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Routing open shop and flow shop scheduling problems

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  • Yu, Wei
  • Liu, Zhaohui
  • Wang, Leiyang
  • Fan, Tijun

Abstract

We consider a generalization of the classical open shop and flow shop scheduling problems where the jobs are located at the vertices of an undirected graph and the machines, initially located at the same vertex, have to travel along the graph to process the jobs. The objective is to minimize the makespan. In the tour-version the makespan means the time by which each machine has processed all jobs and returned to the initial location. While in the path-version the makespan represents the maximum completion time of the jobs. We present improved approximation algorithms for various cases of the open shop problem on a general graph, and the tour-version of the two-machine flow shop problem on a tree. Also, we prove that both versions of the latter problem are NP-hard, which answers an open question posed in the literature.

Suggested Citation

  • Yu, Wei & Liu, Zhaohui & Wang, Leiyang & Fan, Tijun, 2011. "Routing open shop and flow shop scheduling problems," European Journal of Operational Research, Elsevier, vol. 213(1), pages 24-36, August.
    • Handle: RePEc:eee:ejores:v:213:y:2011:i:1:p:24-36
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    References listed on IDEAS

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    1. Averbakh, Igor & Berman, Oded & Chernykh, Ilya, 2006. "The routing open-shop problem on a network: Complexity and approximation," European Journal of Operational Research, Elsevier, vol. 173(2), pages 531-539, September.
    2. Igor Averbakh & Oded Berman, 1999. "A Simple Heuristic for m-Machine Flow-Shop and its Applications in Routing-Scheduling Problems," Operations Research, INFORMS, vol. 47(1), pages 165-170, February.
    3. 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.
    4. Igor Averbakh & Oded Berman, 1996. "Routing Two-Machine Flowshop Problems on Networks with Special Structure," Transportation Science, INFORMS, vol. 30(4), pages 303-314, November.
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    Cited by:

    1. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    2. 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.
    3. Berghman, Lotte & Kergosien, Yannick & Billaut, Jean-Charles, 2023. "A review on integrated scheduling and outbound vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 1-23.
    4. Hosseini, Amir & Otto, Alena & Pesch, Erwin, 2024. "Scheduling in manufacturing with transportation: Classification and solution techniques," European Journal of Operational Research, Elsevier, vol. 315(3), pages 821-843.

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