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On the optimality conditions of the two-machine flow shop problem

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  • Hadda, Hatem
  • Dridi, Najoua
  • Hajji, Mohamed Karim

Abstract

This paper tackles the makespan minimization for the well known two-machine flow shop problem. Several optimality conditions are discussed aiming at the characterization of a large set of optimal solutions. We show that our approach dominates some of the results found in the literature. We also establish a number of necessary optimality conditions and discuss the asymptotic behavior of the optimal makespan when the number of jobs goes to infinity.

Suggested Citation

  • Hadda, Hatem & Dridi, Najoua & Hajji, Mohamed Karim, 2018. "On the optimality conditions of the two-machine flow shop problem," European Journal of Operational Research, Elsevier, vol. 266(2), pages 426-435.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:426-435
    DOI: 10.1016/j.ejor.2017.09.029
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    References listed on IDEAS

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    1. Esswein, Carl & Billaut, Jean-Charles & Strusevich, Vitaly A., 2005. "Two-machine shop scheduling: Compromise between flexibility and makespan value," European Journal of Operational Research, Elsevier, vol. 167(3), pages 796-809, December.
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    3. Brah, Shaukat A. & Loo, Luan Luan, 1999. "Heuristics for scheduling in a flow shop with multiple processors," European Journal of Operational Research, Elsevier, vol. 113(1), pages 113-122, February.
    4. Briand, Cyril & La, H. Trung & Erschler, Jacques, 2006. "A new sufficient condition of optimality for the two-machine flowshop problem," European Journal of Operational Research, Elsevier, vol. 169(3), pages 712-722, March.
    5. Herbert G. Campbell & Richard A. Dudek & Milton L. Smith, 1970. "A Heuristic Algorithm for the n Job, m Machine Sequencing Problem," Management Science, INFORMS, vol. 16(10), pages 630-637, June.
    6. S. David Wu & Eui-Seok Byeon & Robert H. Storer, 1999. "A Graph-Theoretic Decomposition of the Job Shop Scheduling Problem to Achieve Scheduling Robustness," Operations Research, INFORMS, vol. 47(1), pages 113-124, February.
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