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Integrated load distribution and production planning in series-parallel multi-state systems with failure rate depending on load

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  • Nourelfath, Mustapha
  • Yalaoui, Farouk

Abstract

A production system containing a set of machines (also called components) arranged according to a series-parallel configuration is addressed. A set of products must be produced in lots on this production system during a specified finite planning horizon. This paper presents a method for integrating load distribution decisions, and tactical production planning considering the costs of capacity change and the costs of unused capacity. The objective is to minimize the sum of capacity change costs, unused capacity costs, setup costs, holding costs, backorder costs, and production costs. The main constraints consist in satisfying the demand for all products over the entire horizon, and in not exceeding available repair resource. The production series-parallel system is modeled as a multi-state system with binary-state components. The proposed model takes into account the dependence of machines' failure rates on their load. Universal generating function technique can be used in the optimization algorithm for evaluating the expected system production rate in each period. We show how the formulated problem can be solved by comparing the results of several multi-product lot-sizing problems with capacity associated costs. The importance of integrating load distribution decisions and production planning is illustrated through numerical examples.

Suggested Citation

  • Nourelfath, Mustapha & Yalaoui, Farouk, 2012. "Integrated load distribution and production planning in series-parallel multi-state systems with failure rate depending on load," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 138-145.
    • Handle: RePEc:eee:reensy:v:106:y:2012:i:c:p:138-145
    DOI: 10.1016/j.ress.2012.06.006
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    1. WOLSEY, Laurence, 2002. "Solving multi-item lot-sizing problems with an MIP solver using classification and reformulation," LIDAM Discussion Papers CORE 2002012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    5. Nourelfath, Mustapha, 2011. "Service level robustness in stochastic production planning under random machine breakdowns," European Journal of Operational Research, Elsevier, vol. 212(1), pages 81-88, July.
    6. WOLSEY, Laurence A., 2002. "Solving multi-item lot-sizing problems with an MIP solver using classification and reformulation," LIDAM Reprints CORE 1605, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, February.
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    Cited by:

    1. M. López-Campos & F. Kristjanpoller & P. Viveros & R. Pascual, 2018. "Reliability Assessment Methodology for Massive Manufacturing Using Multi-Function Equipment," Complexity, Hindawi, vol. 2018, pages 1-8, February.
    2. 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.
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    4. Li, Yaping & Xia, Tangbin & Chen, Zhen & Pan, Ershun, 2023. "Multiple degradation-driven preventive maintenance policy for serial-parallel multi-station manufacturing systems," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    5. Gajpal, Yuvraj & Nourelfath, Mustapha, 2015. "Two efficient heuristics to solve the integrated load distribution and production planning problem," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 204-214.
    6. Annie Francie, Kouedeu & Jean-Pierre, Kenne & Pierre, Dejax & Victor, Songmene & Vladimir, Polotski, 2014. "Stochastic optimal control of manufacturing systems under production-dependent failure rates," International Journal of Production Economics, Elsevier, vol. 150(C), pages 174-187.
    7. Dao, Cuong D. & Zuo, Ming J., 2017. "Optimal selective maintenance for multi-state systems in variable loading conditions," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 171-180.
    8. Hui Xiao & Rui Peng & Wenbin Wang & Fei Zhao, 2016. "Optimal element loading for linear sliding window systems," Journal of Risk and Reliability, , vol. 230(1), pages 75-84, February.

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