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Scheduling problems on parallel dedicated machines with non-renewable resource

Author

Listed:
  • Baruch Mor

    (Ariel University)

  • Joanna Berlińska

    (Adam Mickiewicz University)

Abstract

We study scheduling problems on parallel dedicated machines and assume that a specific job can only be processed on one specific machine. We concentrate on solving scheduling problems involving convex resource allocation and address three of the most fundamental measures in scheduling theory, i.e., makespan, total load, and total weighted completion time. Firstly, we focus on position-independent workloads, and then we study the setting of general position-dependent workloads, i.e., the workloads are not restricted to be either monotone functions of the job positions or any specific functions. In all problems, we assume a common continuous and non-renewable (limited) resource and adapt known results from scheduling theory to solve the considered problems.

Suggested Citation

  • Baruch Mor & Joanna Berlińska, 2025. "Scheduling problems on parallel dedicated machines with non-renewable resource," Annals of Operations Research, Springer, vol. 346(3), pages 2173-2193, March.
    • Handle: RePEc:spr:annopr:v:346:y:2025:i:3:d:10.1007_s10479-025-06471-5
    DOI: 10.1007/s10479-025-06471-5
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    References listed on IDEAS

    as
    1. Baruch Mor, 2022. "Minmax common flow-allowance problems with convex resource allocation and position-dependent workloads," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 79-97, January.
    2. T.C.E. Cheng & Svetlana A. Kravchenko & Bertrand M. T. Lin, 2019. "Server scheduling on parallel dedicated machines with fixed job sequences," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 321-332, June.
    3. Oron, Daniel, 2016. "Scheduling controllable processing time jobs with position-dependent workloads," International Journal of Production Economics, Elsevier, vol. 173(C), pages 153-160.
    4. Ameni Azzouz & Meriem Ennigrou & Lamjed Ben Said, 2018. "Scheduling problems under learning effects: classification and cartography," International Journal of Production Research, Taylor & Francis Journals, vol. 56(4), pages 1642-1661, February.
    5. Donghun Lee & Hyeongwon Kang & Dongjin Lee & Jeonwoo Lee & Kwanho Kim, 2023. "Deep Reinforcement Learning-Based Scheduler on Parallel Dedicated Machine Scheduling Problem towards Minimizing Total Tardiness," Sustainability, MDPI, vol. 15(4), pages 1-14, February.
    6. Yi-Chun Wang & Ji-Bo Wang, 2023. "Study on Convex Resource Allocation Scheduling with a Time-Dependent Learning Effect," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
    7. 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, June.
    8. Shabtay, Dvir & Kaspi, Moshe, 2006. "Parallel machine scheduling with a convex resource consumption function," European Journal of Operational Research, Elsevier, vol. 173(1), pages 92-107, August.
    9. Daniel Oron, 2016. "Scheduling controllable processing time jobs in a deteriorating environment," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(3), pages 535-535, March.
    10. Shabtay, Dvir, 2022. "Single-machine scheduling with machine unavailability periods and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 296(2), pages 423-439.
    11. T. C. E. Cheng & Svetlana A. Kravchenko & Bertrand M. T. Lin, 2021. "Complexity of server scheduling on parallel dedicated machines subject to fixed job sequences," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(10), pages 2286-2289, October.
    12. Baruch Mor & Gur Mosheiov, 2024. "Scheduling on parallel dedicated machines with job rejection," International Journal of Production Research, Taylor & Francis Journals, vol. 62(19), pages 6933-6940, October.
    13. Baruch Mor & Gur Mosheiov, 2018. "A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection," Annals of Operations Research, Springer, vol. 271(2), pages 1079-1085, December.
    14. Xinyu Sun & Xin-Na Geng & Ji-Bo Wang & Feng Liu, 2019. "Convex resource allocation scheduling in the no-wait flowshop with common flow allowance and learning effect," International Journal of Production Research, Taylor & Francis Journals, vol. 57(6), pages 1873-1891, March.
    15. Jun-Ho Lee & Hoon Jang, 2019. "Uniform Parallel Machine Scheduling with Dedicated Machines, Job Splitting and Setup Resources," Sustainability, MDPI, vol. 11(24), pages 1-23, December.
    16. Xiaoli Zhao & Jian Xu & Ji-Bo Wang & Lin Li, 2022. "Bicriteria Common Flow Allowance Scheduling with Aging Effect, Convex Resource Allocation, and a Rate-Modifying Activity on a Single Machine," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 39(05), pages 1-21, October.
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