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Solving the two-machine open shop problem with a single server with respect to the makespan

Author

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  • Nadia Babou

    (Université Mouloud Mammeri de Tizi-Ouzou
    Université des Sciences et de la Technologie Houari Boumédiène)

  • Djamal Rebaine

    (Université du Québec à Chicoutimi)

  • Mourad Boudhar

    (Université des Sciences et de la Technologie Houari Boumédiène)

Abstract

We address in this paper the two-machine open shop problem with a single server to prepare jobs before going through the processing so as to minimize the makespan. The server is only needed during the preparation phase before becoming available again, leaving the prepared job to complete its processing. We present three lower bounds with respect to the makespan. In addition, we show the $$\mathcal{N}\mathcal{P}$$ N P -completeness of two restricted cases. Then, we present a well solvable case. Finally, we develop two mixed integer linear programming (MILP) models for the general problem along with an experimental study we conducted to analyze their performance.

Suggested Citation

  • Nadia Babou & Djamal Rebaine & Mourad Boudhar, 2024. "Solving the two-machine open shop problem with a single server with respect to the makespan," Annals of Operations Research, Springer, vol. 338(2), pages 857-877, July.
    • Handle: RePEc:spr:annopr:v:338:y:2024:i:2:d:10.1007_s10479-024-06097-z
    DOI: 10.1007/s10479-024-06097-z
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    References listed on IDEAS

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    1. Allahverdi, Ali, 2015. "The third comprehensive survey on scheduling problems with setup times/costs," European Journal of Operational Research, Elsevier, vol. 246(2), pages 345-378.
    2. Ruiz, Ruben & Maroto, Concepcion & Alcaraz, Javier, 2005. "Solving the flowshop scheduling problem with sequence dependent setup times using advanced metaheuristics," European Journal of Operational Research, Elsevier, vol. 165(1), pages 34-54, August.
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    4. Ammar Oulamara & Djamal Rebaine & Mehdi Serairi, 2013. "Scheduling the two-machine open shop problem under resource constraints for setting the jobs," Annals of Operations Research, Springer, vol. 211(1), pages 333-356, December.
    5. Averbakh, Igor & Berman, Oded & Chernykh, Ilya, 2005. "A -approximation algorithm for the two-machine routing open-shop problem on a two-node network," European Journal of Operational Research, Elsevier, vol. 166(1), pages 3-24, October.
    6. Allahverdi, Ali & Gupta, Jatinder N. D. & Aldowaisan, Tariq, 1999. "A review of scheduling research involving setup considerations," Omega, Elsevier, vol. 27(2), pages 219-239, April.
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