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The representation of partially-concurrent open shop problems

Author

Listed:
  • Tal Grinshpoun

    (Ariel University)

  • Hagai Ilani

    (SCE – Shamoon College of Engineering)

  • Elad Shufan

    (SCE – Shamoon College of Engineering)

Abstract

The partially-concurrent open shop scheduling problem is introduced. The standard open shop scheduling problem is generalized by allowing some operations to be processed concurrently. A schedule for the partially-concurrent problem is represented by a digraph. We show that the scheduling problem is equivalent to a problem of orienting a given undirected graph, called a conflict graph. The schedule digraph is then modeled by a matrix, generalizing the rank matrix representation. The problem is shown to be NP-hard. The representation can be used to generalize previously discussed standard open shop issues. It is demonstrated by generalizing the theoretical concept of reducibility and also by using standard open shop heuristic solutions to the partially-concurrent scenario. The presented problem is directly motivated from a real-life timetabling project of assigning technicians to airplanes in an airplane garage.

Suggested Citation

  • Tal Grinshpoun & Hagai Ilani & Elad Shufan, 2017. "The representation of partially-concurrent open shop problems," Annals of Operations Research, Springer, vol. 252(2), pages 455-469, May.
    • Handle: RePEc:spr:annopr:v:252:y:2017:i:2:d:10.1007_s10479-015-1934-1
    DOI: 10.1007/s10479-015-1934-1
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    References listed on IDEAS

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    1. H. Bräsel & M. Harborth & T. Tautenhahn & P. Willenius, 1999. "On the set of solutions of the open shop problem," Annals of Operations Research, Springer, vol. 92(0), pages 241-263, January.
    2. Wagneur, E. & Sriskandarajah, C., 1993. "Openshops with jobs overlap," European Journal of Operational Research, Elsevier, vol. 71(3), pages 366-378, December.
    3. Michael Andresen & Tanka Dhamala, 2012. "New algorithms and complexity status of the reducibility problem of sequences in open shop scheduling minimizing the makespan," Annals of Operations Research, Springer, vol. 196(1), pages 1-26, July.
    4. Taillard, E., 1993. "Benchmarks for basic scheduling problems," European Journal of Operational Research, Elsevier, vol. 64(2), pages 278-285, January.
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    Cited by:

    1. Hagai Ilani & Tal Grinshpoun & Elad Shufan, 2021. "Bounded colouring motivated by the limited resource partially concurrent open shop problem," Annals of Operations Research, Springer, vol. 302(2), pages 461-476, July.
    2. 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.

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