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An O(n2) algorithm for the variable common due date, minimal tardy jobs bicriteria two-machine flow shop problem with ordered machines

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  • Panwalkar, S.S.
  • Koulamas, Christos

Abstract

We consider the ordinary NP- hard two-machine flow shop problem with the objective of determining simultaneously a minimal common due date and the minimal number of tardy jobs. We present an O(n2) algorithm for the problem when the machines are ordered, that is, when each job has its smaller processing time on the first (second) machine. We also discuss the applicability of the proposed algorithm to the corresponding single-objective problem in which the common due date is given.

Suggested Citation

  • Panwalkar, S.S. & Koulamas, Christos, 2012. "An O(n2) algorithm for the variable common due date, minimal tardy jobs bicriteria two-machine flow shop problem with ordered machines," European Journal of Operational Research, Elsevier, vol. 221(1), pages 7-13.
    • Handle: RePEc:eee:ejores:v:221:y:2012:i:1:p:7-13
    DOI: 10.1016/j.ejor.2012.02.020
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    References listed on IDEAS

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    1. M. L. Smith & S. S. Panwalkar & R. A. Dudek, 1975. "Flowshop Sequencing Problem with Ordered Processing Time Matrices," Management Science, INFORMS, vol. 21(5), pages 544-549, January.
    2. Peng Si Ow, 1985. "Focused Scheduling in Proportionate Flowshops," Management Science, INFORMS, vol. 31(7), pages 852-869, July.
    3. Della Croce, Federico & Gupta, Jatinder N. D. & Tadei, Roberto, 2000. "Minimizing tardy jobs in a flowshop with common due date," European Journal of Operational Research, Elsevier, vol. 120(2), pages 375-381, January.
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    Cited by:

    1. Christos Koulamas & Shrikant. S. Panwalkar, 2013. "A note on combined job selection and sequencing problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(6), pages 449-453, September.
    2. Della Croce, Federico & Koulamas, Christos & T'kindt, Vincent, 2017. "A constraint generation approach for two-machine shop problems with jobs selection," European Journal of Operational Research, Elsevier, vol. 259(3), pages 898-905.
    3. S.S. Panwalkar & Milton L. Smith & Christos Koulamas, 2013. "Review of the ordered and proportionate flow shop scheduling research," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 46-55, February.

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