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On scheduling multiple parallel two-stage flowshops with Johnson’s Rule

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  • Guangwei Wu

    (Central South University of Forestry and Technology
    Central South University)

  • Fu Zuo

    (Central South University of Forestry and Technology)

  • Feng Shi

    (Central South University
    Xiangjiang Laboratory)

  • Jianxin Wang

    (Central South University)

Abstract

It is well-known that the classical Johnson’s Rule leads to optimal schedules on a two-stage flowshop. However, it is still unclear how Johnson’s Rule would help in approximation algorithms for scheduling an arbitrary number of parallel two-stage flowshops with the objective of minimizing the makespan. Thus within the paper, we study the problem and propose a new efficient algorithm that incorporates Johnson’s Rule applied on each individual flowshop with a carefully designed job assignment process to flowshops. The algorithm is successfully shown to have a runtime $$O(n \log n)$$ O ( n log n ) and an approximation ratio 7/3, where n is the number of jobs. Compared with the recent PTAS result for the problem (Dong et al. in Eur J Oper Res 218(1):16–24, 2020), our algorithm has a larger approximation ratio, but it is more efficient in practice from the perspective of runtime.

Suggested Citation

  • Guangwei Wu & Fu Zuo & Feng Shi & Jianxin Wang, 2024. "On scheduling multiple parallel two-stage flowshops with Johnson’s Rule," Journal of Combinatorial Optimization, Springer, vol. 47(2), pages 1-20, March.
    • Handle: RePEc:spr:jcomop:v:47:y:2024:i:2:d:10.1007_s10878-024-01107-z
    DOI: 10.1007/s10878-024-01107-z
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    References listed on IDEAS

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    2. Ruiz, Ruben & Maroto, Concepcion, 2005. "A comprehensive review and evaluation of permutation flowshop heuristics," European Journal of Operational Research, Elsevier, vol. 165(2), pages 479-494, September.
    3. Dong, Jianming & Jin, Ruyan & Luo, Taibo & Tong, Weitian, 2020. "A polynomial-time approximation scheme for an arbitrary number of parallel two-stage flow-shops," European Journal of Operational Research, Elsevier, vol. 281(1), pages 16-24.
    4. 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.
    5. Zhang, Xiandong & van de Velde, Steef, 2012. "Approximation algorithms for the parallel flow shop problem," European Journal of Operational Research, Elsevier, vol. 216(3), pages 544-552.
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