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Single Machine Scheduling With Forbidden Intervals And Job Delivery Times

Author

Listed:
  • JINJIANG YUAN

    (Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, China)

  • LEI SHI

    (Department of Mathematics, Anyang Normal University, Anyang, Henan 455000, China)

  • JINWEN OU

    (Department of Administrative Management, Jinan University, Guangzhou, Guangdong 510632, China)

Abstract

We consider a non-preemptive single machine scheduling problem with forbidden intervals. Associated with each job is a given processing time and a delivery time to its customer, when the processing of the job is complete. The objective is to minimize the time taken for all the jobs to be delivered to the customers. The problem is strongly NP-hard in general. In this study, we show that the case with a fixed number of forbidden intervals can be solved by a pseudo-polynomial time algorithm, while no polynomial time approximation algorithm with a fixed performance ratio exists for the case with two forbidden intervals. We also develop a polynomial time approximation scheme (PTAS) for the case with a single forbidden interval.

Suggested Citation

  • Jinjiang Yuan & Lei Shi & Jinwen Ou, 2008. "Single Machine Scheduling With Forbidden Intervals And Job Delivery Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(03), pages 317-325.
    • Handle: RePEc:wsi:apjorx:v:25:y:2008:i:03:n:s0217595908001778
    DOI: 10.1142/S0217595908001778
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    Citations

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    Cited by:

    1. Imed Kacem & Hans Kellerer & Maryam Seifaddini, 2016. "Efficient approximation schemes for the maximum lateness minimization on a single machine with a fixed operator or machine non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 970-981, October.
    2. 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.
    3. Shi-Sheng Li & Ren-Xia Chen, 2022. "Minimizing total weighted late work on a single-machine with non-availability intervals," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1330-1355, September.
    4. 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.
    5. 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.

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