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Approximation algorithms for two-stage flexible flow shop scheduling

Author

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  • Minghui Zhang

    (Dalian Neusoft University of Information
    Dalian University of Technology)

  • Yan Lan

    (Dalian Neusoft University of Information
    Dalian University of Technology)

  • Xin Han

    (Dalian University of Technology)

Abstract

This paper considers a two-stage flexible flow shop scheduling problem, where there are a single machine at the first stage and m parallel machines at the second stage. Each task can be processed by multiple parallel machines at the second stage. The objective is to minimize the makespan. Under some special conditions there is a 3-approximation algorithm for this problem. We propose a new ($$2+\epsilon $$2+ϵ)-approximation algorithm without any condition. For the case where all parallel machines assigned to a task at the second stage must have contiguous addresses, we propose two polynomial time approximation algorithms with approximate ratio less than or equal to 3 by using the existing parallel machine scheduling and strip packing results. Meanwhile two special cases are discussed when the machines number of the second stage is 2 and 3 respectively. Two approximation algorithms with approximation ratios of 2.5 and 2.67 under linear time complexity are proposed. Finally a new lower bound of the model is provided according to the classical Johnson algorithm which improves the previous result.

Suggested Citation

  • Minghui Zhang & Yan Lan & Xin Han, 2020. "Approximation algorithms for two-stage flexible flow shop scheduling," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 1-14, January.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:1:d:10.1007_s10878-019-00449-3
    DOI: 10.1007/s10878-019-00449-3
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    References listed on IDEAS

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    1. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    2. Lin, Hung-Tso & Liao, Ching-Jong, 2003. "A case study in a two-stage hybrid flow shop with setup time and dedicated machines," International Journal of Production Economics, Elsevier, vol. 86(2), pages 133-143, November.
    3. Byung-Cheon Choi & Kangbok Lee, 2013. "Two-stage proportionate flexible flow shop to minimize the makespan," Journal of Combinatorial Optimization, Springer, vol. 25(1), pages 123-134, January.
    4. Almeder, Christian & Hartl, Richard F., 2013. "A metaheuristic optimization approach for a real-world stochastic flexible flow shop problem with limited buffer," International Journal of Production Economics, Elsevier, vol. 145(1), pages 88-95.
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    Cited by:

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    2. Anzhen Peng & Longcheng Liu & Weifeng Lin, 2021. "Improved approximation algorithms for two-stage flexible flow shop scheduling," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 28-42, January.

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