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The proportionate flow shop total tardiness problem

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  • Koulamas, Christos

Abstract

We consider the proportionate flow shop total tardiness problem and show how to implement Lawler's (1977) pseudo-polynomial dynamic programming (DP) algorithm for the single-machine total tardiness problem to the multi-machine environment of proportionate flow shop. We also present solvable special cases including one with small/big jobs that has not been considered for the corresponding single-machine problem. We then convert the DP algorithm for the proportionate flow shop to a fully polynomial time approximation scheme (FPTAS). Finally, we show by a counterexample that Pinedo's (2002, p. 140) statement that “the elimination criteria for the single-machine total weighted tardiness problem also apply to the proportionate flow shop total weighted tardiness problem” does not always hold and present an appropriately revised statement.

Suggested Citation

  • Koulamas, Christos, 2020. "The proportionate flow shop total tardiness problem," European Journal of Operational Research, Elsevier, vol. 284(2), pages 439-444.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:2:p:439-444
    DOI: 10.1016/j.ejor.2020.01.002
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    1. J. J. Kanet, 2007. "New Precedence Theorems for One-Machine Weighted Tardiness," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 579-588, August.
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    5. Enrique Gerstl & Baruch Mor & Gur Mosheiov, 2019. "Scheduling on a proportionate flowshop to minimise total late work," International Journal of Production Research, Taylor & Francis Journals, vol. 57(2), pages 531-543, January.
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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. Jin Qian & Haiyan Han, 2022. "Improved algorithms for proportionate flow shop scheduling with due-window assignment," Annals of Operations Research, Springer, vol. 309(1), pages 249-258, February.

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