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A periodic review production and maintenance model with random demand, deteriorating equipment, and binomial yield

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  • T W Sloan

    (University of Miami)

Abstract

In many environments, product yield is heavily influenced by equipment condition. Despite this fact, previous research has either focused on the issue of maintenance, ignoring the effect of equipment condition on yield, or has focused on the issue of production, omitting the possibility of actively changing the machine state. We formulate a Markov decision process model of a single-stage production system in which demand is random. The product yield has a binomial distribution that depends on the equipment condition, which deteriorates over time. The objective is to choose simultaneously the equipment maintenance schedule as well as the quantity to produce in a way that minimizes the sum of expected production, backorder, and holding costs. After proving some results about the structural properties of the optimal policy, numerical problems are used to compare this method to the typical approach of solving the maintenance and production problems sequentially. The results show that the simultaneous solution provides substantial gains over the sequential approach. In the cases studied, the proposed method resulted in an average cost savings of approximately 18%.

Suggested Citation

  • T W Sloan, 2004. "A periodic review production and maintenance model with random demand, deteriorating equipment, and binomial yield," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(6), pages 647-656, June.
  • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:6:d:10.1057_palgrave.jors.2601725
    DOI: 10.1057/palgrave.jors.2601725
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    References listed on IDEAS

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    Cited by:

    1. Huidong Zhang & Dragan Djurdjanovic, 2022. "Integrated production and maintenance planning under uncertain demand with concurrent learning of yield rate," Flexible Services and Manufacturing Journal, Springer, vol. 34(2), pages 429-450, June.
    2. Zhang, Nan & Cai, Kaiquan & Deng, Yingjun & Zhang, Jun, 2023. "Determining the optimal production–maintenance policy of a parallel production system with stochastically interacted yield and deterioration," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    3. Liu, Yu & Chen, Yiming & Jiang, Tao, 2020. "Dynamic selective maintenance optimization for multi-state systems over a finite horizon: A deep reinforcement learning approach," European Journal of Operational Research, Elsevier, vol. 283(1), pages 166-181.
    4. Zequeira, Romulo I. & Valdes, Jose E. & Berenguer, Christophe, 2008. "Optimal buffer inventory and opportunistic preventive maintenance under random production capacity availability," International Journal of Production Economics, Elsevier, vol. 111(2), pages 686-696, February.
    5. Thomas Sloan, 2008. "Simultaneous determination of production and maintenance schedules using in‐line equipment condition and yield information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(2), pages 116-129, March.
    6. Borrero, J.S. & Akhavan-Tabatabaei, R., 2013. "Time and inventory dependent optimal maintenance policies for single machine workstations: An MDP approach," European Journal of Operational Research, Elsevier, vol. 228(3), pages 545-555.
    7. Uit Het Broek, Michiel A.J. & Teunter, Ruud H. & de Jonge, Bram & Veldman, Jasper, 2021. "Joint condition-based maintenance and load-sharing optimization for two-unit systems with economic dependency," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1119-1131.
    8. Choi, Sungyong & Jeon, Sumin & Kim, Jinmin & Park, Kwangtae, 2019. "A newsvendor analysis of a binomial yield production process," European Journal of Operational Research, Elsevier, vol. 273(3), pages 983-991.
    9. Nabil Nahas, 2017. "Buffer allocation and preventive maintenance optimization in unreliable production lines," Journal of Intelligent Manufacturing, Springer, vol. 28(1), pages 85-93, January.
    10. Xiaodong Yao & Xiaolan Xie & Michael C. Fu & Steven I. Marcus, 2005. "Optimal joint preventive maintenance and production policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(7), pages 668-681, October.
    11. Michiel A. J. uit het Broek & Ruud H. Teunter & Bram de Jonge & Jasper Veldman & Nicky D. Van Foreest, 2020. "Condition-Based Production Planning: Adjusting Production Rates to Balance Output and Failure Risk," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 792-811, July.
    12. Kutzner, Sarah C. & Kiesmüller, Gudrun P., 2013. "Optimal control of an inventory-production system with state-dependent random yield," European Journal of Operational Research, Elsevier, vol. 227(3), pages 444-452.
    13. Zhang, Nan & Cai, Kaiquan & Deng, Yingjun & Zhang, Jun, 2024. "Joint optimization of condition-based maintenance and condition-based production of a single equipment considering random yield and maintenance delay," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    14. Abdelhamid Boudjelida, 2019. "On the robustness of joint production and maintenance scheduling in presence of uncertainties," Journal of Intelligent Manufacturing, Springer, vol. 30(4), pages 1515-1530, April.
    15. David L. Kaufman & Mark E. Lewis, 2007. "Machine maintenance with workload considerations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(7), pages 750-766, October.
    16. Karamatsoukis, C.C. & Kyriakidis, E.G., 2010. "Optimal maintenance of two stochastically deteriorating machines with an intermediate buffer," European Journal of Operational Research, Elsevier, vol. 207(1), pages 297-308, November.
    17. Ekin, Tahir, 2018. "Integrated maintenance and production planning with endogenous uncertain yield," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 52-61.
    18. Kazaz, Burak & Sloan, Thomas W., 2013. "The impact of process deterioration on production and maintenance policies," European Journal of Operational Research, Elsevier, vol. 227(1), pages 88-100.

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