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Optimal Semi-Online Algorithm for Scheduling on Two Parallel Batch Processing Machines

Author

Listed:
  • Ming Liu

    (School of Economics and Management, Tongji University, Shanghai 200092, P. R. China)

  • Feifeng Zheng

    (Glorious Sun School of Business and Management, Donghua University, Shanghai 200092, P. R. China)

  • Zhanguo Zhu

    (School of Economics and Management, Nanjing Agricultural University, Nanjing 210095, P. R. China;
    Laboratoire d'Informatique, Biologie Intégrative et Systèmes Complexes (IBISC), EA 4526, Université d'Evry Val d'Essonne 91020, Evry Cedex, France)

  • Chengbin Chu

    (Laboratoire Génie Industriel, Ecole Centrale Paris, Grande Voie des Vignes, 92295, Châtenay-Malabry Cedex, France)

Abstract

Batch processing machine scheduling in uncertain environment attracts more and more attention in the last decade. This paper deals with semi-online scheduling on two parallel batch processing machines with non-decreasing processing time of job. Jobs arrive over time in the online paradigm, and the processing time of any batch is equal to the length of the last arrival job in the batch. We study the unbounded model where each processing batch may contain an unlimited number of jobs, and the objective is to minimize the makespan. Given any job Jj together with its following job Jj+1, it is assumed that their processing times satisfy pj+1 ≥ αpj where α ≥ 1 is a constant. That is, jobs arrive in a non-decreasing order of processing times. We mainly propose an optimal ϕ-competitive online algorithm where ϕ ≥ 1 is a solution of equation ϕ3 + (α-1)ϕ2 + (α2 - α - 1)ϕ - α2 = 0.

Suggested Citation

  • Ming Liu & Feifeng Zheng & Zhanguo Zhu & Chengbin Chu, 2014. "Optimal Semi-Online Algorithm for Scheduling on Two Parallel Batch Processing Machines," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-10.
    • Handle: RePEc:wsi:apjorx:v:31:y:2014:i:05:n:s0217595914500389
    DOI: 10.1142/S0217595914500389
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    References listed on IDEAS

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