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Single-machine scheduling with periodic due dates to minimize the total earliness and tardy penalty

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  • Byung-Cheon Choi

    (Chungnam National University)

  • Myoung-Ju Park

    (Kyung Hee University)

Abstract

We consider a single-machine scheduling problem such that the due dates are assigned to each job depending on its order, and the lengths of the intervals between consecutive due dates are identical. The objective is to minimize the total penalty for the earliness and tardiness of each job. The early penalty proportionally increases according to the earliness amount, while the tardy penalty increases according to the step function. We show that the problem is strongly NP-hard, and furthermore, polynomially solvable if the two types of processing times exist.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:41:y:2021:i:4:d:10.1007_s10878-021-00714-4
    DOI: 10.1007/s10878-021-00714-4
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    References listed on IDEAS

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    1. Nicholas G. Hall & 'Maseka Lesaoana & Chris N. Potts, 2001. "Scheduling with Fixed Delivery Dates," Operations Research, INFORMS, vol. 49(1), pages 134-144, February.
    2. 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.
    3. 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.
    4. 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.
    5. Feng Li & Zhi-Long Chen & Zhi-Long Chen, 2017. "Integrated Production, Inventory and Delivery Problems: Complexity and Algorithms," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 232-250, May.
    6. 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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    8. Han, Dongya & Yang, Yongjian & Wang, Dujuan & Cheng, T.C.E. & Yin, Yunqiang, 2019. "Integrated production, inventory, and outbound distribution operations with fixed departure times in a three-stage supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 125(C), pages 334-347.
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