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Single machine scheduling with general positional deterioration and rate-modifying maintenance


  • Rustogi, Kabir
  • Strusevich, Vitaly A.


We present polynomial-time algorithms for single machine problems with generalized positional deterioration effects and machine maintenance. The decisions should be taken regarding possible sequences of jobs and on the number of maintenance activities to be included into a schedule in order to minimize the overall makespan. We deal with general non-decreasing functions to represent deterioration rates of job processing times. Another novel extension of existing models is our assumption that a maintenance activity does not necessarily fully restore the machine to its original perfect state. In the resulting schedules, the jobs are split into groups, a particular group to be sequenced after a particular maintenance period, and the actual processing time of a job is affected by the group that job is placed into and its position within the group.

Suggested Citation

  • Rustogi, Kabir & Strusevich, Vitaly A., 2012. "Single machine scheduling with general positional deterioration and rate-modifying maintenance," Omega, Elsevier, vol. 40(6), pages 791-804.
  • Handle: RePEc:eee:jomega:v:40:y:2012:i:6:p:791-804
    DOI: 10.1016/

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    References listed on IDEAS

    1. Mosheiov, Gur & Sidney, Jeffrey B., 2003. "Scheduling with general job-dependent learning curves," European Journal of Operational Research, Elsevier, vol. 147(3), pages 665-670, June.
    2. Biskup, Dirk, 2008. "A state-of-the-art review on scheduling with learning effects," European Journal of Operational Research, Elsevier, vol. 188(2), pages 315-329, July.
    3. Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
    4. Lee, C. -Y. & Leon, V. J., 2001. "Machine scheduling with a rate-modifying activity," European Journal of Operational Research, Elsevier, vol. 128(1), pages 119-128, January.
    5. Chen, Jen-Shiang, 2008. "Optimization models for the tool change scheduling problem," Omega, Elsevier, vol. 36(5), pages 888-894, October.
    6. Lodree Jr., Emmett J. & Geiger, Christopher D., 2010. "A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration," European Journal of Operational Research, Elsevier, vol. 201(2), pages 644-648, March.
    7. Yang, Suh-Jenq & Yang, Dar-Li, 2010. "Minimizing the makespan on single-machine scheduling with aging effect and variable maintenance activities," Omega, Elsevier, vol. 38(6), pages 528-533, December.
    8. Biskup, Dirk, 1999. "Single-machine scheduling with learning considerations," European Journal of Operational Research, Elsevier, vol. 115(1), pages 173-178, May.
    9. Gordon, Valery S. & Strusevich, Vitaly A., 2009. "Single machine scheduling and due date assignment with positionally dependent processing times," European Journal of Operational Research, Elsevier, vol. 198(1), pages 57-62, October.
    10. Mosheiov, Gur, 2001. "Scheduling problems with a learning effect," European Journal of Operational Research, Elsevier, vol. 132(3), pages 687-693, August.
    11. Mohan Gopalakrishnan & Sanjay L. Ahire & David M. Miller, 1997. "Maximizing the Effectiveness of a Preventive Maintenance System: An Adaptive Modeling Approach," Management Science, INFORMS, vol. 43(6), pages 827-840, June.
    12. Chen, Wen-Jinn, 2009. "Minimizing number of tardy jobs on a single machine subject to periodic maintenance," Omega, Elsevier, vol. 37(3), pages 591-599, June.
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    Cited by:

    1. Gawiejnowicz, Stanisław & Kurc, Wiesław, 2015. "Structural properties of time-dependent scheduling problems with the lp norm objective," Omega, Elsevier, vol. 57(PB), pages 196-202.
    2. Xu, Dehua & Wan, Long & Liu, Aihua & Yang, Dar-Li, 2015. "Single machine total completion time scheduling problem with workload-dependent maintenance duration," Omega, Elsevier, vol. 52(C), pages 101-106.
    3. repec:eee:apmaco:v:273:y:2016:i:c:p:570-583 is not listed on IDEAS
    4. Liliana Grigoriu & Dirk Briskorn, 2017. "Scheduling jobs and maintenance activities subject to job-dependent machine deteriorations," Journal of Scheduling, Springer, vol. 20(2), pages 183-197, April.
    5. 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.
    6. Gara-Ali, Ahmed & Finke, Gerd & Espinouse, Marie-Laure, 2016. "Parallel-machine scheduling with maintenance: Praising the assignment problem," European Journal of Operational Research, Elsevier, vol. 252(1), pages 90-97.
    7. repec:spr:jsched:v:20:y:2017:i:6:d:10.1007_s10951-016-0497-6 is not listed on IDEAS
    8. Rustogi, Kabir & Strusevich, Vitaly A., 2012. "Simple matching vs linear assignment in scheduling models with positional effects: A critical review," European Journal of Operational Research, Elsevier, vol. 222(3), pages 393-407.
    9. Yin, Yunqiang & Wang, Yan & Cheng, T.C.E. & Liu, Wenqi & Li, Jinhai, 2017. "Parallel-machine scheduling of deteriorating jobs with potential machine disruptions," Omega, Elsevier, vol. 69(C), pages 17-28.
    10. Yang, Lixing & Zhou, Xuesong & Gao, Ziyou, 2014. "Credibility-based rescheduling model in a double-track railway network: a fuzzy reliable optimization approach," Omega, Elsevier, vol. 48(C), pages 75-93.


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