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Polynomial-time solutions for minimizing total load on unrelated machines with position-dependent processing times and rate-modifying activities

Author

Listed:
  • Baruch Mor

    (Ariel University)

  • Gur Mosheiov

    (The Hebrew University
    Lev Academic Center)

  • Dvir Shabtay

    (Ben-Gurion University of the Negev)

Abstract

We study the problem of minimizing total load on parallel unrelated machines. Job processing times are assumed to be machine- and position-dependent in the most general way. The scheduler may perform a rate-modifying maintenance activity on each machine. The processing times of the jobs scheduled after the maintenance are reduced. The maintenance time and the impact on the following jobs are machine-dependent. We introduce a solution algorithm which is polynomial when a constant bounds the number of machines. The special case of (general) job deterioration, the more general case in which job rejection is allowed, and the extension to the setting of job processing times, which are controllable through allocating a limited resource, are also studied. All these scheduling problems are shown to be solved in polynomial time.

Suggested Citation

  • Baruch Mor & Gur Mosheiov & Dvir Shabtay, 2025. "Polynomial-time solutions for minimizing total load on unrelated machines with position-dependent processing times and rate-modifying activities," Journal of Scheduling, Springer, vol. 28(4), pages 377-390, August.
    • Handle: RePEc:spr:jsched:v:28:y:2025:i:4:d:10.1007_s10951-025-00848-x
    DOI: 10.1007/s10951-025-00848-x
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    References listed on IDEAS

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    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. Baruch Mor & Gur Mosheiov, 2021. "A note: flowshop scheduling with linear deterioration and job-rejection," 4OR, Springer, vol. 19(1), pages 103-111, March.
    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. Baruch Mor & Gur Mosheiov & Dana Shapira, 2020. "Flowshop scheduling with learning effect and job rejection," Journal of Scheduling, Springer, vol. 23(6), pages 631-641, December.
    5. Phosavanh, Johnson & Oron, Daniel, 2024. "Two-agent single-machine scheduling with a rate-modifying activity," European Journal of Operational Research, Elsevier, vol. 312(3), pages 866-876.
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    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, December.
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