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Online scheduling on parallel machines with two GoS levels

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  • Yiwei Jiang

    (Zhejiang Sci-Tech University)

Abstract

This paper investigates the online scheduling problem on parallel and identical machines with a new feature that service requests from various customers are entitled to many different grade of service (GoS) levels. Hence each job and machine are labeled with the GoS levels, and each job can be processed by a particular machine only when the GoS level of the job is not less than that of the machine. The goal is to minimize the makespan. In this paper, we consider the problem with two GoS levels. It assumes that the GoS levels of the first k machines and the last m−k machines are 1 and 2, respectively. And every job has a GoS level of 1 alternatively or 2. We first prove the lower bound of the problem under consideration is at least 2. Then we discuss the performance of algorithm AW presented in Azar et al. (J. Algorithms 18:221–237, 1995) for the problem and show it has a tight bound of 4−1/m. Finally, we present an approximation algorithm with competitive ratio $\frac{12+4\sqrt{2}}{7}\approx 2.522$ .

Suggested Citation

  • Yiwei Jiang, 2008. "Online scheduling on parallel machines with two GoS levels," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 28-38, July.
    • Handle: RePEc:spr:jcomop:v:16:y:2008:i:1:d:10.1007_s10878-007-9095-z
    DOI: 10.1007/s10878-007-9095-z
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    References listed on IDEAS

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    1. T C E Cheng & L Y Kang & C T Ng, 2007. "Due-date assignment and parallel-machine scheduling with deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(8), pages 1103-1108, August.
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    Cited by:

    1. Zhiyi Tan & An Zhang, 2010. "A note on hierarchical scheduling on two uniform machines," Journal of Combinatorial Optimization, Springer, vol. 20(1), pages 85-95, July.
    2. Shlomo Karhi & Dvir Shabtay, 2013. "On the optimality of the TLS algorithm for solving the online-list scheduling problem with two job types on a set of multipurpose machines," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 198-222, July.
    3. Ming Liu & Chengbin Chu & Yinfeng Xu & Feifeng Zheng, 2011. "Semi-online scheduling on 2 machines under a grade of service provision with bounded processing times," Journal of Combinatorial Optimization, Springer, vol. 21(1), pages 138-149, January.
    4. Karhi, Shlomo & Shabtay, Dvir, 2014. "Online scheduling of two job types on a set of multipurpose machines," International Journal of Production Economics, Elsevier, vol. 150(C), pages 155-162.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Jueliang Hu & Yiwei Jiang & Ping Zhou & An Zhang & Qinghui Zhang, 2017. "Total completion time minimization in online hierarchical scheduling of unit-size jobs," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 866-881, April.
    10. 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.
    11. Islam Akaria & Leah Epstein, 2023. "Bin stretching with migration on two hierarchical machines," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 111-153, August.
    12. Li-ying Hou & Liying Kang, 2012. "Online scheduling on uniform machines with two hierarchies," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 593-612, November.
    13. Lee, Kangbok & Hwang, Hark-Chin & Lim, Kyungkuk, 2014. "Semi-online scheduling with GoS eligibility constraints," International Journal of Production Economics, Elsevier, vol. 153(C), pages 204-214.
    14. Zhenbo Wang & Wenxun Xing, 2010. "Worst-case analysis for on-line service policies," Journal of Combinatorial Optimization, Springer, vol. 19(1), pages 107-122, January.
    15. Islam Akaria & Leah Epstein, 2022. "Online scheduling with migration on two hierarchical machines," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3535-3548, December.

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