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The flow shop problem with no-idle constraints: A review and approximation

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  • Goncharov, Yaroslav
  • Sevastyanov, Sergey

Abstract

The makespan minimization problem in flow shops with no-idle constraints on machines is considered. The latter means that each machine, once started, must process all its operations without intermediate idle time until all those operations are completed. The problem is known to be strongly NP-hard already for three machines. While being based on a geometrical approach, we propose several polynomial time heuristics (for the general case and for special cases of 3 and 4 machines) which provide asymptotically optimal solutions for the increasing number of jobs. A comprehensive review of relevant results is also presented.

Suggested Citation

  • Goncharov, Yaroslav & Sevastyanov, Sergey, 2009. "The flow shop problem with no-idle constraints: A review and approximation," European Journal of Operational Research, Elsevier, vol. 196(2), pages 450-456, July.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:2:p:450-456
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    References listed on IDEAS

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    1. Saadani, Nour El Houda & Guinet, Alain & Moalla, Mohamed, 2005. "A travelling salesman approach to solve the F/no-idle/Cmax problem," European Journal of Operational Research, Elsevier, vol. 161(1), pages 11-20, February.
    2. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    3. C. A. Glass & J. N. D. Gupta & C. N. Potts, 1999. "Two-Machine No-Wait Flow Shop Scheduling with Missing Operations," Mathematics of Operations Research, INFORMS, vol. 24(4), pages 911-924, November.
    4. Sergey Sevastianov, 1998. "Nonstrict vector summationin multi-operation scheduling," Annals of Operations Research, Springer, vol. 83(0), pages 179-212, October.
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    Cited by:

    1. Guo-Sheng Liu & Jin-Jin Li & Ying-Si Tang, 2018. "Minimizing Total Idle Energy Consumption in the Permutation Flow Shop Scheduling Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-19, December.
    2. S. S. Panwalkar & Christos Koulamas, 2020. "Three-stage ordered flow shops with either synchronous flow, blocking or no-idle machines," Journal of Scheduling, Springer, vol. 23(1), pages 145-154, February.
    3. Bailin Wang & Kai Huang & Tieke Li, 2018. "Two-stage hybrid flowshop scheduling with simultaneous processing machines," Journal of Scheduling, Springer, vol. 21(4), pages 387-411, August.
    4. Tolga Bektaş & Alper Hamzadayı & Rubén Ruiz, 2020. "Benders decomposition for the mixed no-idle permutation flowshop scheduling problem," Journal of Scheduling, Springer, vol. 23(4), pages 513-523, August.
    5. Federico Della Croce & Andrea Grosso & Fabio Salassa, 2021. "Minimizing total completion time in the two-machine no-idle no-wait flow shop problem," Journal of Heuristics, Springer, vol. 27(1), pages 159-173, April.
    6. J.-C. Billaut & F. Della Croce & F. Salassa & V. T’kindt, 2019. "No-idle, no-wait: when shop scheduling meets dominoes, Eulerian paths and Hamiltonian paths," Journal of Scheduling, Springer, vol. 22(1), pages 59-68, February.

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