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Applying “Peeling Onion” approach for competitive analysis in online scheduling with rejection

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  • Ma, Ran
  • Guo, Sainan

Abstract

In this study, we consider the classical online scheduling problem with rejection on identical parallel machines. In particular, a series of independent jobs arriving online over time will be scheduled on the identical machines with the flexibility of rejection, which implies that each job is either rejected with a penalty cost or accepted and scheduled on one of the identical machines. In addition, the knowledge of each job Jj, including the processing time pj, release date rj, and penalty cost ej, is disclosed upon arrival of this job. Our goal is to minimize the total completion time of the accepted jobs plus the total penalty cost of the rejected jobs. For this problem, we provide a deterministic polynomial time online algorithm named as Delayed Shortest Processing Time with Rejection, shortly as DSPTR. For the sake of analyzing the competitive ratio of DSPTR, we introduce an interesting and efficient approach entitled as “Peeling Onion”. By means of “Peeling Onion”, we demonstrate that DSPTR is a 2-competitive online algorithm and the bound is tight. We believe that the introduction of the analysis approach “Peeling Onion” could also be applied to other online optimization problems and yield a new perspective on competitive analysis in general.

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  • Ma, Ran & Guo, Sainan, 2021. "Applying “Peeling Onion” approach for competitive analysis in online scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 290(1), pages 57-67.
    • Handle: RePEc:eee:ejores:v:290:y:2021:i:1:p:57-67
    DOI: 10.1016/j.ejor.2020.08.009
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    References listed on IDEAS

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    1. Hermelin, Danny & Pinedo, Michael & Shabtay, Dvir & Talmon, Nimrod, 2019. "On the parameterized tractability of single machine scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 273(1), pages 67-73.
    2. Edmund Burke & Michael Pinedo, 2019. "Journal of scheduling (2019)," Journal of Scheduling, Springer, vol. 22(1), pages 1-2, February.
    3. Edward J. Anderson & Chris N. Potts, 2004. "Online Scheduling of a Single Machine to Minimize Total Weighted Completion Time," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 686-697, August.
    4. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
    5. Zhang, An & Qi, Xiangtong & Li, Guanhua, 2020. "Machine scheduling with soft precedence constraints," European Journal of Operational Research, Elsevier, vol. 282(2), pages 491-505.
    6. Nicole Megow & Marc Uetz & Tjark Vredeveld, 2006. "Models and Algorithms for Stochastic Online Scheduling," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 513-525, August.
    7. Lee, Kangbok & Zheng, Feifeng & Pinedo, Michael L., 2019. "Online scheduling of ordered flow shops," European Journal of Operational Research, Elsevier, vol. 272(1), pages 50-60.
    8. Ran Ma & Jinjiang Yuan, 2017. "Online scheduling to minimize the total weighted completion time plus the rejection cost," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 483-503, August.
    9. Nicholas G. Hall & Marc E. Posner & Chris N. Potts, 2009. "Online Scheduling with Known Arrival Times," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 92-102, February.
    10. Robbert Fokkink & Thomas Lidbetter & László A. Végh, 2019. "On Submodular Search and Machine Scheduling," Management Science, INFORMS, vol. 44(4), pages 1431-1449, November.
    11. Lu, Lingfa & Ng, C.T. & Zhang, Liqi, 2011. "Optimal algorithms for single-machine scheduling with rejection to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 130(2), pages 153-158, April.
    12. Zhang, Liqi & Lu, Lingfa & Yuan, Jinjiang, 2009. "Single machine scheduling with release dates and rejection," European Journal of Operational Research, Elsevier, vol. 198(3), pages 975-978, November.
    13. Shi-Sheng Li & Ren-Xia Chen & Qi Feng & Cheng-Wen Jiao, 2019. "Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 957-971, October.
    14. Cheng, Yushao & Sun, Shijie, 2009. "Scheduling linear deteriorating jobs with rejection on a single machine," European Journal of Operational Research, Elsevier, vol. 194(1), pages 18-27, April.
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    Cited by:

    1. Jiamin Lu & Nishan Chen & Xin Feng, 2023. "Competitive Analysis of the Online Leasing Problem for Scarce Resources," IJERPH, MDPI, vol. 20(1), pages 1-11, January.
    2. Jiang, Yiwei & Wu, Mengjing & Chen, Xin & Dong, Jianming & Cheng, T.C.E. & Blazewicz, Jacek & Ji, Min, 2024. "Online early work scheduling on parallel machines," European Journal of Operational Research, Elsevier, vol. 315(3), pages 855-862.

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