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Minimizing total flow time in the single-machine scheduling problem with periodic maintenance

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  • W J Chen

    (Chung Kuo Institute of Technology)

Abstract

This paper deals with a single-machine scheduling problem with limited machine availability. The limited availability of machine results from periodic maintenance activities. In our research, a periodic maintenance schedule consists of several maintenance periods. Each maintenance period is scheduled after a periodic time interval. The objective is to find a schedule that minimizes the total flow time subject to periodic maintenance and nonresumable jobs. Some important theorems are proved for the problem. A branch-and-bound algorithm that utilizes several theorems is proposed to find the optimal schedule. We also develop a heuristic to solve large sized problems. In this paper, computational results show that the proposed heuristic is highly accurate and efficient.

Suggested Citation

  • W J Chen, 2006. "Minimizing total flow time in the single-machine scheduling problem with periodic maintenance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 410-415, April.
    • Handle: RePEc:pal:jorsoc:v:57:y:2006:i:4:d:10.1057_palgrave.jors.2601998
    DOI: 10.1057/palgrave.jors.2601998
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    References listed on IDEAS

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    1. Lee, Chung-Yee & Lin, Chen-Sin, 2001. "Single-machine scheduling with maintenance and repair rate-modifying activities," European Journal of Operational Research, Elsevier, vol. 135(3), pages 493-513, December.
    2. I. Adiri & E. Frostig & A. H. G. Rinnooy Kan, 1991. "Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 261-271, April.
    3. 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.
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    Citations

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    Cited by:

    1. 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.
    2. Yunqiang Yin & Jianyou Xu & T. C. E. Cheng & Chin‐Chia Wu & Du‐Juan Wang, 2016. "Approximation schemes for single‐machine scheduling with a fixed maintenance activity to minimize the total amount of late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 172-183, March.
    3. Babu, Sona & Girish, B.S., 2024. "Pareto-optimal front generation for the bi-objective JIT scheduling problems with a piecewise linear trade-off between objectives," Operations Research Perspectives, Elsevier, vol. 12(C).
    4. R. Jamshidi & Mir Seyyed Esfahani, 2014. "Human resources scheduling to improve the product quality according to exhaustion limit," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1028-1041, October.
    5. 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.
    6. Imed Kacem, 2009. "Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 117-133, February.
    7. Sun, Kaibiao & Li, Hongxing, 2010. "Scheduling problems with multiple maintenance activities and non-preemptive jobs on two identical parallel machines," International Journal of Production Economics, Elsevier, vol. 124(1), pages 151-158, March.
    8. 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.
    9. Kacem, Imed & Chu, Chengbin, 2008. "Efficient branch-and-bound algorithm for minimizing the weighted sum of completion times on a single machine with one availability constraint," International Journal of Production Economics, Elsevier, vol. 112(1), pages 138-150, March.
    10. Jing Fan & Xiwen Lu, 2015. "Supply chain scheduling problem in the hospital with periodic working time on a single machine," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 892-905, November.
    11. Hanane Krim & Rachid Benmansour & David Duvivier & Daoud Aït-Kadi & Said Hanafi, 2020. "Heuristics for the single machine weighted sum of completion times scheduling problem with periodic maintenance," Computational Optimization and Applications, Springer, vol. 75(1), pages 291-320, January.

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