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Single machine scheduling with time-dependent linear deterioration and rate-modifying maintenance

Author

Listed:
  • Kabir Rustogi

    (University of Greenwich, London, UK)

  • Vitaly A Strusevich

    (University of Greenwich, London, UK)

Abstract

We study single machine scheduling problems with linear time-dependent deterioration effects and maintenance activities. Maintenance periods (MPs) are included into the schedule, so that the machine, that gets worse during the processing, can be restored to a better state. We deal with a job-independent version of the deterioration effects, that is, all jobs share a common deterioration rate. However, we introduce a novel extension to such models and allow the deterioration rates to change after every MP. We study several versions of this generalized problem and design a range of polynomial-time solution algorithms that enable the decision-maker to determine possible sequences of jobs and MPs in the schedule, so that the makespan objective can be minimized. We show that all problems reduce to a linear assignment problem with a product matrix and can be solved by methods very similar to those used for solving problems with positional effects.

Suggested Citation

  • Kabir Rustogi & Vitaly A Strusevich, 2015. "Single machine scheduling with time-dependent linear deterioration and rate-modifying maintenance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(3), pages 500-515, March.
    • Handle: RePEc:pal:jorsoc:v:66:y:2015:i:3:p:500-515
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    Citations

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    Cited by:

    1. Finke, Gerd & Gara-Ali, Ahmed & Espinouse, Marie-Laure & Jost, Vincent & Moncel, Julien, 2017. "Unified matrix approach to solve production-maintenance problems on a single machine," Omega, Elsevier, vol. 66(PA), pages 140-146.
    2. Hans Kellerer & Vitaly A. Strusevich, 2016. "Optimizing the half-product and related quadratic Boolean functions: approximation and scheduling applications," Annals of Operations Research, Springer, vol. 240(1), pages 39-94, May.
    3. Kabir Rustogi & Vitaly A. Strusevich, 2017. "Single machine scheduling with a generalized job-dependent cumulative effect," Journal of Scheduling, Springer, vol. 20(6), pages 583-592, December.
    4. Mosheiov, Gur & Sarig, Assaf & Strusevich, Vitaly A & Mosheiff, Jonathan, 2018. "Two-machine flow shop and open shop scheduling problems with a single maintenance window," European Journal of Operational Research, Elsevier, vol. 271(2), pages 388-400.
    5. Shi-Sheng Li & Ren-Xia Chen, 2017. "Scheduling with Rejection and a Deteriorating Maintenance Activity on a Single Machine," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(02), pages 1-17, April.
    6. Anna Arigliano & Gianpaolo Ghiani & Antonio Grieco & Emanuela Guerriero, 2017. "Single-machine time-dependent scheduling problems with fixed rate-modifying activities and resumable jobs," 4OR, Springer, vol. 15(2), pages 201-215, June.
    7. Wang, Ting & Baldacci, Roberto & Lim, Andrew & Hu, Qian, 2018. "A branch-and-price algorithm for scheduling of deteriorating jobs and flexible periodic maintenance on a single machine," European Journal of Operational Research, Elsevier, vol. 271(3), pages 826-838.
    8. Xinyu Sun & Tao Liu & Xin-Na Geng & Yang Hu & Jing-Xiao Xu, 2023. "Optimization of scheduling problems with deterioration effects and an optional maintenance activity," Journal of Scheduling, Springer, vol. 26(3), pages 251-266, June.

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