0090) 1991; 29 Sahni (10.1016/j.tcs.2016.04.046_br0180) 1976; 23 Wang (10.1016/j.tcs.2016.04.046_br0210) 2005; 22 Hochbaum (10.1016/j.tcs.2016.04.046_br0120) 1987; 34 Hoogeveen (10.1016/j.tcs.2016.04.046_br0130) 1996; 89 Williamson (10.1016/j.tcs.2016.04.046_br0220) 1997; 45 Chen (10.1016/j.tcs.2016.04.046_br0010) 1995; 46 Garey (10.1016/j.tcs.2016.04.046_br0040) 1979 Chen (10.1016/j.tcs.2016.04.046_br0020) 1996; 44 Gupta (10.1016/j.tcs.2016.04.046_br0080) 1997; 69 Conway (10.1016/j.tcs.2016.04.046_br0030) 1967 Hall (10.1016/j.tcs.2016.04.046_br0100) 1998; 82 Johnson (10.1016/j.tcs.2016.04.046_br0150) 1954; 1 Schuurman (10.1016/j.tcs.2016.04.046_br0190) 2000; 237 Jansen (10.1016/j.tcs.2016.04.046_br0140) 2000; vol. 1770 Ruiz (10.1016/j.tcs.2016.04.046_br0170) 2010; 205 Zhang (10.1016/j.tcs.2016.04.046_br0230) 2012; 216 Gonzalez (10.1016/j.tcs.2016.04.046_br0060) 1978; 26 Gupta (10.1016/j.tcs.2016.04.046_br0070) 1988; 39 He (10.1016/j.tcs.2016.04.046_br0110) 1996; 28 |
| References_xml | – volume: 26 start-page: 36 year: 1978 end-page: 52 ident: br0060 article-title: Flowshop and jobshop schedules: complexity and approximation publication-title: Oper. Res. – volume: 1 start-page: 61 year: 1954 end-page: 68 ident: br0150 article-title: Optimal two- and three-stage production schedules with setup times included publication-title: Nav. Res. Logist. Q. – volume: 69 start-page: 171 year: 1997 end-page: 191 ident: br0080 article-title: Scheduling a two-stage hybrid flow shop with parallel machines at the first stage publication-title: Ann. Oper. Res. – volume: 1 start-page: 117 year: 1976 end-page: 129 ident: br0050 article-title: The complexity of flowshop and jobshop scheduling publication-title: Math. Oper. Res. – volume: 32 start-page: 687 year: 2000 end-page: 699 ident: br0200 article-title: The use of flowlines to simplify routing complexity in two-stage flowshops publication-title: IIE Trans. – volume: 216 start-page: 544 year: 2012 end-page: 552 ident: br0230 article-title: Approximation algorithms for the parallel flow shop problem publication-title: European J. Oper. Res. – volume: 22 start-page: 78 year: 2005 end-page: 85 ident: br0210 article-title: Flexible flow shop scheduling: optimum, heuristics and artificial intelligence solutions publication-title: Expert Syst. – volume: 45 start-page: 288 year: 1997 end-page: 294 ident: br0220 article-title: Short shop schedules publication-title: Oper. Res. – year: 1979 ident: br0040 article-title: Computers and Intractability: A Guide to the Theory of NP-Completeness – volume: 29 start-page: 1489 year: 1991 end-page: 1502 ident: br0090 article-title: Schedules for a two-stage hybrid flowshop with parallel machines at the second stage publication-title: Int. J. Prod. Res. – volume: 28 start-page: 129 year: 1996 end-page: 139 ident: br0110 article-title: A scheduling problem in glass manufacturing publication-title: IIE Trans. – volume: 39 start-page: 359 year: 1988 end-page: 364 ident: br0070 article-title: Two-stage, hybrid flowshop scheduling problem publication-title: J. Oper. Res. Soc. – volume: vol. 1770 start-page: 455 year: 2000 end-page: 465 ident: br0140 article-title: Polynomial time approximation schemes for the multiprocessor open and flow shop scheduling problem publication-title: STACS – year: 1967 ident: br0030 article-title: Theory of Scheduling – volume: 205 start-page: 1 year: 2010 end-page: 18 ident: br0170 article-title: The hybrid flow shop scheduling problem publication-title: European J. Oper. Res. – volume: 16 start-page: 149 year: 1994 end-page: 158 ident: br0160 article-title: Minimizing makespan in hybrid flowshops publication-title: Oper. Res. Lett. – volume: 82 start-page: 175 year: 1998 end-page: 190 ident: br0100 article-title: Approximability of flow shop scheduling publication-title: Math. Program. – volume: 89 start-page: 172 year: 1996 end-page: 175 ident: br0130 article-title: Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard publication-title: European J. Oper. Res. – volume: 46 start-page: 234 year: 1995 end-page: 244 ident: br0010 article-title: Analysis of classes of heuristics for scheduling a two-stage flow shop with parallel machines at one stage publication-title: J. Oper. Res. Soc. – volume: 44 start-page: 891 year: 1996 end-page: 898 ident: br0020 article-title: A new heuristic for three-machine flow shop scheduling publication-title: Oper. Res. – volume: 23 start-page: 116 year: 1976 end-page: 127 ident: br0180 article-title: Algorithms for scheduling independent tasks publication-title: J. ACM – volume: 34 start-page: 144 year: 1987 end-page: 162 ident: br0120 article-title: Using dual approximation algorithms for scheduling problems theoretical and practical results publication-title: J. ACM – volume: 237 start-page: 105 year: 2000 end-page: 122 ident: br0190 article-title: A polynomial time approximation scheme for the two-stage multiprocessor flow shop problem publication-title: Theoret. Comput. Sci. – volume: 82 start-page: 175 year: 1998 ident: 10.1016/j.tcs.2016.04.046_br0100 article-title: Approximability of flow shop scheduling publication-title: Math. Program. doi: 10.1007/BF01585870 – volume: 45 start-page: 288 year: 1997 ident: 10.1016/j.tcs.2016.04.046_br0220 article-title: Short shop schedules publication-title: Oper. Res. doi: 10.1287/opre.45.2.288 – volume: 26 start-page: 36 year: 1978 ident: 10.1016/j.tcs.2016.04.046_br0060 article-title: Flowshop and jobshop schedules: complexity and approximation publication-title: Oper. Res. doi: 10.1287/opre.26.1.36 – volume: 16 start-page: 149 year: 1994 ident: 10.1016/j.tcs.2016.04.046_br0160 article-title: Minimizing makespan in hybrid flowshops publication-title: Oper. Res. Lett. doi: 10.1016/0167-6377(94)90026-4 – volume: 32 start-page: 687 year: 2000 ident: 10.1016/j.tcs.2016.04.046_br0200 article-title: The use of flowlines to simplify routing complexity in two-stage flowshops publication-title: IIE Trans. doi: 10.1080/07408170008967427 – year: 1967 ident: 10.1016/j.tcs.2016.04.046_br0030 – volume: 28 start-page: 129 year: 1996 ident: 10.1016/j.tcs.2016.04.046_br0110 article-title: A scheduling problem in glass manufacturing publication-title: IIE Trans. doi: 10.1080/07408179608966258 – volume: 34 start-page: 144 year: 1987 ident: 10.1016/j.tcs.2016.04.046_br0120 article-title: Using dual approximation algorithms for scheduling problems theoretical and practical results publication-title: J. ACM doi: 10.1145/7531.7535 – volume: vol. 1770 start-page: 455 year: 2000 ident: 10.1016/j.tcs.2016.04.046_br0140 article-title: Polynomial time approximation schemes for the multiprocessor open and flow shop scheduling problem – volume: 29 start-page: 1489 year: 1991 ident: 10.1016/j.tcs.2016.04.046_br0090 article-title: Schedules for a two-stage hybrid flowshop with parallel machines at the second stage publication-title: Int. J. Prod. Res. doi: 10.1080/00207549108948025 – volume: 1 start-page: 117 year: 1976 ident: 10.1016/j.tcs.2016.04.046_br0050 article-title: The complexity of flowshop and jobshop scheduling publication-title: Math. Oper. Res. doi: 10.1287/moor.1.2.117 – volume: 23 start-page: 116 year: 1976 ident: 10.1016/j.tcs.2016.04.046_br0180 article-title: Algorithms for scheduling independent tasks publication-title: J. ACM doi: 10.1145/321921.321934 – volume: 46 start-page: 234 year: 1995 ident: 10.1016/j.tcs.2016.04.046_br0010 article-title: Analysis of classes of heuristics for scheduling a two-stage flow shop with parallel machines at one stage publication-title: J. Oper. Res. Soc. doi: 10.1057/jors.1995.28 – volume: 39 start-page: 359 year: 1988 ident: 10.1016/j.tcs.2016.04.046_br0070 article-title: Two-stage, hybrid flowshop scheduling problem publication-title: J. Oper. Res. Soc. doi: 10.1057/jors.1988.63 – year: 1979 ident: 10.1016/j.tcs.2016.04.046_br0040 – volume: 89 start-page: 172 year: 1996 ident: 10.1016/j.tcs.2016.04.046_br0130 article-title: Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard publication-title: European J. Oper. Res. doi: 10.1016/0377-2217(94)00235-5 – volume: 1 start-page: 61 year: 1954 ident: 10.1016/j.tcs.2016.04.046_br0150 article-title: Optimal two- and three-stage production schedules with setup times included publication-title: Nav. Res. Logist. Q. doi: 10.1002/nav.3800010110 – volume: 22 start-page: 78 year: 2005 ident: 10.1016/j.tcs.2016.04.046_br0210 article-title: Flexible flow shop scheduling: optimum, heuristics and artificial intelligence solutions publication-title: Expert Syst. doi: 10.1111/j.1468-0394.2005.00297.x – volume: 216 start-page: 544 year: 2012 ident: 10.1016/j.tcs.2016.04.046_br0230 article-title: Approximation algorithms for the parallel flow shop problem publication-title: European J. Oper. Res. doi: 10.1016/j.ejor.2011.08.007 – volume: 44 start-page: 891 year: 1996 ident: 10.1016/j.tcs.2016.04.046_br0020 article-title: A new heuristic for three-machine flow shop scheduling publication-title: Oper. Res. doi: 10.1287/opre.44.6.891 – volume: 69 start-page: 171 year: 1997 ident: 10.1016/j.tcs.2016.04.046_br0080 article-title: Scheduling a two-stage hybrid flow shop with parallel machines at the first stage publication-title: Ann. Oper. Res. doi: 10.1023/A:1018976827443 – volume: 205 start-page: 1 year: 2010 ident: 10.1016/j.tcs.2016.04.046_br0170 article-title: The hybrid flow shop scheduling problem publication-title: European J. Oper. Res. doi: 10.1016/j.ejor.2009.09.024 – volume: 237 start-page: 105 year: 2000 ident: 10.1016/j.tcs.2016.04.046_br0190 article-title: A polynomial time approximation scheme for the two-stage multiprocessor flow shop problem publication-title: Theoret. Comput. Sci. doi: 10.1016/S0304-3975(98)00157-1 |
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| Title | An FPTAS for the parallel two-stage flowshop problem |
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