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Non-permutation flowshop scheduling problem with minimal and maximal time lags: theoretical study and heuristic

Author

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  • E. Dhouib

    (Unité de recherche LOgistique Gestion Industrielle et de la Qualité (LOGIQ), Institut Supérieur de Gestion Industrielle de Sfax, Université de Sfax)

  • J. Teghem

    (Service de Mathématique et de Recherche Opérationnelle (MathRO), Université de Mons/Faculté Polytechnique)

  • T. Loukil

    (Unité de recherche LOgistique Gestion Industrielle et de la Qualité (LOGIQ), Institut Supérieur de Gestion Industrielle de Sfax, Université de Sfax)

Abstract

In this paper, we address the non-permutation flowshop scheduling problem with minimal and maximal time lags between successive operations of each job. For this problem, the set of permutation schedules is not a dominant set but not all non-permutation schedules are feasible because they are not always able to satisfy all time lag constraints. We present a theoretical study, limited to the two-machine case, and related to the change on one machine of the order of two successive jobs of a permutation schedule. This study gives first the necessary conditions to make such move with regard to the feasibility of the schedule; secondly the necessary conditions to make such move interesting with regard to either the makespan or the number of tardy jobs. Through this analysis, we obtain new properties of dominance of permutation schedules. The results of the study are incorporated into a heuristic algorithm which starts the search with optimal permutation schedules and tries to improve them so as to obtain better non-permutation schedules. We also propose a mixed integer linear programming model. The objective function is to minimize lexicographically the number of tardy jobs as primary criterion and the makespan as secondary one. Computational experiments are performed to compare permutation with non-permutation schedules.

Suggested Citation

  • E. Dhouib & J. Teghem & T. Loukil, 2018. "Non-permutation flowshop scheduling problem with minimal and maximal time lags: theoretical study and heuristic," Annals of Operations Research, Springer, vol. 267(1), pages 101-134, August.
    • Handle: RePEc:spr:annopr:v:267:y:2018:i:1:d:10.1007_s10479-018-2775-5
    DOI: 10.1007/s10479-018-2775-5
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    References listed on IDEAS

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    1. Imen Hamdi & Ammar Oulamara & Taïcir Loukil, 2015. "A branch and bound algorithm to minimise the total tardiness in the two-machine permutation flowshop scheduling problem with minimal time lags," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 23(4), pages 387-405.
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    Cited by:

    1. Mohamed Amine Mkadem & Aziz Moukrim & Mehdi Serairi, 2021. "Exact method for the two-machine flow-shop problem with time delays," Annals of Operations Research, Springer, vol. 298(1), pages 375-406, March.

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