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Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection

Author

Listed:
  • Shi-Sheng Li

    (Zhongyuan University of Technology)

  • Ren-Xia Chen

    (Zhongyuan University of Technology)

  • Qi Feng

    (Zhongyuan University of Technology)

  • Cheng-Wen Jiao

    (Zhongyuan University of Technology)

Abstract

We study a parallel-machine scheduling problem in which job rejection is allowed and the actual processing time of a job depends on the sum of certain parameters associated with the jobs scheduled earlier. The goal is to minimize the sum of the makespan of the accepted jobs and total rejection penalty of the rejected jobs. When the number of machines is fixed, we develop an exact dynamic programming algorithm and a fully polynomial-time approximation scheme for solving it. When the number of machines is restricted to one, we reformulate the problem as a variant of a half-product problem, which allows us to design a fully polynomial-time approximation scheme with the best possible running time.

Suggested Citation

  • Shi-Sheng Li & Ren-Xia Chen & Qi Feng & Cheng-Wen Jiao, 2019. "Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 957-971, October.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:3:d:10.1007_s10878-019-00429-7
    DOI: 10.1007/s10878-019-00429-7
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    References listed on IDEAS

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    Cited by:

    1. Lei Pan & Xinyu Sun & Ji-Bo Wang & Li-Han Zhang & Dan-Yang Lv, 2023. "Due date assignment single-machine scheduling with delivery times, position-dependent weights and deteriorating jobs," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-16, May.
    2. Ma, Ran & Guo, Sainan, 2021. "Applying “Peeling Onion” approach for competitive analysis in online scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 290(1), pages 57-67.
    3. Baruch Mor & Dana Shapira, 2022. "Single machine scheduling with non-availability interval and optional job rejection," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 480-497, August.
    4. Shaojun Lu & Jun Pei & Xinbao Liu & Panos M. Pardalos, 2020. "Robust parallel-batching scheduling with fuzzy deteriorating processing time and variable delivery time in smart manufacturing," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 333-357, September.

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