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New characteristics of optimal solutions for the two-machine flowshop problem with unlimited buffers

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  • Ghaith Rabadi
  • Mohamed Kais Msakni
  • Elkin Rodriguez-Velasquez
  • William Alvarez-Bermudez

Abstract

The two-machine flowshop problem with unlimited buffers with the objective of minimising the makespan (F2||Cmax) is addressed. Johnson’s algorithm finds optimal solutions (permutations) to this problem, but are not necessarily the only optimal solutions. We show in this paper that certain jobs that we define as Critical Jobs, must occupy specific positions in any optimal sequence, not only in Johnson’s solutions. We also prove that jobs that precede a critical job cannot be exchanged with jobs that succeed it in an optimal sequence, which reduces the number of enumerations necessary to identify all optimal solutions. The findings of this research can be useful in reducing the search space for optimal enumeration algorithms such as branch-and-bound.

Suggested Citation

  • Ghaith Rabadi & Mohamed Kais Msakni & Elkin Rodriguez-Velasquez & William Alvarez-Bermudez, 2019. "New characteristics of optimal solutions for the two-machine flowshop problem with unlimited buffers," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(6), pages 962-973, June.
    • Handle: RePEc:taf:tjorxx:v:70:y:2019:i:6:p:962-973
    DOI: 10.1080/01605682.2018.1475114
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    Cited by:

    1. Geser, Philine & Le, Hoang Thanh & Hartmann, Tom & Middendorf, Martin, 2022. "On permutation schedules for two-machine flow shops with buffer constraints and constant processing times on one machine," European Journal of Operational Research, Elsevier, vol. 303(2), pages 593-601.

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