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Flow-Shop Scheduling with the Branch-and-Bound Method

Author

Listed:
  • G. B. McMahon

    (CSIRO Wool Research Laboratories, Ryde, Sydney, Australia)

  • P. G. Burton

    (CSIRO Wool Research Laboratories, Ryde, Sydney, Australia)

Abstract

The branch-and-bound technique has been applied to the three machine flow shop problem where the objective is to minimize makespan. A new method of obtaining the bound has been developed. Rules for ordering the machines and listing the jobs prior to application of the algorithm have been proposed. Computational results are given for a large number of job sets up to 10 jobs, and for a few cases up to 45 jobs.

Suggested Citation

  • G. B. McMahon & P. G. Burton, 1967. "Flow-Shop Scheduling with the Branch-and-Bound Method," Operations Research, INFORMS, vol. 15(3), pages 473-481, June.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:3:p:473-481
    DOI: 10.1287/opre.15.3.473
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    Cited by:

    1. Janiak, Adam & Kozan, Erhan & Lichtenstein, Maciej & Oguz, Ceyda, 2007. "Metaheuristic approaches to the hybrid flow shop scheduling problem with a cost-related criterion," International Journal of Production Economics, Elsevier, vol. 105(2), pages 407-424, February.
    2. Sündüz Dağ, 2013. "An Application On Flowshop Scheduling," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 1(1), pages 47-56, December.
    3. N Madhushini & C Rajendran & Y Deepa, 2009. "Branch-and-bound algorithms for scheduling in permutation flowshops to minimize the sum of weighted flowtime/sum of weighted tardiness/sum of weighted flowtime and weighted tardiness/sum of weighted f," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(7), pages 991-1004, July.
    4. Gowrishankar, K. & Rajendran, Chandrasekharan & Srinivasan, G., 2001. "Flow shop scheduling algorithms for minimizing the completion time variance and the sum of squares of completion time deviations from a common due date," European Journal of Operational Research, Elsevier, vol. 132(3), pages 643-665, August.
    5. Ganesan, Viswanath Kumar & Sivakumar, Appa Iyer, 2006. "Scheduling in static jobshops for minimizing mean flowtime subject to minimum total deviation of job completion times," International Journal of Production Economics, Elsevier, vol. 103(2), pages 633-647, October.
    6. Kim, Yeong-Dae, 1995. "Minimizing total tardiness in permutation flowshops," European Journal of Operational Research, Elsevier, vol. 85(3), pages 541-555, September.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Deepak Gupta & Sonia Goel & Neeraj Mangla, 2022. "Optimization of production scheduling in two stage Flow Shop Scheduling problem with m equipotential machines at first stage," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(3), pages 1162-1169, June.

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