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Scheduling Three-Operation Jobs in a Two-Machine Flow Shop to Minimize Makespan

Author

Listed:
  • Jatinder Gupta
  • Christos Koulamas
  • George Kyparisis
  • Chris Potts
  • Vitaly Strusevich

Abstract

This paper considers a variant of the classical problem of minimizing makespan in a two-machine flow shop. In this variant, each job has three operations, where the first operation must be performed on the first machine, the second operation can be performed on either machine but cannot be preempted, and the third operation must be performed on the second machine. The NP-hard nature of the problem motivates the design and analysis of approximation algorithms. It is shown that a schedule in which the operations are sequenced arbitrarily, but without inserted machine idle time, has a worst-case performance ratio of 2. Also, an algorithm that constructs four schedules and selects the best is shown to have a worst-case performance ratio of 3/2. A polynomial time approximation scheme (PTAS) is also presented. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Jatinder Gupta & Christos Koulamas & George Kyparisis & Chris Potts & Vitaly Strusevich, 2004. "Scheduling Three-Operation Jobs in a Two-Machine Flow Shop to Minimize Makespan," Annals of Operations Research, Springer, vol. 129(1), pages 171-185, July.
    • Handle: RePEc:spr:annopr:v:129:y:2004:i:1:p:171-185:10.1023/b:anor.0000030687.72169.c7
    DOI: 10.1023/B:ANOR.0000030687.72169.c7
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    Citations

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    Cited by:

    1. Bagchi, Tapan P. & Gupta, Jatinder N.D. & Sriskandarajah, Chelliah, 2006. "A review of TSP based approaches for flowshop scheduling," European Journal of Operational Research, Elsevier, vol. 169(3), pages 816-854, March.
    2. Gultekin, Hakan, 2012. "Scheduling in flowshops with flexible operations: Throughput optimization and benefits of flexibility," International Journal of Production Economics, Elsevier, vol. 140(2), pages 900-911.
    3. S. Knust & N. V. Shakhlevich & S. Waldherr & C. Weiß, 2019. "Shop scheduling problems with pliable jobs," Journal of Scheduling, Springer, vol. 22(6), pages 635-661, December.
    4. Lin-Hui Sun & Kai Cui & Ju-Hong Chen & Jun Wang & Xian-Chen He, 2013. "Some results of the worst-case analysis for flow shop scheduling with a learning effect," Annals of Operations Research, Springer, vol. 211(1), pages 481-490, December.
    5. Bertrand M. T. Lin & F. J. Hwang & Jatinder N. D. Gupta, 2017. "Two-machine flowshop scheduling with three-operation jobs subject to a fixed job sequence," Journal of Scheduling, Springer, vol. 20(3), pages 293-302, June.
    6. Matthias Bultmann & Sigrid Knust & Stefan Waldherr, 2018. "Flow shop scheduling with flexible processing times," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 809-829, July.

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