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A New Heuristic for Three-Machine Flow Shop Scheduling

Author

Listed:
  • Bo Chen

    (University of Warwick, Coventry, United Kingdom)

  • Celia A. Glass

    (University of Southampton, Southampton, United Kingdom)

  • Chris N. Potts

    (University of Southampton, Southampton, United Kingdom)

  • Vitaly A. Strusevich

    (University of Greenwich, London, United Kingdom)

Abstract

This paper considers the problem of sequencing n jobs in a three-machine flow shop with the objective of minimizing the makespan, which is the completion time of the last job. An O ( n log n ) time heuristic that is based on Johnson's algorithm is presented. It is shown to generate a schedule with length at most 5/3 times that of an optimal schedule, thereby reducing the previous best available worst-case performance ratio of 2. An application to the general flow shop is also discussed.

Suggested Citation

  • Bo Chen & Celia A. Glass & Chris N. Potts & Vitaly A. Strusevich, 1996. "A New Heuristic for Three-Machine Flow Shop Scheduling," Operations Research, INFORMS, vol. 44(6), pages 891-898, December.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:6:p:891-898
    DOI: 10.1287/opre.44.6.891
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    Citations

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    Cited by:

    1. Gupta, Jatinder N.D. & Koulamas, Christos & Kyparisis, George J., 2006. "Performance guarantees for flowshop heuristics to minimize makespan," European Journal of Operational Research, Elsevier, vol. 169(3), pages 865-872, March.
    2. Riane, Fouad & Artiba, Abdelhakim & E. Elmaghraby, Salah, 1998. "A hybrid three-stage flowshop problem: Efficient heuristics to minimize makespan," European Journal of Operational Research, Elsevier, vol. 109(2), pages 321-329, September.
    3. 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.
    4. Yong Chen & Yinhui Cai & Longcheng Liu & Guangting Chen & Randy Goebel & Guohui Lin & Bing Su & An Zhang, 2022. "Path cover with minimum nontrivial paths and its application in two-machine flow-shop scheduling with a conflict graph," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 571-588, April.
    5. Kameng Nip & Zhenbo Wang & Fabrice Talla Nobibon & Roel Leus, 2015. "A combination of flow shop scheduling and the shortest path problem," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 36-52, January.
    6. Kalczynski, Pawel Jan & Kamburowski, Jerzy, 2007. "On the NEH heuristic for minimizing the makespan in permutation flow shops," Omega, Elsevier, vol. 35(1), pages 53-60, February.
    7. Jianming Dong & Joshua Chang & Bing Su & Jueliang Hu & Guohui Lin, 2020. "Two-stage open-shop scheduling with a two-machine flow shop as a stage: approximation algorithms and empirical experiments," Journal of Scheduling, Springer, vol. 23(5), pages 595-608, October.
    8. D Bai & L Tang, 2010. "New heuristics for flow shop problem to minimize makespan," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(6), pages 1032-1040, June.
    9. Wu, Lingxiao & Yang, Dong & Wang, Shuaian & Yuan, Yun, 2020. "Evacuating offshore working barges from a land reclamation site in storm emergencies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 137(C).
    10. Jianming Dong & Ruyan Jin & Jueliang Hu & Guohui Lin, 2019. "A fully polynomial time approximation scheme for scheduling on parallel identical two-stage openshops," Journal of Combinatorial Optimization, Springer, vol. 37(2), pages 668-684, February.
    11. Benavides, Alexander J. & Ritt, Marcus & Miralles, Cristóbal, 2014. "Flow shop scheduling with heterogeneous workers," European Journal of Operational Research, Elsevier, vol. 237(2), pages 713-720.
    12. Drobouchevitch, I. G. & Strusevich, V. A., 2000. "Heuristics for the two-stage job shop scheduling problem with a bottleneck machine," European Journal of Operational Research, Elsevier, vol. 123(2), pages 229-240, June.

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