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The two-stage no-wait/blocking proportionate super shop scheduling problem

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  • Christos Koulamas
  • S.S. Panwalkar

Abstract

We analyze the ‘no-wait’ proportionate two-stage super shop scheduling problem with the objective of minimising the maximum job completion time (makespan). The existing simple sorting procedures for the open shop and the job shop do not work on the super shop. We show that the problem is still solvable in $ \hbox{O}({{n^3}} ) $ O(n3) time using a procedure based on dynamic programming (DP). A unique feature of this procedure is that the state variable is defined based on the number of jobs; thus, reducing the complexity to polynomial. The same procedure solves the super shop problem with the blocking constraint. We also consider the case of machine dominance and show that the problem can be solved in linear $ \hbox{O}(n ) $ O(n) time. Finally, we highlight the differences between the super shop with ‘no-wait’ and ‘synchronous’ processing modes via a numerical example.

Suggested Citation

  • Christos Koulamas & S.S. Panwalkar, 2019. "The two-stage no-wait/blocking proportionate super shop scheduling problem," International Journal of Production Research, Taylor & Francis Journals, vol. 57(10), pages 2956-2965, May.
    • Handle: RePEc:taf:tprsxx:v:57:y:2019:i:10:p:2956-2965
    DOI: 10.1080/00207543.2018.1518603
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    Cited by:

    1. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    2. Sun, Yige & Chung, Sai-Ho & Wen, Xin & Ma, Hoi-Lam, 2021. "Novel robotic job-shop scheduling models with deadlock and robot movement considerations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    3. Koulamas, Christos & Kyparisis, George J., 2023. "Two-stage no-wait proportionate flow shop scheduling with minimal service time variation and optional job rejection," European Journal of Operational Research, Elsevier, vol. 305(2), pages 608-616.

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