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Polynomial time algorithms for two special classes of the proportionate multiprocessor open shop

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  • Matta, Marie E.
  • Elmaghraby, Salah E.

Abstract

This paper describes a complex scheduling problem taken from a hospital diagnostic testing center that schedules hundreds of patients in an open shop environment consisting of multiple facilities and multiple processors. This scheduling problem, known as the multiprocessor open shop (MPOS) problem, is strongly NP-hard with few published results. Realizing that in many MPOS environments processing times are stage-dependent, not both job and stage-dependent, this paper examines a new class of problems for the MPOS--proportionate ones. This paper exploits the structural nature of the proportionate MPOS and defines new terms. Despite the enormous complexity of the MPOS problem, this work demonstrates that polynomial time algorithms exist for two special cases. Since other applications of this problem exist in service and manufacturing environments, solving the proportionate MPOS problem is not only significant in the theory of optimization, but also in many real-world applications.

Suggested Citation

  • Matta, Marie E. & Elmaghraby, Salah E., 2010. "Polynomial time algorithms for two special classes of the proportionate multiprocessor open shop," European Journal of Operational Research, Elsevier, vol. 201(3), pages 720-728, March.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:3:p:720-728
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    References listed on IDEAS

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    Cited by:

    1. Shahaboddin Shamshirband & Mohammad Shojafar & A. Hosseinabadi & Maryam Kardgar & M. Nasir & Rodina Ahmad, 2015. "OSGA: genetic-based open-shop scheduling with consideration of machine maintenance in small and medium enterprises," Annals of Operations Research, Springer, vol. 229(1), pages 743-758, June.
    2. Zeynep Adak & Mahmure Övül Arıoğlu Akan & Serol Bulkan, 0. "Multiprocessor open shop problem: literature review and future directions," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-23.
    3. Zeynep Adak & Mahmure Övül Arıoğlu & Serol Bulkan, 2022. "An ant colony optimization approach for the proportionate multiprocessor open shop," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 785-817, May.
    4. Jiawei Zhang & Ling Wang & Lining Xing, 2019. "Large-scale medical examination scheduling technology based on intelligent optimization," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 385-404, January.
    5. Agnihothri, Saligrama & Cappanera, Paola & Nonato, Maddalena & Visintin, Filippo, 2024. "Appointment scheduling in surgery pre-admission testing clinics," Omega, Elsevier, vol. 123(C).
    6. Tamer Abdelmaguid & Mohamed Shalaby & Mohamed Awwad, 2014. "A tabu search approach for proportionate multiprocessor open shop scheduling," Computational Optimization and Applications, Springer, vol. 58(1), pages 187-203, May.
    7. Zeynep Adak & Mahmure Övül Arıoğlu Akan & Serol Bulkan, 2020. "Multiprocessor open shop problem: literature review and future directions," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 547-569, August.

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