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Online Scheduling of Incompatible Family Jobs with Equal Length on an Unbounded Parallel-Batch Machine with Job Delivery

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  • Qijia Liu

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, People’s Republic of China2College of Information and Management Science, Henan Agricultural University, Zhengzhou, Henan 450003, People’s Republic of China)

  • Jinjiang Yuan

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, People’s Republic of China)

Abstract

In this paper, we consider the online scheduling of incompatible family jobs with equal length on an unbounded parallel-batch machine with job delivery. The jobs arrive online over time and belong to f incompatible job families, where f is known in advance. The jobs are first processed in batches on an unbounded parallel-batch machine and then the completed jobs are delivered in batches by a vehicle with infinite capacity to their customers. The jobs from distinct families cannot be processed and delivered in the same batch. The objective is to minimize the maximum delivery completion time of the jobs. For this problem, we present an online algorithm with the best competitive ratio of 1 + 4f2 +1−1 2f.

Suggested Citation

  • Qijia Liu & Jinjiang Yuan, 2018. "Online Scheduling of Incompatible Family Jobs with Equal Length on an Unbounded Parallel-Batch Machine with Job Delivery," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-12, August.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:04:n:s0217595918500264
    DOI: 10.1142/S0217595918500264
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    References listed on IDEAS

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    1. Nong, Qingqin & Yuan, Jinjiang & Fu, Ruyan & Lin, Lin & Tian, Ji, 2008. "The single-machine parallel-batching on-line scheduling problem with family jobs to minimize makespan," International Journal of Production Economics, Elsevier, vol. 111(2), pages 435-440, February.
    2. Jinjiang Yuan & Shisheng Li & Ji Tian & Ruyan Fu, 2009. "A best on-line algorithm for the single machine parallel-batch scheduling with restricted delivery times," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 206-213, February.
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