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Just-In-Time Scheduling with Generalized Due Dates and Identical Due Date Intervals

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  • Byung-Cheon Choi

    (School of Business, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Korea)

  • Myoung-Ju Park

    (Department of Industrial and Management Systems Engineering, Kyung Hee University, 1732, Deogyeong-daero, Giheung-gu, Yongin-si, Kyunggi-do 17104, Korea)

Abstract

We consider a single-machine scheduling problem such that the due dates are assigned not to the jobs but to the position at which the job is processed. We focus on the case with identical due date intervals. The objective is to minimize the weighted number of early and tardy jobs. First, we show that the problem is strongly NP-hard and has no ρ-approximation algorithm for any fixed value ρ > 1. Then, we investigate polynomially solvable cases. Finally, we show that the preemption version is weakly NP-hard through its equivalence to the problem of minimizing the weighted number of tardy jobs.

Suggested Citation

  • Byung-Cheon Choi & Myoung-Ju Park, 2018. "Just-In-Time Scheduling with Generalized Due Dates and Identical Due Date Intervals," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-13, December.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:06:n:s021759591850046x
    DOI: 10.1142/S021759591850046X
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    References listed on IDEAS

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    1. Nicholas G. Hall & Wieslaw Kubiak & Suresh P. Sethi, 1991. "Earliness–Tardiness Scheduling Problems, II: Deviation of Completion Times About a Restrictive Common Due Date," Operations Research, INFORMS, vol. 39(5), pages 847-856, October.
    2. Nicholas G. Hall & Marc E. Posner, 1991. "Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date," Operations Research, INFORMS, vol. 39(5), pages 836-846, October.
    3. Hall, Nicholas G. & Sethi, Suresh P. & Sriskandarajah, Chelliah, 1991. "On the complexity of generalized due date scheduling problems," European Journal of Operational Research, Elsevier, vol. 51(1), pages 100-109, March.
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    Cited by:

    1. Myoung-Ju Park & Byung-Cheon Choi & Yunhong Min & Kyung Min Kim, 2020. "Two-Machine Ordered Flow Shop Scheduling with Generalized Due Dates," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-16, January.
    2. Byung-Cheon Choi & Myoung-Ju Park, 2021. "Single-machine scheduling with periodic due dates to minimize the total earliness and tardy penalty," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 781-793, May.

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