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Fast approximation algorithms for uniform machine scheduling with processing set restrictions

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  • Leung, Joseph Y-T.
  • Ng, C.T.

Abstract

We consider the problem of nonpreemptively scheduling a set of independent jobs on a set of uniform machines, where each job has a set of machines to which it can be assigned. This kind of restriction is called the processing set restriction. In the literature there are many kinds of processing set restrictions that have been studied. In this paper we consider two kinds: the “inclusive processing set” and the “tree-hierarchical processing set”. Epstein and Levin (2011) have given Polynomial Time Approximation Schemes (PTAS) to solve both classes. However, the running times of their PTAS are rather high. In this paper, we give fast approximation algorithms for both cases and show that they both have a worst-case performance bound of 4/3. Moreover, we show that the bounds are achievable.

Suggested Citation

  • Leung, Joseph Y-T. & Ng, C.T., 2017. "Fast approximation algorithms for uniform machine scheduling with processing set restrictions," European Journal of Operational Research, Elsevier, vol. 260(2), pages 507-513.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:2:p:507-513
    DOI: 10.1016/j.ejor.2017.01.013
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    References listed on IDEAS

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    1. Chung-Lun Li & Kangbok Lee, 2016. "A note on scheduling jobs with equal processing times and inclusive processing set restrictions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(1), pages 83-86, January.
    2. Li, Chung-Lun & Wang, Xiuli, 2010. "Scheduling parallel machines with inclusive processing set restrictions and job release times," European Journal of Operational Research, Elsevier, vol. 200(3), pages 702-710, February.
    3. Chung-Lun Li & Qingying Li, 2015. "Scheduling jobs with release dates, equal processing times, and inclusive processing set restrictions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(3), pages 516-523, March.
    4. Leung, Joseph Y.-T. & Li, Chung-Lun, 2016. "Scheduling with processing set restrictions: A literature update," International Journal of Production Economics, Elsevier, vol. 175(C), pages 1-11.
    5. Leung, Joseph Y.-T. & Li, Chung-Lun, 2008. "Scheduling with processing set restrictions: A survey," International Journal of Production Economics, Elsevier, vol. 116(2), pages 251-262, December.
    6. Epstein, Leah & Levin, Asaf, 2011. "Scheduling with processing set restrictions: PTAS results for several variants," International Journal of Production Economics, Elsevier, vol. 133(2), pages 586-595, October.
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    Cited by:

    1. Chi To Ng & T. C. E. Cheng & Eugene Levner & Boris Kriheli, 2021. "Optimal bi-criterion planning of rescue and evacuation operations for marine accidents using an iterative scheduling algorithm," Annals of Operations Research, Springer, vol. 296(1), pages 407-420, January.

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