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Scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan

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  • Chen, Jen-Shiang

Abstract

This study addresses a single machine scheduling problem with periodic maintenance, where the machine is assumed to be stopped periodically for maintenance for a constant time w during the scheduling period. Meanwhile, the maintenance period [u, v] is assumed to have been previously arranged and the time w is assumed not to exceed the available maintenance period [u, v] (i.e. w [less-than-or-equals, slant] v - u). The time u(v) is the earliest (latest) time at which the machine starts (stops) its maintenance. The objective is to minimize the makespan. Two mixed binary integer programming (BIP) models are provided for deriving the optimal solution. Additionally, an efficient heuristic is proposed for finding the near-optimal solution for large-sized problems. Finally, computational results are provided to demonstrate the efficiency of the models and the effectiveness of the heuristics. The mixed BIP model can optimally solve up to 100-job instances, while the average percentage error of the heuristic is below 1%.

Suggested Citation

  • Chen, Jen-Shiang, 2008. "Scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan," European Journal of Operational Research, Elsevier, vol. 190(1), pages 90-102, October.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:1:p:90-102
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    References listed on IDEAS

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    1. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    2. X Qi & T Chen & F Tu, 1999. "Scheduling the maintenance on a single machine," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(10), pages 1071-1078, October.
    3. 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.
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    Cited by:

    1. 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.
    2. Kuschel, Torben & Bock, Stefan, 2016. "The weighted uncapacitated planned maintenance problem: Complexity and polyhedral properties," European Journal of Operational Research, Elsevier, vol. 250(3), pages 773-781.
    3. Seyed Habib A. Rahmati & Abbas Ahmadi & Kannan Govindan, 2018. "A novel integrated condition-based maintenance and stochastic flexible job shop scheduling problem: simulation-based optimization approach," Annals of Operations Research, Springer, vol. 269(1), pages 583-621, October.
    4. Janiak, Adam & Janiak, Władysław A. & Krysiak, Tomasz & Kwiatkowski, Tomasz, 2015. "A survey on scheduling problems with due windows," European Journal of Operational Research, Elsevier, vol. 242(2), pages 347-357.
    5. Briskorn, Dirk & Choi, Byung-Cheon & Lee, Kangbok & Leung, Joseph & Pinedo, Michael, 2009. "Genetic algorithms for inventory constrained scheduling on a single machine," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 649, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    6. Xu, Dehua & Yin, Yunqiang & Li, Hongxing, 2009. "A note on "scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan"," European Journal of Operational Research, Elsevier, vol. 197(2), pages 825-827, September.
    7. 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.
    8. Behrooz Shahbazi & Seyed Habib A. Rahmati, 2021. "Developing a Flexible Manufacturing Control System Considering Mixed Uncertain Predictive Maintenance Model: a Simulation-Based Optimization Approach," SN Operations Research Forum, Springer, vol. 2(4), pages 1-43, December.
    9. Wenchang Luo & Yao Xu & Weitian Tong & Guohui Lin, 2019. "Single-machine scheduling with job-dependent machine deterioration," Journal of Scheduling, Springer, vol. 22(6), pages 691-707, December.
    10. 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.
    11. Nesello, Vitor & Subramanian, Anand & Battarra, Maria & Laporte, Gilbert, 2018. "Exact solution of the single-machine scheduling problem with periodic maintenances and sequence-dependent setup times," European Journal of Operational Research, Elsevier, vol. 266(2), pages 498-507.
    12. von Hoyningen-Huene, Wiebke & Kiesmüller, Gudrun P., 2015. "Maintenance and Production Scheduling on a Single Machine with Stochastic Failures," EconStor Preprints 106608, ZBW - Leibniz Information Centre for Economics.
    13. Xia, Tangbin & Jin, Xiaoning & Xi, Lifeng & Ni, Jun, 2015. "Production-driven opportunistic maintenance for batch production based on MAM–APB scheduling," European Journal of Operational Research, Elsevier, vol. 240(3), pages 781-790.
    14. Hoyningen-Huene, Wiebke von, 2015. "Heuristics for an Integrated Maintenance and Production Scheduling Problem on Parallel Machines with Stochastic Failures and Non-Resumable Jobs," EconStor Preprints 112746, ZBW - Leibniz Information Centre for Economics.
    15. von Hoyningen-Huene, W. & Kiesmüller, G.P., 2015. "Evaluation of the expected makespan of a set of non-resumable jobs on parallel machines with stochastic failures," European Journal of Operational Research, Elsevier, vol. 240(2), pages 439-446.

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