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Bounded colouring motivated by the limited resource partially concurrent open shop problem

Author

Listed:
  • Hagai Ilani

    (SCE – Shamoon College of Engineering)

  • Tal Grinshpoun

    (Ariel University)

  • Elad Shufan

    (SCE – Shamoon College of Engineering)

Abstract

Partially Concurrent Open Shop Scheduling (PCOSS) is a relaxation of the well-known Open Shop Scheduling (OSS), where some of the operations that refer to the same job may be processed concurrently. Here we extend the study of the PCOSS model by considering an additional resource, which is limited to several units. We deal with the case of preemption PCOSS, where a few polynomial algorithms are known for its OSS counterpart. The scheduling problem is equivalent to the problem of conflict graph colouring. The restriction on the number of resource units bounds the size of colour classes. We thus study the problem of bounded vertex colouring. A new bound for the makespan is presented, and it is shown that for a 2-bounded colouring the bound is attainable. Some insight about a special case of PCOSS, composed of identical jobs, is given. The model correlates to a real-life timetabling project of assigning technicians to vehicles in a garage, with an additional resource, such as vehicle lift.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:302:y:2021:i:2:d:10.1007_s10479-019-03503-9
    DOI: 10.1007/s10479-019-03503-9
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    References listed on IDEAS

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    1. Hagai Ilani & Elad Shufan & Tal Grinshpoun, 2017. "Partially concurrent open shop scheduling with integral preemptions," Annals of Operations Research, Springer, vol. 259(1), pages 157-171, December.
    2. 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.
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