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Scheduling with processing set restrictions: A literature update

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  • Leung, Joseph Y.-T.
  • Li, Chung-Lun

Abstract

In 2008, we published a survey paper on machine scheduling with processing set restrictions [Leung, J.Y.-T., Li, C.-L., 2008. Scheduling with processing set restrictions: a survey. Int. J. Prod. Econ. 116 (2), 251–262]. Since the appearance of that survey paper, there has been a significant increase in interest in this field. In this paper, we provide an expository update of this line of research. Our survey covers five types of processing set restrictions, namely inclusive processing sets, nested processing sets, interval processing sets, tree-hierarchical processing sets, and arbitrary processing sets, and it covers both offline and online problems. While our main focus is on scheduling models with a makespan objective, other performance criteria are also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:proeco:v:175:y:2016:i:c:p:1-11
    DOI: 10.1016/j.ijpe.2014.09.038
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    16. An Zhang & Yiwei Jiang & Lidan Fan & Jueliang Hu, 2015. "Optimal online algorithms on two hierarchical machines with tightly-grouped processing times," Journal of Combinatorial Optimization, Springer, vol. 29(4), pages 781-795, May.
    17. 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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    20. Wu, Yong & Ji, Min & Yang, Qifan, 2012. "Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision," International Journal of Production Economics, Elsevier, vol. 135(1), pages 367-371.
    21. Weidong Li & Jianping Li & Tongquan Zhang, 2012. "Two Approximation Schemes For Scheduling On Parallel Machines Under A Grade Of Service Provision," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-12.
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    Cited by:

    1. 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.
    2. Li, Shuguang, 2017. "Approximation algorithms for scheduling jobs with release times and arbitrary sizes on batch machines with non-identical capacities," European Journal of Operational Research, Elsevier, vol. 263(3), pages 815-826.
    3. Jinwen Ou & Xueling Zhong & Xiangtong Qi, 2016. "Scheduling parallel machines with inclusive processing set restrictions and job rejection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 667-681, December.
    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.
    5. Li, Shuguang, 2017. "Parallel batch scheduling with inclusive processing set restrictions and non-identical capacities to minimize makespan," European Journal of Operational Research, Elsevier, vol. 260(1), pages 12-20.

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