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An asymptotic PTAS for batch scheduling with nonidentical job sizes to minimize makespan

Author

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  • Yuzhong Zhang

    (Qufu Normal University)

  • Zhigang Cao

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

Abstract

Motivated by the existence of an APTAS (Asymptotic PTAS) for bin packing problem, we consider the batch scheduling problem with nonidentical job sizes to minimize makespan. For the proportional special version, i.e., there exists a fixed number α such that p j =α s j for every 1≤j≤n, we first present a lower bound of 3/2 for the approximation ratio and then design an APTAS.

Suggested Citation

  • Yuzhong Zhang & Zhigang Cao, 2008. "An asymptotic PTAS for batch scheduling with nonidentical job sizes to minimize makespan," Journal of Combinatorial Optimization, Springer, vol. 16(2), pages 119-126, August.
    • Handle: RePEc:spr:jcomop:v:16:y:2008:i:2:d:10.1007_s10878-007-9128-7
    DOI: 10.1007/s10878-007-9128-7
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    References listed on IDEAS

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    1. Jolai Ghazvini, Fariborz & Dupont, Lionel, 1998. "Minimizing mean flow times criteria on a single batch processing machine with non-identical jobs sizes," International Journal of Production Economics, Elsevier, vol. 55(3), pages 273-280, August.
    2. 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.
    3. 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. Jun Pei & Xinbao Liu & Panos M. Pardalos & Wenjuan Fan & Ling Wang & Shanlin Yang, 2016. "Solving a supply chain scheduling problem with non-identical job sizes and release times by applying a novel effective heuristic algorithm," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(4), pages 765-776, March.

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