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A General Bounding Scheme for the Permutation Flow-Shop Problem

Author

Listed:
  • B. J. Lageweg

    (Mathematisch Centrum, Amsterdam, The Netherlands)

  • J. K. Lenstra

    (Mathematisch Centrum, Amsterdam, The Netherlands)

  • A. H. G. Rinnooy Kan

    (Erasmus University, Rotterdam, The Netherlands)

Abstract

Branch-and-bound methods are commonly used to find a permutation schedule that minimizes maximum completion time in an m -machine flow-shop. In this paper we describe a classification scheme for lower bounds that generates most previously known bounds and leads to a number of promising new ones as well. After a discussion of dominance relations within this scheme and of the implementation of each bound, we report on computational experience that indicates the superiority of one of the new bounds.

Suggested Citation

  • B. J. Lageweg & J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "A General Bounding Scheme for the Permutation Flow-Shop Problem," Operations Research, INFORMS, vol. 26(1), pages 53-67, February.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:1:p:53-67
    DOI: 10.1287/opre.26.1.53
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    Citations

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    Cited by:

    1. Lemesre, J. & Dhaenens, C. & Talbi, E.G., 2007. "An exact parallel method for a bi-objective permutation flowshop problem," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1641-1655, March.
    2. E F Stafford & F T Tseng & J N D Gupta, 2005. "Comparative evaluation of MILP flowshop models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(1), pages 88-101, January.
    3. Chung, Chia-Shin & Flynn, James & Kirca, Omer, 2002. "A branch and bound algorithm to minimize the total flow time for m-machine permutation flowshop problems," International Journal of Production Economics, Elsevier, vol. 79(3), pages 185-196, October.
    4. Sündüz Dağ, 2013. "An Application On Flowshop Scheduling," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 1(1), pages 47-56, December.
    5. Huq, Faizul & Cutright, Kenneth & Martin, Clarence, 2004. "Employee scheduling and makespan minimization in a flow shop with multi-processor work stations: a case study," Omega, Elsevier, vol. 32(2), pages 121-129, April.
    6. Chung, Chia-Shin & Flynn, James & Kirca, Omer, 2006. "A branch and bound algorithm to minimize the total tardiness for m-machine permutation flowshop problems," European Journal of Operational Research, Elsevier, vol. 174(1), pages 1-10, October.
    7. Kim, Yeong-Dae, 1995. "Minimizing total tardiness in permutation flowshops," European Journal of Operational Research, Elsevier, vol. 85(3), pages 541-555, September.
    8. Blazewicz, Jacek & Domschke, Wolfgang & Pesch, Erwin, 1996. "The job shop scheduling problem: Conventional and new solution techniques," European Journal of Operational Research, Elsevier, vol. 93(1), pages 1-33, August.
    9. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    10. Jan Gmys, 2022. "Exactly Solving Hard Permutation Flowshop Scheduling Problems on Peta-Scale GPU-Accelerated Supercomputers," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2502-2522, September.
    11. Selcuk Karabati & Panagiotis Kouvelis, 1993. "The permutation flow shop problem with sum‐of‐completion times performance criterion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(6), pages 843-862, October.
    12. B-J Joo & Y-D Kim, 2009. "A branch-and-bound algorithm for a two-machine flowshop scheduling problem with limited waiting time constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(4), pages 572-582, April.
    13. Bo Liu & Ling Wang & Ying Liu & Shouyang Wang, 2011. "A unified framework for population-based metaheuristics," Annals of Operations Research, Springer, vol. 186(1), pages 231-262, June.
    14. Olivier Ploton & Vincent T’kindt, 2023. "Moderate worst-case complexity bounds for the permutation flowshop scheduling problem using Inclusion–Exclusion," Journal of Scheduling, Springer, vol. 26(2), pages 137-145, April.
    15. J M Framinan & J N D Gupta & R Leisten, 2004. "A review and classification of heuristics for permutation flow-shop scheduling with makespan objective," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1243-1255, December.
    16. Gupta, Jatinder N.D. & Stafford, Edward Jr., 2006. "Flowshop scheduling research after five decades," European Journal of Operational Research, Elsevier, vol. 169(3), pages 699-711, March.
    17. M Haouari & T Ladhari, 2003. "A branch-and-bound-based local search method for the flow shop problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(10), pages 1076-1084, October.
    18. Lei Shang & Christophe Lenté & Mathieu Liedloff & Vincent T’Kindt, 2018. "Exact exponential algorithms for 3-machine flowshop scheduling problems," Journal of Scheduling, Springer, vol. 21(2), pages 227-233, April.
    19. Nour El Houda Tellache & Mourad Boudhar, 2018. "Flow shop scheduling problem with conflict graphs," Annals of Operations Research, Springer, vol. 261(1), pages 339-363, February.
    20. Gmys, Jan & Mezmaz, Mohand & Melab, Nouredine & Tuyttens, Daniel, 2020. "A computationally efficient Branch-and-Bound algorithm for the permutation flow-shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 284(3), pages 814-833.
    21. Xiao, Yiyong & Yuan, Yingying & Zhang, Ren-Qian & Konak, Abdullah, 2015. "Non-permutation flow shop scheduling with order acceptance and weighted tardiness," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 312-333.
    22. Liaw, Ching-Fang, 2005. "Scheduling preemptive open shops to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 162(1), pages 173-183, April.

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