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Service level robustness in stochastic production planning under random machine breakdowns

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  • Nourelfath, Mustapha

Abstract

In this paper, we consider a multi-period, multi-product production planning problem where the production rate and the customer service level are random variables due to machine breakdowns. In order to determine robust production plans, constraints are introduced in the stochastic capacitated lot-sizing problem to ensure that a pre-specified customer service level is met with high probability. The probability of meeting a service level is evaluated by using the first passage time theory of a Wiener process to a boundary. A two-step optimization approach is proposed to solve the developed model. In the first step, the mean-value deterministic model is solved. Then, a method is proposed in the second step to improve the probability of meeting service level. The resulting approach has the advantage of not being a scenario-based one. It is shown that substantial improvements in service level robustness are often possible with minimal increases in expected cost.

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  • 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.
    • Handle: RePEc:eee:ejores:v:212:y:2011:i:1:p:81-88
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    3. Yarong Chen & Hongming Zhou & Peiyu Huang & FuhDer Chou & Shenquan Huang, 2022. "A refined order release method for achieving robustness of non-repetitive dynamic manufacturing system performance," Annals of Operations Research, Springer, vol. 311(1), pages 65-79, April.
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    5. Taş, Duygu & Gendreau, Michel & Jabali, Ola & Jans, Raf, 2019. "A capacitated lot sizing problem with stochastic setup times and overtime," European Journal of Operational Research, Elsevier, vol. 273(1), pages 146-159.
    6. 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.
    7. Mustapha Nourelfath & Tariq Aldowaisan & Jawad Hassan, 2016. "Evaluating Six Sigma failure rate for inverse Gaussian cycle times," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6092-6101, October.
    8. Sunney Fotedar & Ann-Brith Strömberg & Torgny Almgren & Stefan Cedergren, 2023. "A criterion space decomposition approach to generalized tri-objective tactical resource allocation," Computational Management Science, Springer, vol. 20(1), pages 1-28, December.
    9. 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.
    10. 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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