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Improved bounds for batch scheduling with nonidentical job sizes

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  • Gyorgy Dosa
  • Zhiyi Tan
  • Zsolt Tuza
  • Yujie Yan
  • Cecília Sik Lányi

Abstract

Here, we revisit the bounded batch scheduling problem with nonidentical job sizes on single and parallel identical machines, with the objective of minimizing the makespan. For the single machine case, we present an algorithm which calls an online algorithm P (chosen arbitrarily) for the one‐dimensional bin‐packing problem as a sub‐procedure, and prove that its worst‐case ratio is the same as the absolute performance ratio of P . Hence, there exists an algorithm with worst‐case ratio 17 10 , which is better than any known upper bound on this problem. For the parallel machines case, we prove that there does not exist any polynomial‐time algorithm with worst‐case ratio smaller than 2 unless P = NP, even if all jobs have unit processing time. Then we present an algorithm with worst‐case ratio arbitrarily close to 2. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 351–358, 2014

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:61:y:2014:i:5:p:351-358
    DOI: 10.1002/nav.21587
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    References listed on IDEAS

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    1. Guochuan Zhang & Xiaoqiang Cai & C.‐Y Lee & C.K Wong, 2001. "Minimizing makespan on a single batch processing machine with nonidentical job sizes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 226-240, April.
    2. 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.
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    Cited by:

    1. Yuanxiao Wu & Xiwen Lu, 2022. "Capacitated vehicle routing problem on line with unsplittable demands," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1953-1963, October.
    2. Jing Fan & Hui Shi, 2022. "Non-resumable scheduling on a single bounded parallel-batch machine with periodic maintenance," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1645-1654, July.
    3. Yuanxiao Wu & Xiwen Lu, 0. "Capacitated vehicle routing problem on line with unsplittable demands," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-11.
    4. Florian Jaehn & Sergey Kovalev & Mikhail Y. Kovalyov & Erwin Pesch, 2014. "Multiproduct batching and scheduling with buffered rework: The case of a car paint shop," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(6), pages 458-471, September.
    5. 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.
    6. Cheng, Bayi & Leung, Joseph Y.-T. & Li, Kai & Yang, Shanlin, 2019. "Integrated optimization of material supplying, manufacturing, and product distribution: Models and fast algorithms," European Journal of Operational Research, Elsevier, vol. 277(1), pages 100-111.

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