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Johnson's algorithm: A key to solve optimally or approximately flow shop scheduling problems with unavailability periods

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  • Allaoui, Hamid
  • Artiba, AbdelHakim

Abstract

Johnson's algorithm (JA) is perhaps the most classical algorithm in the scheduling area. JA gives the optimal solution to the two machine flow shop to minimize the makespan in polynomial time. Researchers have tried to extend this notorious result to obtain polynomial time algorithms for more general cases. Such importance motivated us to devote this paper to JA applied to three flow shop problems with unavailability periods to minimize the makespan. First we focus on the optimality condition of JA. Then we propose a modification of JA. After we calculate new performances of JA as a heuristic. Last we deal with an extension of JA.

Suggested Citation

  • Allaoui, Hamid & Artiba, AbdelHakim, 2009. "Johnson's algorithm: A key to solve optimally or approximately flow shop scheduling problems with unavailability periods," International Journal of Production Economics, Elsevier, vol. 121(1), pages 81-87, September.
    • Handle: RePEc:eee:proeco:v:121:y:2009:i:1:p:81-87
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    References listed on IDEAS

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    1. Liu, Shi Qiang & Kozan, Erhan, 2009. "Scheduling a flow shop with combined buffer conditions," International Journal of Production Economics, Elsevier, vol. 117(2), pages 371-380, February.
    2. Lee, Chung-Yee, 1999. "Two-machine flowshop scheduling with availability constraints," European Journal of Operational Research, Elsevier, vol. 114(2), pages 420-429, April.
    3. Leung, Joseph Y.-T. & Li, Chung-Lun, 2008. "Scheduling with processing set restrictions: A survey," International Journal of Production Economics, Elsevier, vol. 116(2), pages 251-262, December.
    4. Sriskandarajah, C. & Sethi, S. P., 1989. "Scheduling algorithms for flexible flowshops: Worst and average case performance," European Journal of Operational Research, Elsevier, vol. 43(2), pages 143-160, November.
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    Cited by:

    1. Shijin Wang & Ming Liu, 2016. "Two-machine flow shop scheduling integrated with preventive maintenance planning," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(3), pages 672-690, February.
    2. Lee, Wen-Chiung & Shiau, Yau-Ren & Chen, Shiuan-Kang & Wu, Chin-Chia, 2010. "A two-machine flowshop scheduling problem with deteriorating jobs and blocking," International Journal of Production Economics, Elsevier, vol. 124(1), pages 188-197, March.

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