IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v212y2011i1p81-88.html
   My bibliography  Save this article

Service level robustness in stochastic production planning under random machine breakdowns

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(11)00086-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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).
    2. James H. Bookbinder & Jin-Yan Tan, 1988. "Strategies for the Probabilistic Lot-Sizing Problem with Service-Level Constraints," Management Science, INFORMS, vol. 34(9), pages 1096-1108, September.
    3. Laurence A. Wolsey, 2002. "Solving Multi-Item Lot-Sizing Problems with an MIP Solver Using Classification and Reformulation," Management Science, INFORMS, vol. 48(12), pages 1587-1602, December.
    4. Panda, D. & Kar, S. & Maity, K. & Maiti, M., 2008. "A single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints," European Journal of Operational Research, Elsevier, vol. 188(1), pages 121-139, July.
    5. George B. Dantzig, 1955. "Linear Programming under Uncertainty," Management Science, INFORMS, vol. 1(3-4), pages 197-206, 04-07.
    6. Tempelmeier, Horst, 2007. "On the stochastic uncapacitated dynamic single-item lotsizing problem with service level constraints," European Journal of Operational Research, Elsevier, vol. 181(1), pages 184-194, August.
    7. Chew, E. P. & Johnson, L. A., 1996. "Service level approximations for multiechelon inventory systems," European Journal of Operational Research, Elsevier, vol. 91(3), pages 440-455, June.
    8. Tarim, S. Armagan & Kingsman, Brian G., 2004. "The stochastic dynamic production/inventory lot-sizing problem with service-level constraints," International Journal of Production Economics, Elsevier, vol. 88(1), pages 105-119, March.
    9. Tan, Bar[iota]s, 1999. "Variance of the output as a function of time: Production line dynamics," European Journal of Operational Research, Elsevier, vol. 117(3), pages 470-484, September.
    10. 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).
    11. Chen, Huifen & Chang, Kuo-Hwa & Cheng, Liuying, 2004. "Estimation of means and covariances of inverse-Gaussian order statistics," European Journal of Operational Research, Elsevier, vol. 155(1), pages 154-169, May.
    12. Lee, Hsu-Hua, 2008. "The investment model in preventive maintenance in multi-level production systems," International Journal of Production Economics, Elsevier, vol. 112(2), pages 816-828, April.
    13. Hausman, Warren H. & Lee, Hau L. & Zhang, Alex X., 1998. "Joint demand fulfillment probability in a multi-item inventory system with independent order-up-to policies," European Journal of Operational Research, Elsevier, vol. 109(3), pages 646-659, September.
    14. Cho, Danny I. & Parlar, Mahmut, 1991. "A survey of maintenance models for multi-unit systems," European Journal of Operational Research, Elsevier, vol. 51(1), pages 1-23, March.
    15. Tarim, S. Armagan & Kingsman, Brian G., 2006. "Modelling and computing (Rn, Sn) policies for inventory systems with non-stationary stochastic demand," European Journal of Operational Research, Elsevier, vol. 174(1), pages 581-599, October.
    16. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
    17. Sana, Shib Sankar, 2010. "An economic production lot size model in an imperfect production system," European Journal of Operational Research, Elsevier, vol. 201(1), pages 158-170, February.
    18. Leung, Stephen C.H. & Tsang, Sally O.S. & Ng, W.L. & Wu, Yue, 2007. "A robust optimization model for multi-site production planning problem in an uncertain environment," European Journal of Operational Research, Elsevier, vol. 181(1), pages 224-238, August.
    19. Mula, J. & Poler, R. & Garcia-Sabater, J.P. & Lario, F.C., 2006. "Models for production planning under uncertainty: A review," International Journal of Production Economics, Elsevier, vol. 103(1), pages 271-285, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nourelfath, Mustapha & Hassan, Jawad, 2015. "Six Sigma performance for non-normal processesAuthor-Name: Aldowaisan, Tariq," European Journal of Operational Research, Elsevier, vol. 247(3), pages 968-977.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Chiu, Yuan-Shyi Peter & Chang, Huei-Hsin, 2014. "Optimal run time for EPQ model with scrap, rework and stochastic breakdowns: A note," Economic Modelling, Elsevier, vol. 37(C), pages 143-148.
    7. Anna Timonina‐Farkas & René Y. Glogg & Ralf W. Seifert, 2022. "Limiting the impact of supply chain disruptions in the face of distributional uncertainty in demand," Production and Operations Management, Production and Operations Management Society, vol. 31(10), pages 3788-3805, October.
    8. 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.
    9. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Özen, Ulaş & Doğru, Mustafa K. & Armagan Tarim, S., 2012. "Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem," Omega, Elsevier, vol. 40(3), pages 348-357.
    2. Sereshti, Narges & Adulyasak, Yossiri & Jans, Raf, 2021. "The value of aggregate service levels in stochastic lot sizing problems," Omega, Elsevier, vol. 102(C).
    3. Nourelfath, Mustapha & Nahas, Nabil & Ben-Daya, Mohamed, 2016. "Integrated preventive maintenance and production decisions for imperfect processes," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 21-31.
    4. E Aghezzaf, 2005. "Capacity planning and warehouse location in supply chains with uncertain demands," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(4), pages 453-462, April.
    5. Rossi, Roberto & Tarim, S. Armagan & Hnich, Brahim & Prestwich, Steven, 2010. "Computing the non-stationary replenishment cycle inventory policy under stochastic supplier lead-times," International Journal of Production Economics, Elsevier, vol. 127(1), pages 180-189, September.
    6. Roberto Rossi & S. Tarim & Brahim Hnich & Steven Prestwich, 2012. "Constraint programming for stochastic inventory systems under shortage cost," Annals of Operations Research, Springer, vol. 195(1), pages 49-71, May.
    7. Roberto Rossi & S. Armagan Tarim & Ramesh Bollapragada, 2012. "Constraint-Based Local Search for Inventory Control Under Stochastic Demand and Lead Time," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 66-80, February.
    8. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    9. Choudhary, Devendra & Shankar, Ravi, 2015. "The value of VMI beyond information sharing in a single supplier multiple retailers supply chain under a non-stationary (Rn, Sn) policy," Omega, Elsevier, vol. 51(C), pages 59-70.
    10. Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2015. "Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing," Omega, Elsevier, vol. 50(C), pages 126-140.
    11. Julian Englberger & Frank Herrmann & Michael Manitz, 2016. "Two-stage stochastic master production scheduling under demand uncertainty in a rolling planning environment," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6192-6215, October.
    12. Kilic, Onur A. & Tunc, Huseyin & Tarim, S. Armagan, 2018. "Heuristic policies for the stochastic economic lot sizing problem with remanufacturing under service level constraints," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1102-1109.
    13. Céline Gicquel & Jianqiang Cheng, 2018. "A joint chance-constrained programming approach for the single-item capacitated lot-sizing problem with stochastic demand," Annals of Operations Research, Springer, vol. 264(1), pages 123-155, May.
    14. G. Rius-Sorolla & J. Maheut & S. Estellés-Miguel & J. P. García-Sabater, 2021. "Operations planning test bed under rolling horizons, multiproduct, multiechelon, multiprocess for capacitated production planning modelling with strokes," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(4), pages 1289-1315, December.
    15. Almeder, Christian & Klabjan, Diego & Traxler, Renate & Almada-Lobo, Bernardo, 2015. "Lead time considerations for the multi-level capacitated lot-sizing problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 727-738.
    16. Liu, Kanglin & Zhang, Zhi-Hai, 2018. "Capacitated disassembly scheduling under stochastic yield and demand," European Journal of Operational Research, Elsevier, vol. 269(1), pages 244-257.
    17. Toledo, Franklina Maria Bragion & Armentano, Vinicius Amaral, 2006. "A Lagrangian-based heuristic for the capacitated lot-sizing problem in parallel machines," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1070-1083, December.
    18. 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.
    19. Brian T. Denton & John Forrest & R. John Milne, 2006. "IBM Solves a Mixed-Integer Program to Optimize Its Semiconductor Supply Chain," Interfaces, INFORMS, vol. 36(5), pages 386-399, October.
    20. Rossi, Roberto & Tarim, S. Armagan & Hnich, Brahim & Prestwich, Steven, 2011. "A state space augmentation algorithm for the replenishment cycle inventory policy," International Journal of Production Economics, Elsevier, vol. 133(1), pages 377-384, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:212:y:2011:i:1:p:81-88. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.