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A semi-online algorithm and its competitive analysis for parallel-machine scheduling problem with rejection

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  • Ma, Ran
  • Guo, Sainan
  • Miao, Cuixia

Abstract

In this paper, we focus on a semi-online scheduling problem with rejection on identical parallel machines, where “semi-online” means that the ratio of the longest processing time among all jobs to the shortest one is no more than γ with γ ≥ 1. In particular, in this setting, there are a coupling of independent jobs arriving online over time with the flexibility of rejection, which implies that each job will be either accepted and scheduled on one of identical machines or rejected at the cost of penalty cost. Our objective is minimizing the total completion time of the accepted jobs plus the total penalty cost of the rejected jobs. For this problem, we design a deterministic polynomial time semi-online algorithm entitled as α Delayed Shortest Processing Time with Rejection (ADSPTR). In competitive analysis, by adopting the approach “Improved Instance Reduction”, we obtain the competitive ratio of ADSPTR is at most 1+1+γ(γ−1)−1γ.

Suggested Citation

  • Ma, Ran & Guo, Sainan & Miao, Cuixia, 2021. "A semi-online algorithm and its competitive analysis for parallel-machine scheduling problem with rejection," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306238
    DOI: 10.1016/j.amc.2020.125670
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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. Richard L. Daniels & Joseph B. Mazzola & Dailun Shi, 2004. "Flow Shop Scheduling with Partial Resource Flexibility," Management Science, INFORMS, vol. 50(5), pages 658-669, May.
    3. Viswanath Nagarajan & Maxim Sviridenko, 2009. "Tight Bounds for Permutation Flow Shop Scheduling," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 417-427, May.
    4. 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.
    5. 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.
    6. 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.
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