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Single Machine Scheduling With Job Delivery To Minimize Makespan

Author

Listed:
  • LINGFA LU

    (Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China)

  • JINJIANG YUAN

    (Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China)

Abstract

In the single machine scheduling problem with job delivery to minimize makespan, jobs are processed on a single machine and delivered by a capacitated vehicle to their respective customers. We first consider the special case with a single customer, that is, all jobs have the same transportation time. Chang and Lee (2004) proved that this case is strongly NP-hard. They also provided a heuristic with the worst-case performance ratio$\frac{5}{3}$, and pointed out that no heuristic can have a worst-case performance ratio less than$\frac{3}{2}$unlessP=NP. In this paper, we provide a new heuristic which has the best possible worst-case performance ratio$\frac{3}{2}$. We also consider an extended version in which the jobs have non-identical transportation times and the transportation time of a delivery batch is defined as the maximum transportation time of the jobs contained in it. We provide a heuristic with the worst-case performance ratio 2 for the extended version, and show that this bound is tight.

Suggested Citation

  • Lingfa Lu & Jinjiang Yuan, 2008. "Single Machine Scheduling With Job Delivery To Minimize Makespan," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(01), pages 1-10.
    • Handle: RePEc:wsi:apjorx:v:25:y:2008:i:01:n:s0217595908001596
    DOI: 10.1142/S0217595908001596
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    Citations

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    Cited by:

    1. Söhnke Maecker & Liji Shen, 2020. "Solving parallel machine problems with delivery times and tardiness objectives," Annals of Operations Research, Springer, vol. 285(1), pages 315-334, February.
    2. Liu, Peihai & Lu, Xiwen, 2016. "Integrated production and job delivery scheduling with an availability constraint," International Journal of Production Economics, Elsevier, vol. 176(C), pages 1-6.
    3. Liang-Liang Fu & Mohamed Ali Aloulou & Christian Artigues, 2018. "Integrated production and outbound distribution scheduling problems with job release dates and deadlines," Journal of Scheduling, Springer, vol. 21(4), pages 443-460, August.
    4. Jianming Dong & Xueshi Wang & Jueliang Hu & Guohui Lin, 2018. "Single machine scheduling with job delivery to multiple customers," Journal of Scheduling, Springer, vol. 21(3), pages 337-348, June.
    5. Low, Chinyao & Chang, Chien-Min & Li, Rong-Kwei & Huang, Chia-Ling, 2014. "Coordination of production scheduling and delivery problems with heterogeneous fleet," International Journal of Production Economics, Elsevier, vol. 153(C), pages 139-148.
    6. Han, Bin & Zhang, Wenjun & Lu, Xiwen & Lin, Yingzi, 2015. "On-line supply chain scheduling for single-machine and parallel-machine configurations with a single customer: Minimizing the makespan and delivery cost," European Journal of Operational Research, Elsevier, vol. 244(3), pages 704-714.
    7. 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.

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