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Heuristics for the Unrelated Parallel Machine Scheduling Problem with Setup Times

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Abstract

The problem addressed in this paper is the non-preemptive unrelated parallel machine scheduling problem with the objective of minimizing the makespan. Machine-dependent and job sequence-dependent setup times are considered, all jobs are available at time zero, and all times are deterministic. This is a NP-hard problem and in this paper, optimal solutions are found for small problems only. For larger problems, a new meta-heuristic, Meta-RaPS, is introduced and its performance is evaluated by comparing its solutions to the solutions of an existing heuristic for the same problem. The results show that Meta-RaPS found all optimal solutions for the small problems and outperformed the solutions obtained by the existing heuristic for larger problems.

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References

  • R.M. Aiex S. Binato M.G.C. Resende (2003) ArticleTitleParallel GRASP with path-relinking for job shop scheduling Parallel Computing 29 393–430 Occurrence Handle10.1016/S0167-8191(03)00014-0

    Article  Google Scholar 

  • A. Al-Salem (2004) ArticleTitleScheduling to minimize makespan on unrelated parallel machines with sequence dependent setup times. Engineering Journal of the University of Qatar 17 177–187

    Google Scholar 

  • A. Allahverdi J.N.D. Gupta T. Aldowaisan (1999) ArticleTitleA review of scheduling research involving setup considerations. Omega 27 219–239 Occurrence Handle10.1016/S0305-0483(98)00042-5

    Article  Google Scholar 

  • A.L. Arcus (1966) ArticleTitleCOMSOAL: a computer method of sequencing operations for assembly lines International Journal of Production Research 4 259–277

    Google Scholar 

  • M. Azizoglu O. Kirka (1999) ArticleTitleScheduling jobs on unrelated parallel machines to minimize regular total cost functions. IIE Transactions 31 153–159 Occurrence Handle10.1023/A:1007516602473

    Article  Google Scholar 

  • J. Bank F. Werner (2001) ArticleTitleHeuristic algorithms for unrelated parallel machine scheduling with a common due date, release dates, and linear earliness and tardiness penalties Mathematical and Computer Modelling 33 363–383 Occurrence Handle10.1016/S0895-7177(00)00250-8

    Article  Google Scholar 

  • L.G. Bruno E.G. Coffman R. Sethi (1974) ArticleTitleScheduling independent tasks to reduce mean finishing time Communications of the ACM 17 382–387 Occurrence Handle10.1145/361011.361064

    Article  Google Scholar 

  • T. Cheng C. Sin (1990) ArticleTitleA state-of-the-art review of parallel-machine scheduling research European Journal of Operational Research 47 271–292 Occurrence Handle10.1016/0377-2217(90)90215-W

    Article  Google Scholar 

  • G. DePuy G.E. Whitehouse (2001) ArticleTitleA simple and effective heuristic for the multiple resource allocation problem International Journal of Production Research 32 IssueID4 24–31

    Google Scholar 

  • G. W. DePuy R. J. Moraga G. E. Whitehouse (2005) Transportation Research Part E: Logistics and Transportation Review 41 IssueID2 115–130 Occurrence Handle10.1016/j.tre.2004.02.001

    Article  Google Scholar 

  • C. Dhaenens-Flipo (2001) ArticleTitleA bicriterion approach to deal with a constrained single-objective problem International Journal of Production Economics 74 93–101 Occurrence Handle10.1016/S0925-5273(01)00110-4

    Article  Google Scholar 

  • S. Dunstall A. Wirth (2005) ArticleTitleHeuristic methods for the identical parallel machine flowtime problem with set-up times Computers & Operations Research 32 2479–2491 Occurrence Handle10.1016/j.cor.2004.03.013

    Article  Google Scholar 

  • T. Feo M. Resende (1995) ArticleTitleGreedy randomized adaptive search procedures Journal of Global Optimization 6 109–133 Occurrence Handle10.1007/BF01096763

    Article  Google Scholar 

  • T.A. Feo K. Sarathy J. McGahan (1996) ArticleTitleA GRASP for single machine scheduling with sequence dependent setup costs and linear delay penalties Computers & Operations Research 23 881–895 Occurrence Handle10.1016/0305-0548(95)00084-4

    Article  Google Scholar 

  • T.A. Feo K. Venkatraman J.F. Bard (1991) ArticleTitleA GRASP for a difficult single machine scheduling problem Computers & Operations Research 18 635–643 Occurrence Handle10.1016/0305-0548(91)90001-8

    Article  Google Scholar 

  • P.M. Franca M. Gendreau G. Laporte F.M. Muller (1996) ArticleTitleA tabu search heuristic for the multiprocessor scheduling problem with sequence dependent setup times International Journal of Production Economics 43 79–89

    Google Scholar 

  • M.R. Garey D.S. Johnson (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness W. H. Freeman and Company New York

    Google Scholar 

  • M. Gendreau L. Laporte E.M. Guimaraes (2001) ArticleTitleA divide and merge heuristic for the multiprocessor scheduling problem with sequence dependent setup times European Journal of Operational Research 133 183–189 Occurrence Handle10.1016/S0377-2217(00)00197-1

    Article  Google Scholar 

  • M. Ghirardi C.N. Potts (2005) ArticleTitleMakespan minimization for scheduling unrelated parallel machines: A recovering beam search approach European Journal of Operational Research 165 IssueID2 457–467 Occurrence Handle10.1016/j.ejor.2004.04.015

    Article  Google Scholar 

  • C.A. Glass C.N. Potts P. Shade (1994) ArticleTitleUnrelated parallel machine scheduling using local search Mathematical and Computer Modeling 20 IssueID2 41–52

    Google Scholar 

  • S.C. Graves (1981) ArticleTitleA review of production scheduling Operations Research 29 646–675

    Google Scholar 

  • A. Guinet (1991) ArticleTitleTextile production systems: a succession of non-identical parallel processor shops Journal of Operational Research Society 42 IssueID8 655–671

    Google Scholar 

  • A.M.A. Hariri C.N. Potts (1991) ArticleTitleHeuristics for scheduling unrelated parallel machines Computers and Operations Research 18 IssueID3 323–331 Occurrence Handle10.1016/0305-0548(91)90034-O

    Article  Google Scholar 

  • W.A. Horn (1973) ArticleTitleMinimizing average flow time with parallel machines Operations Research 21 846–847

    Google Scholar 

  • R.M. Karp (1972) Reducibility among combinatorial problems R.E. Miller JW Tatcher (Eds) Complexity of Computer Computations. Plenum Press New York 85–103

    Google Scholar 

  • Kim D.W., Kim K.H., Jang W. and Chen F.F. (2002) Unrelated parallel machine scheduling with setup times using simulated annealing. Robotics and Computer Integrated Manufacturing 18:3–4, 223–231.

    Google Scholar 

  • Kim D. W., Na, D. G. and Chen, F. F. (2003) Unrelated parallel machine scheduling with setup times and total weighted tardiness objective. Robotics and Computer Integrated Manufacturing 19(1–2), 173–181.

    Google Scholar 

  • M.E. Kurz R.G. Askin (2001) ArticleTitleHeuristic scheduling of parallel machines with sequence-dependent set-up times International Journal of Production Research 39 3747–3769

    Google Scholar 

  • M. Laguna J.L. González-Velarde (1991) ArticleTitleA search heuristic for just-in-time scheduling in parallel machines Journal of Intelligent Manufacturing 2 253–260

    Google Scholar 

  • G. Lancia (2000) ArticleTitleScheduling jobs with release dates and tails on two unrelated parallel machines to minimize the makespan. European Journal of Operational Research 120 277–288 Occurrence Handle10.1016/S0377-2217(99)00156-3

    Article  Google Scholar 

  • Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G. and Shmoys, D. B. (1993) Sequencing and scheduling: algorithms and complexity. Handbooks in Operations Research and Management Science 4, Logistics of Production and Inventory, North Holland, Amsterdam, 445–524.

  • H. Lee K. Bhaskaran M. Pinedo (1997) ArticleTitleA heuristic to minimize the total weighted tardiness with sequence-dependent setups IIE Transactions 100 464–474

    Google Scholar 

  • C.F. Liaw Y.K. Lin C.Y. Chen M. Chen (2003) ArticleTitleScheduling unrelated parallel machines to minimize total weighted tardiness Computers & Operations Research 30 1777–1789

    Google Scholar 

  • Y. Lin L. Wenhua (2004) ArticleTitleParallel machine scheduling of machine-dependent jobs with unit-length European Journal of Operational Research 156 261–266 Occurrence Handle10.1016/S0377-2217(02)00914-1

    Article  Google Scholar 

  • S. Martello F. Soumis P. Toth (1997) ArticleTitleExact and approximation algorithms for makespan minimization on unrelated parallel machines Discrete Applied Mathematics 75 169–188 Occurrence Handle10.1016/S0166-218X(96)00087-X

    Article  Google Scholar 

  • R. McNaughton (1959) ArticleTitleScheduling with deadlines and loss function Management Science 6 1–12

    Google Scholar 

  • E. Mokotoff (2001) ArticleTitleParallel machine scheduling problems: a survey, Asia-Pacific Journal of Operational research 18 193–242

    Google Scholar 

  • R.J. Moraga G.W. DePuy G.E. Whitehouse (2005) ArticleTitleMeta-RaPS approach for the 0–1 multidimensional knapsack problem Computers and Industrial Engineering 48 IssueID2 83–96

    Google Scholar 

  • R.J. Moraga (2002) Meta-RaPS: An Effective Solution Approach for Combinatorial Problems University of Central Florida Orlando, FL

    Google Scholar 

  • M. Pinedo (2002) Scheduling: Theory, Algorithms, and Systems EditionNumber2 Printce Hall New Jersey

    Google Scholar 

  • M. Rabadi G. Mollaghasemi G.C. Anagnostopoulos (2004) ArticleTitleA branch-and-bound algorithm for the early/tardy machine scheduling problem with a common due-date and sequence-dependent setup time Computers & Operations Research Journal 31 IssueID10 1727–1751

    Google Scholar 

  • S. Radhakrishnan J.A. Ventura (2000) ArticleTitleSimulated annealing for parallel machine scheduling with earliness/tardiness penalties and sequence-dependent set-up times International Journal of Production Research 38 2233–2252

    Google Scholar 

  • Rojanasoonthon, S. and Bard, J. F. (2005) A GRASP for parallel machine scheduling with time windows. To appear in, v17, n 1, INFORMS Journal on Computing.

  • S.U. Randhawa C.H. Kuo (1997) ArticleTitleEvaluating scheduling heuristics for non-identical parallel processors International Journal of Production Research 35 969–981

    Google Scholar 

  • Scheduling Research (2005) http://www.SchedulingResearch.coma web site that includes benchmark problem data sets and solutions for scheduling problems

  • B. Srivastava (1997) ArticleTitleAn effective heuristic for minimizing makespan on unrelated parallel machines Journal of the Operational Research Society 49 886–894

    Google Scholar 

  • P. Hentenryck ParticleVan (2001) ILOG OPL Studio 3.5 Language Manual ILOG France

    Google Scholar 

  • M. Weng J. Lu H. Ren (2001) ArticleTitleUnrelated parallel machine scheduling with setup consideration and a total weighted completion time objective International Journal of Production Economics 70 215–226 Occurrence Handle10.1016/S0925-5273(00)00066-9

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Engineering Management and Systems Engineering, Old Dominion University, Norfolk, Virginia, 23529, USA

    Ghaith Rabadi

  2. Department of Industrial Engineering, Universidad del Bío Bío, Concepción, Chile

    Reinaldo J. Moraga

  3. Department of Mechanical Engineering, University of Qatar, Doha, Qatar

    Ameer Al-Salem

Authors
  1. Ghaith Rabadi
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  2. Reinaldo J. Moraga
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  3. Ameer Al-Salem
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Correspondence to Ghaith Rabadi.

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Rabadi, G., Moraga, R.J. & Al-Salem, A. Heuristics for the Unrelated Parallel Machine Scheduling Problem with Setup Times. J Intell Manuf 17, 85–97 (2006). https://doi.org/10.1007/s10845-005-5514-0

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