An approximate decomposition algorithm for scheduling on parallel machines with heads and tails
We address the makespan minimization for parallel identical machines subject to heads and tails. This problem is NP -hard in the strong sense. We show that the worst-case performance of Jackson's algorithm is improved by using a preprocessing algorithm, and we propose an approximate decompositi...
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| Published in | Computers & operations research Vol. 34; no. 3; pp. 868 - 883 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Elsevier Ltd
01.03.2007
Elsevier Science Pergamon Press Inc |
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| Online Access | Get full text |
| ISSN | 0305-0548 1873-765X 0305-0548 |
| DOI | 10.1016/j.cor.2005.05.012 |
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| Abstract | We address the makespan minimization for parallel identical machines subject to heads and tails. This problem is
NP
-hard in the strong sense. We show that the worst-case performance of Jackson's algorithm is improved by using a preprocessing algorithm, and we propose an approximate decomposition algorithm which requires iteratively solving a sequence of two-machine problems. We present the results of an extensive computational study on large instances with up to 2000 jobs and 100 machines which show that the proposed heuristic is fast and yields in most cases schedules with relative deviation from a lower bound less than 0.2%. |
|---|---|
| AbstractList | We address the makespan minimization for parallel identical machines subject to heads and tails. This problem is
NP
-hard in the strong sense. We show that the worst-case performance of Jackson's algorithm is improved by using a preprocessing algorithm, and we propose an approximate decomposition algorithm which requires iteratively solving a sequence of two-machine problems. We present the results of an extensive computational study on large instances with up to 2000 jobs and 100 machines which show that the proposed heuristic is fast and yields in most cases schedules with relative deviation from a lower bound less than 0.2%. We address the makespan minimization for parallel identical machines subject to heads and tails. This problem is ...-hard in the strong sense. We show that the worst-case performance of Jackson's algorithm is improved by using a preprocessing algorithm, and we propose an approximate decomposition algorithm which requires iteratively solving a sequence of two-machine problems. We present the results of an extensive computational study on large instances with up to 2000 jobs and 100 machines which show that the proposed heuristic is fast and yields in most cases schedules with relative deviation from a lower bound less than 0.2%. |
| Author | Haouari, Mohamed Gharbi, Anis |
| Author_xml | – sequence: 1 givenname: Anis surname: Gharbi fullname: Gharbi, Anis email: anis.gharbi@ept.rnu.tn organization: Combinatorial Optimization Research Group—ROI, Ecole Polytechnique de Tunisie, BP 743, 2078 La Marsa, Tunisia – sequence: 2 givenname: Mohamed surname: Haouari fullname: Haouari, Mohamed email: mohamed.haouari@ept.rnu.tn organization: Combinatorial Optimization Research Group—ROI, Ecole Polytechnique de Tunisie, BP 743, 2078 La Marsa, Tunisia |
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| Cites_doi | 10.1016/0377-2217(86)90191-8 10.1016/j.dam.2004.12.003 10.1002/nav.3800210113 10.1023/A:1018968332237 10.1023/B:ANOR.0000030688.31785.40 10.1137/0218048 10.1051/ro/1991250303111 10.1287/moor.17.1.22 10.1016/S0377-2217(82)80007-6 10.1051/ro:2000103 10.1016/0377-2217(87)90243-8 10.1002/1520-6750(199509)42:6<935::AID-NAV3220420606>3.0.CO;2-D 10.1016/0305-0483(83)90088-9 10.1287/opre.28.6.1436 10.1002/jos.103 10.1016/S0167-6377(02)00177-3 10.1016/0196-6774(84)90035-X |
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| Keywords | Delivery times Scheduling Identical parallel machines Release dates Heuristic Lower bound Parallel algorithm Worst case method Parallel machines Minimization Makespan Delivery lead time Heuristic method |
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| References | Gharbi A, Haouari M. Optimal parallel machines scheduling with initial and final availability constraints. Proceedings of the ninth international workshop on project management and scheduling PMS, 2004. p. 218–21. Haouari, Gharbi (bib14) 2004; 129 Ho, Wong (bib20) 1995; 42 Potts (bib4) 1980; 28 Gharbi A, Haouari M. Optimal parallel machines scheduling with availability constraints. Discrete Applied Mathematics 2005;148:63–87. Perregaard M. Branch-and-bound method for the multiprocessor jobshop and flowshop scheduling problem. Master thesis, Datalogisk institut Københavns Universitet, 1995. Gusfield (bib19) 1984; 5 Carlier, Latapie (bib11) 1991; 25 Haouari, Gharbi (bib13) 2003; 31 Simons, Warmuth (bib6) 1989; 18 Hoogeveen H, Hurkens C, Lenstra JK, Vandevelde A. Lower bounds for the multiprocessor flow shop. Second Workshop on Models and Algorithms for Planning and Scheduling, Wernigerode, 1995. Carlier (bib1) 1982; 11 Grabowski, Nowicki, Zdrzalka (bib2) 1986; 26 Carlier, Néron (bib7) 2000; 34 Vandevelde A. Minimizing the makespan in a multiprocessor flow shop. Master thesis, Eindhoven University of Technology, The Netherlands, 1994. Carlier (bib15) 1987; 29 Carlier, Pinson (bib12) 1998; 83 Gharbi, Haouari (bib16) 2002; 5 Horn (bib5) 1974; 21 Nawaz, Enscore, Ham (bib21) 1983; 11 Hall, Shmoys (bib3) 1992; 17 Gharbi (10.1016/j.cor.2005.05.012_bib16) 2002; 5 Horn (10.1016/j.cor.2005.05.012_bib5) 1974; 21 Simons (10.1016/j.cor.2005.05.012_bib6) 1989; 18 Haouari (10.1016/j.cor.2005.05.012_bib13) 2003; 31 Carlier (10.1016/j.cor.2005.05.012_bib15) 1987; 29 Gusfield (10.1016/j.cor.2005.05.012_bib19) 1984; 5 Carlier (10.1016/j.cor.2005.05.012_bib7) 2000; 34 Nawaz (10.1016/j.cor.2005.05.012_bib21) 1983; 11 10.1016/j.cor.2005.05.012_bib8 10.1016/j.cor.2005.05.012_bib18 10.1016/j.cor.2005.05.012_bib17 Carlier (10.1016/j.cor.2005.05.012_bib1) 1982; 11 10.1016/j.cor.2005.05.012_bib9 Ho (10.1016/j.cor.2005.05.012_bib20) 1995; 42 Hall (10.1016/j.cor.2005.05.012_bib3) 1992; 17 Carlier (10.1016/j.cor.2005.05.012_bib11) 1991; 25 Haouari (10.1016/j.cor.2005.05.012_bib14) 2004; 129 Grabowski (10.1016/j.cor.2005.05.012_bib2) 1986; 26 10.1016/j.cor.2005.05.012_bib10 Carlier (10.1016/j.cor.2005.05.012_bib12) 1998; 83 Potts (10.1016/j.cor.2005.05.012_bib4) 1980; 28 |
| References_xml | – volume: 18 start-page: 690 year: 1989 end-page: 710 ident: bib6 article-title: A fast algorithm for multiprocessor scheduling of unit-length jobs publication-title: SIAM Journal on Computing – volume: 42 start-page: 935 year: 1995 end-page: 948 ident: bib20 article-title: Makespan minimization for publication-title: Naval Research Logistics – volume: 5 start-page: 329 year: 2002 end-page: 355 ident: bib16 article-title: Minimizing makespan on parallel machines subject to release dates and delivery times publication-title: Journal of Scheduling – volume: 11 start-page: 42 year: 1982 end-page: 47 ident: bib1 article-title: The one machine sequencing problem publication-title: European Journal of Operational Research – volume: 5 start-page: 1 year: 1984 end-page: 6 ident: bib19 article-title: Bounds for naive multiple machine scheduling with release times and deadlines publication-title: Journal of Algorithms – volume: 28 start-page: 1436 year: 1980 end-page: 1441 ident: bib4 article-title: Analysis of a heuristic for one machine with release dates and delivery times publication-title: Operations Research – volume: 83 start-page: 41 year: 1998 end-page: 58 ident: bib12 article-title: Jackson's pseudo preemptive schedule for the publication-title: Annals of Operations Research – volume: 34 start-page: 1 year: 2000 end-page: 25 ident: bib7 article-title: An exact algorithm for solving the multiprocessor flowshop publication-title: RAIRO—Operations Research – volume: 11 start-page: 91 year: 1983 end-page: 95 ident: bib21 article-title: A Heuristic algorithm for the publication-title: Omega – reference: Perregaard M. 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Optimal parallel machines scheduling with initial and final availability constraints. Proceedings of the ninth international workshop on project management and scheduling PMS, 2004. p. 218–21. – reference: Gharbi A, Haouari M. Optimal parallel machines scheduling with availability constraints. 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| Snippet | We address the makespan minimization for parallel identical machines subject to heads and tails. This problem is
NP
-hard in the strong sense. We show that the... We address the makespan minimization for parallel identical machines subject to heads and tails. This problem is ...-hard in the strong sense. We show that the... We address the makespan minimization for parallel identical machines subject to heads and tails. This problem is -hard in the strong sense. We show that the... |
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| SubjectTerms | Algorithms Applied sciences Delivery times Exact sciences and technology Heuristic Identical parallel machines Job shops Machinery Operational research. Management science Release dates Scheduling Scheduling algorithms Studies |
| Title | An approximate decomposition algorithm for scheduling on parallel machines with heads and tails |
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