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A tight approximation algorithm for problem $$P2\rightarrow D|v=1,c=1|C_{\max }$$ P 2 → D | v = 1 , c = 1 | C max

Author

Listed:
  • Yinling Wang

    (Dalian University of Technology)

  • Yan Lan

    (Dalian Minzu University)

  • Xin Chen

    (Liaoning University of Technology)

  • Xin Han

    (Dalian University of Technology)

  • Yong Piao

    (Dalian University of Technology)

Abstract

This paper focuses on the scheduling problem on two parallel machines with delivery coordination. In particular, given a set of n jobs, we aim to find a schedule with a minimal makespan such that all jobs are first executed on two parallel machines then delivered at the destination with a transporter. This problem is known to be NP-hard Chang and Lee (Eur J Oper Res 158(2):470–487, 2004), cannot be solved with an approximation ratio strictly less than 3/2 unless P=NP. We close the gap by proposing a polynomial time algorithm whose approximation ratio is $$3/2+\varepsilon $$ 3 / 2 + ε with $$\varepsilon >0$$ ε > 0 , improve the previous best ratio $$14/9 + \epsilon $$ 14 / 9 + ϵ .

Suggested Citation

  • Yinling Wang & Yan Lan & Xin Chen & Xin Han & Yong Piao, 2022. "A tight approximation algorithm for problem $$P2\rightarrow D|v=1,c=1|C_{\max }$$ P 2 → D | v = 1 , c = 1 | C max," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2195-2206, November.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:4:d:10.1007_s10878-020-00593-1
    DOI: 10.1007/s10878-020-00593-1
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    References listed on IDEAS

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    1. Zhong, Weiya & Dosa, Gyorgy & Tan, Zhiyi, 2007. "On the machine scheduling problem with job delivery coordination," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1057-1072, November.
    2. Chang, Yung-Chia & Lee, Chung-Yee, 2004. "Machine scheduling with job delivery coordination," European Journal of Operational Research, Elsevier, vol. 158(2), pages 470-487, October.
    3. C. N. Potts, 1980. "Technical Note—Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times," Operations Research, INFORMS, vol. 28(6), pages 1436-1441, December.
    4. Li, Chung-Lun & Vairaktarakis, George & Lee, Chung-Yee, 2005. "Machine scheduling with deliveries to multiple customer locations," European Journal of Operational Research, Elsevier, vol. 164(1), pages 39-51, July.
    5. Leslie A. Hall & David B. Shmoys, 1992. "Jackson's Rule for Single-Machine Scheduling: Making a Good Heuristic Better," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 22-35, February.
    6. 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.
    7. Scott Webster & Kenneth R. Baker, 1995. "Scheduling Groups of Jobs on a Single Machine," Operations Research, INFORMS, vol. 43(4), pages 692-703, August.
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