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Batch scheduling of nonidentical job sizes with minsum criteria

Author

Listed:
  • Rongqi Li

    (Zhejiang University)

  • Zhiyi Tan

    (Zhejiang University)

  • Qianyu Zhu

    (Zhejiang University)

Abstract

This paper concerns the problem of scheduling jobs with unit processing time and nonidentical sizes on single or parallel identical batch machines. The objective is to minimize the total completion time of all jobs. We show that the worst-case ratio of the algorithm based on the bin-packing algorithm First Fit Increasing lies in the interval $$\left[ \frac{109}{82}, \frac{2+\sqrt{2}}{2}\right] \approx [1.3293, 1.7071]$$ 109 82 , 2 + 2 2 ≈ [ 1.3293 , 1.7071 ] for the single machine case, and is no more than $$\frac{6+\sqrt{2}}{4}\approx 1.8536$$ 6 + 2 4 ≈ 1.8536 for the parallel machines case.

Suggested Citation

  • Rongqi Li & Zhiyi Tan & Qianyu Zhu, 0. "Batch scheduling of nonidentical job sizes with minsum criteria," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-22.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-019-00419-9
    DOI: 10.1007/s10878-019-00419-9
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    References listed on IDEAS

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    1. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    2. Dorit S. Hochbaum & Dan Landy, 1997. "Scheduling Semiconductor Burn-In Operations to Minimize Total Flowtime," Operations Research, INFORMS, vol. 45(6), pages 874-885, December.
    3. Shoshana Anily & Julien Bramel & David Simchi-Levi, 1994. "Worst-Case Analysis of Heuristics for the Bin Packing Problem with General Cost Structures," Operations Research, INFORMS, vol. 42(2), pages 287-298, April.
    4. Gyorgy Dosa & Zhiyi Tan & Zsolt Tuza & Yujie Yan & Cecília Sik Lányi, 2014. "Improved bounds for batch scheduling with nonidentical job sizes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 351-358, August.
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