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An optimal online algorithm for single machine scheduling with bounded delivery times

Author

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  • Liu, Ming
  • Chu, Chengbin
  • Xu, Yinfeng
  • Zheng, Feifeng

Abstract

We study an online scheduling problem on a single machine with delivery times. The problem is online in the sense that all jobs arrive over time. Each job's characteristics, such as processing time and delivery time, become known at its arrival time. Preemption is not allowed and once the processing of a job is completed we delivery it to the destination by a vehicle. The objective is to minimize the time by which all jobs have been delivered. In this paper, we assume that all jobs have bounded delivery times, which means that given a certain positive number , for each job Jj, we have a release time rj[greater-or-equal, slanted]0 and [beta]qj[less-than-or-equals, slant]pj, where pj,qj denote the processing time and the delivery time of job Jj, respectively. We use 1online,rj,[beta]qj[less-than-or-equals, slant]pjLmax to denote the problem for short, where Lmax denote the time by which all jobs have been delivered. We prove a lower bound of competitive ratios for all online algorithms and propose an optimal online algorithm with a competitive ratio of .

Suggested Citation

  • Liu, Ming & Chu, Chengbin & Xu, Yinfeng & Zheng, Feifeng, 2010. "An optimal online algorithm for single machine scheduling with bounded delivery times," European Journal of Operational Research, Elsevier, vol. 201(3), pages 693-700, March.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:3:p:693-700
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    Citations

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    Cited by:

    1. Wenqiang Dai & Meng Zheng & Xu Chen & Zhuolin Yang, 0. "Online economic ordering problem for deteriorating items with limited price information," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-23.
    2. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    3. Lixin Tang & Feng Li & Zhi-Long Chen, 2019. "Integrated Scheduling of Production and Two-Stage Delivery of Make-to-Order Products: Offline and Online Algorithms," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 493-514, July.
    4. Wenjie Li & Jinjiang Yuan, 2021. "Single-machine online scheduling of jobs with non-delayed processing constraint," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 830-843, May.
    5. Zhang, Jun & Liu, Feng & Tang, Jiafu & Li, Yanhui, 2019. "The online integrated order picking and delivery considering Pickers’ learning effects for an O2O community supermarket," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 123(C), pages 180-199.
    6. Dai, Wenqiang & Dong, Yucheng & Zhang, Xiaotian, 2016. "Competitive analysis of the online financial lease problem," European Journal of Operational Research, Elsevier, vol. 250(3), pages 865-873.
    7. Peihai Liu & Xiwen Lu, 2015. "Online scheduling on two parallel machines with release dates and delivery times," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 347-359, August.
    8. Wenqiang Dai & Meng Zheng & Xu Chen & Zhuolin Yang, 2022. "Online economic ordering problem for deteriorating items with limited price information," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2246-2268, November.
    9. Ji Tian & Yan Zhou & Ruyan Fu, 2020. "An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 170-180, July.

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