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Single machine scheduling problems involving job-dependent step-deterioration dates and job rejection

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  • Baruch Mor

    (Ariel University)

Abstract

This research focuses on scheduling problems with step-deteriorating job processing times. This phenomenon reflects various real-life settings where the processing time of the jobs, processed after their pre-determined and job-dependent deterioration date, is defined by a step function. A single machine setting is assumed, and optional job rejection is considered. The scheduling measure focused on in this study is makespan, and three variants of the basic problem are considered: (i) minimizing the sum of the scheduling measure and total rejection cost; (ii) minimizing the scheduling criterion, given an upper bound on the total rejection cost; and (iii) minimizing the total rejection cost, subject to a constraint on the scheduling measure. As minimizing the makespan on a single machine with step deterioration is known to be ordinary NP-hard, even if all jobs share a common deterioration date, all presented problems are NP-hard. For all problems, pseudo-polynomial time dynamic-programming (DP) algorithms are presented, establishing that they remain ordinary NP-hard. Furthermore, an extensive experimental study was conducted to determine the efficiency of the proposed algorithms.

Suggested Citation

  • Baruch Mor, 2023. "Single machine scheduling problems involving job-dependent step-deterioration dates and job rejection," Operational Research, Springer, vol. 23(1), pages 1-19, March.
    • Handle: RePEc:spr:operea:v:23:y:2023:i:1:d:10.1007_s12351-023-00754-0
    DOI: 10.1007/s12351-023-00754-0
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    References listed on IDEAS

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    1. Baruch Mor & Dana Shapira, 2019. "Improved algorithms for scheduling on proportionate flowshop with job-rejection," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(11), pages 1997-2003, November.
    2. Cheng, T. C. E. & Ding, Q., 2001. "Single machine scheduling with step-deteriorating processing times," European Journal of Operational Research, Elsevier, vol. 134(3), pages 623-630, November.
    3. Baoyu Liao & Qingru Song & Jun Pei & Shanlin Yang & Panos M. Pardalos, 2020. "Parallel-machine group scheduling with inclusive processing set restrictions, outsourcing option and serial-batching under the effect of step-deterioration," Journal of Global Optimization, Springer, vol. 78(4), pages 717-742, December.
    4. Baruch Mor & Gur Mosheiov, 2016. "Minimizing maximum cost on a single machine with two competing agents and job rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1524-1531, December.
    5. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Time-Changing Effects and Rate-Modifying Activities," International Series in Operations Research and Management Science, Springer, number 978-3-319-39574-6, September.
    6. Xueling Zhong & Jinwen Ou, 2017. "Improved approximation algorithms for parallel machine scheduling with release dates and job rejection," 4OR, Springer, vol. 15(4), pages 387-406, December.
    7. Oron, Daniel, 2021. "Two-agent scheduling problems under rejection budget constraints," Omega, Elsevier, vol. 102(C).
    8. Baruch Mor & Gur Mosheiov & Dvir Shabtay, 2021. "Minimizing the total tardiness and job rejection cost in a proportionate flow shop with generalized due dates," Journal of Scheduling, Springer, vol. 24(6), pages 553-567, December.
    9. Lalla-Ruiz, Eduardo & Voß, Stefan, 2016. "Modeling the Parallel Machine Scheduling Problem with Step Deteriorating Jobs," European Journal of Operational Research, Elsevier, vol. 255(1), pages 21-33.
    10. Shi-Sheng Li & De-Liang Qian & Ren-Xia Chen, 2017. "Proportionate Flow Shop Scheduling with Rejection," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-13, August.
    11. Baruch Mor & Gur Mosheiov, 2022. "Single machine scheduling to maximize the weighted number of on-time jobs with job-rejection," Operational Research, Springer, vol. 22(3), pages 2707-2719, July.
    12. Baruch Mor & Gur Mosheiov, 2012. "Batch scheduling with step‐deteriorating processing times to minimize flowtime," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(8), pages 587-600, December.
    13. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Rate-Modifying Activities," International Series in Operations Research & Management Science, in: Scheduling with Time-Changing Effects and Rate-Modifying Activities, chapter 0, pages 317-331, Springer.
    14. Du-Juan Wang & Yunqiang Yin & Mengqi Liu, 2016. "Bicriteria scheduling problems involving job rejection, controllable processing times and rate-modifying activity," International Journal of Production Research, Taylor & Francis Journals, vol. 54(12), pages 3691-3705, June.
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    1. C. K. Sivashankari & R. Valarmathi, 2023. "Optimal pricing and production lot-size policies in imperfect production system with price-sensitive demand, reworking, scrap, and sales return," Operational Research, Springer, vol. 23(3), pages 1-28, September.

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