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Parallel machine scheduling with nested processing set restrictions

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  • Huo, Yumei
  • Leung, Joseph Y.-T.

Abstract

We consider the problem of scheduling a set of n independent jobs on m parallel machines, where each job can only be scheduled on a subset of machines called its processing set. The machines are linearly ordered, and the processing set of job j is given by two machine indexes aj and bj; i.e., job j can only be scheduled on machines aj,aj+1,...,bj. Two distinct processing sets are either nested or disjoint. Preemption is not allowed. Our goal is to minimize the makespan. It is known that the problem is strongly NP-hard and that there is a list-type algorithm with a worst-case bound of 2-1/m. In this paper we give an improved algorithm with a worst-case bound of 7/4. For two and three machines, the algorithm gives a better worst-case bound of 5/4 and 3/2, respectively.

Suggested Citation

  • Huo, Yumei & Leung, Joseph Y.-T., 2010. "Parallel machine scheduling with nested processing set restrictions," European Journal of Operational Research, Elsevier, vol. 204(2), pages 229-236, July.
    • Handle: RePEc:eee:ejores:v:204:y:2010:i:2:p:229-236
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    References listed on IDEAS

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    1. 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.
    2. Li, Chung-Lun, 2006. "Scheduling unit-length jobs with machine eligibility restrictions," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1325-1328, October.
    3. 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.
    4. Lin, Yixun & Li, Wenhua, 2004. "Parallel machine scheduling of machine-dependent jobs with unit-length," European Journal of Operational Research, Elsevier, vol. 156(1), pages 261-266, July.
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    Cited by:

    1. 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.
    2. Kangbok Lee & Joseph Leung & Michael Pinedo, 2013. "Makespan minimization in online scheduling with machine eligibility," Annals of Operations Research, Springer, vol. 204(1), pages 189-222, April.
    3. 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.
    4. Huiqiao Su & Michael Pinedo & Guohua Wan, 2017. "Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 249-267, April.

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