IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v330y2026i3p800-815.html

The optimal repair policy for an unreliable production system with limited available spare parts

Author

Listed:
  • Brieditis, Ludwig
  • Kiesmüller, Gudrun P.
  • Malmberg, Filip

Abstract

In this study, a serial production system consisting of two machines and an intermediate finite buffer is considered. The machines have random processing times, and each machine contains one unit of a common critical component that is subject to random breakdown. Broken components must be replaced from an inventory of ready-for-use spare parts to restore machine functionality. This inventory is replenished according to a one-for-one replenishment policy with an externally given base stock level. Due to the limited availability of spare parts, the sequence in which the machines are to be repaired and whether they should be repaired immediately must be decided. The objective of our study is the maximization of the expected total discounted revenue per time unit over an infinite planning horizon.

Suggested Citation

  • Brieditis, Ludwig & Kiesmüller, Gudrun P. & Malmberg, Filip, 2026. "The optimal repair policy for an unreliable production system with limited available spare parts," European Journal of Operational Research, Elsevier, vol. 330(3), pages 800-815.
    • Handle: RePEc:eee:ejores:v:330:y:2026:i:3:p:800-815
    DOI: 10.1016/j.ejor.2025.09.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221725007246
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2025.09.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Steven A. Lippman, 1975. "Applying a New Device in the Optimization of Exponential Queuing Systems," Operations Research, INFORMS, vol. 23(4), pages 687-710, August.
    2. FadIloglu, Mehmet Murat & Bulut, Önder, 2010. "A dynamic rationing policy for continuous-review inventory systems," European Journal of Operational Research, Elsevier, vol. 202(3), pages 675-685, May.
    3. Haque, Lani & Armstrong, Michael J., 2007. "A survey of the machine interference problem," European Journal of Operational Research, Elsevier, vol. 179(2), pages 469-482, June.
    4. Christian Weckenborg & Karsten Kieckhäfer & Christoph Müller & Martin Grunewald & Thomas S. Spengler, 2020. "Balancing of assembly lines with collaborative robots," Business Research, Springer;German Academic Association for Business Research, vol. 13(1), pages 93-132, April.
    5. Christoph Müller & Martin Grunewald & Thomas Stefan Spengler, 2018. "Redundant configuration of robotic assembly lines with stochastic failures," International Journal of Production Research, Taylor & Francis Journals, vol. 56(10), pages 3662-3682, May.
    6. Pedram Sahba & Barış Balcıog̃lu & Dragan Banjevic, 2018. "Multilevel rationing policy for spare parts when demand is state dependent," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 751-780, July.
    7. Teunter, Ruud H. & Klein Haneveld, Willem K., 2008. "Dynamic inventory rationing strategies for inventory systems with two demand classes, Poisson demand and backordering," European Journal of Operational Research, Elsevier, vol. 190(1), pages 156-178, October.
    8. Shaoxiang Chen & Jianjun Xu & Youyi Feng, 2010. "A partial characterization of the optimal ordering/rationing policy for a periodic review system with two demand classes and backordering," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(4), pages 330-341, June.
    9. Kahan, Tomer & Bukchin, Yossi & Menassa, Roland & Ben-Gal, Irad, 2009. "Backup strategy for robots' failures in an automotive assembly system," International Journal of Production Economics, Elsevier, vol. 120(2), pages 315-326, August.
    10. Kiesmüller, G.P. & Sachs, F.E., 2020. "Spare parts or buffer? How to design a transfer line with unreliable machines," European Journal of Operational Research, Elsevier, vol. 284(1), pages 121-134.
    11. Donald M. Topkis, 1968. "Optimal Ordering and Rationing Policies in a Nonstationary Dynamic Inventory Model with n Demand Classes," Management Science, INFORMS, vol. 15(3), pages 160-176, November.
    12. Wong, H. & van Houtum, G.J. & Cattrysse, D. & Oudheusden, D. Van, 2006. "Multi-item spare parts systems with lateral transshipments and waiting time constraints," European Journal of Operational Research, Elsevier, vol. 171(3), pages 1071-1093, June.
    13. Sachs, F.E. & Helber, S. & Kiesmüller, G.P., 2022. "Evaluation of Unreliable Flow Lines with Limited Buffer Capacities and Spare Part Provisioning," European Journal of Operational Research, Elsevier, vol. 302(2), pages 544-559.
    14. Lopes, Thiago Cantos & Sikora, C.G.S. & Molina, Rafael Gobbi & Schibelbain, Daniel & Rodrigues, L.C.A. & Magatão, Leandro, 2017. "Balancing a robotic spot welding manufacturing line: An industrial case study," European Journal of Operational Research, Elsevier, vol. 263(3), pages 1033-1048.
    15. Patrik Alfredsson & Jos Verrijdt, 1999. "Modeling Emergency Supply Flexibility in a Two-Echelon Inventory System," Management Science, INFORMS, vol. 45(10), pages 1416-1431, October.
    16. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    17. Seyed M.R. Iravani & Izak Duenyas & Tava Lennon Olsen, 2000. "A Production/Inventory System Subject to Failure with Limited Repair Capacity," Operations Research, INFORMS, vol. 48(6), pages 951-964, December.
    18. Gudrun P. Kiesmüller & Julia Zimmermann, 2018. "The influence of spare parts provisioning on buffer size in a production system," IISE Transactions, Taylor & Francis Journals, vol. 50(5), pages 367-380, May.
    Full references (including those not matched with items on IDEAS)

    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. van Wijk, A.C.C. & Adan, I.J.B.F. & van Houtum, G.J., 2019. "Optimal lateral transshipment policies for a two location inventory problem with multiple demand classes," European Journal of Operational Research, Elsevier, vol. 272(2), pages 481-495.
    2. Bing Lin & Shaoxiang Chen & Yi Feng & Jianjun Xu, 2018. "The Joint Stock and Capacity Rationings of a Make-To-Stock System with Flexible Demand," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-27, February.
    3. Kiesmüller, G.P. & Sachs, F.E., 2020. "Spare parts or buffer? How to design a transfer line with unreliable machines," European Journal of Operational Research, Elsevier, vol. 284(1), pages 121-134.
    4. Sachs, F.E. & Helber, S. & Kiesmüller, G.P., 2022. "Evaluation of Unreliable Flow Lines with Limited Buffer Capacities and Spare Part Provisioning," European Journal of Operational Research, Elsevier, vol. 302(2), pages 544-559.
    5. Pourakbar, Morteza & Dekker, Rommert, 2012. "Customer differentiated end-of-life inventory problem," European Journal of Operational Research, Elsevier, vol. 222(1), pages 44-53.
    6. Lu Wang & Vidyadhar Kulkarni & Hanqin Zhang, 2023. "Inventory dispensation and restocking in multiclass inventory systems: A decoupling approach," Production and Operations Management, Production and Operations Management Society, vol. 32(2), pages 469-484, February.
    7. van Wijk, A.C.C. & Adan, I.J.B.F. & van Houtum, G.J., 2012. "Approximate evaluation of multi-location inventory models with lateral transshipments and hold back levels," European Journal of Operational Research, Elsevier, vol. 218(3), pages 624-635.
    8. ElHafsi, Mohsen & Fang, Jianxin & Hamouda, Essia, 2021. "Optimal production and inventory control of multi-class mixed backorder and lost sales demand class models," European Journal of Operational Research, Elsevier, vol. 291(1), pages 147-161.
    9. Battaïa, Olga & Dolgui, Alexandre, 2022. "Hybridizations in line balancing problems: A comprehensive review on new trends and formulations," International Journal of Production Economics, Elsevier, vol. 250(C).
    10. Alfieri, Arianna & Pastore, Erica & Zotteri, Giulio, 2017. "Dynamic inventory rationing: How to allocate stock according to managerial priorities. An empirical study," International Journal of Production Economics, Elsevier, vol. 189(C), pages 14-29.
    11. Topan, E. & Eruguz, A.S. & Ma, W. & van der Heijden, M.C. & Dekker, R., 2020. "A review of operational spare parts service logistics in service control towers," European Journal of Operational Research, Elsevier, vol. 282(2), pages 401-414.
    12. Zümbül Atan & Lawrence V. Snyder & George R. Wilson, 2018. "Transshipment policies for systems with multiple retailers and two demand classes," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 159-186, January.
    13. Tiemessen, H.G.H. & Fleischmann, M. & van Houtum, G.J. & van Nunen, J.A.E.E. & Pratsini, E., 2013. "Dynamic demand fulfillment in spare parts networks with multiple customer classes," European Journal of Operational Research, Elsevier, vol. 228(2), pages 367-380.
    14. Liu, Shudong & Song, Miao & Tan, Kok Choon & Zhang, Changyong, 2015. "Multi-class dynamic inventory rationing with stochastic demands and backordering," European Journal of Operational Research, Elsevier, vol. 244(1), pages 153-163.
    15. Pinto, Roberto, 2012. "Stock rationing under service level constraints in a vertically integrated distribution system," International Journal of Production Economics, Elsevier, vol. 136(1), pages 231-240.
    16. Bao, Lina & Liu, Zhiying & Yu, Yimin & Zhang, Wei, 2018. "On the decomposition property for a dynamic inventory rationing problem with multiple demand classes and backorder," European Journal of Operational Research, Elsevier, vol. 265(1), pages 99-106.
    17. Quan-Lin Li & Yi-Meng Li & Jing-Yu Ma & Heng-Li Liu, 2023. "A complete algebraic solution to the optimal dynamic rationing policy in the stock-rationing queue with two demand classes," Journal of Combinatorial Optimization, Springer, vol. 45(3), pages 1-54, April.
    18. Satır, Benhür & Erenay, Fatih Safa & Bookbinder, James H., 2018. "Shipment consolidation with two demand classes: Rationing the dispatch capacity," European Journal of Operational Research, Elsevier, vol. 270(1), pages 171-184.
    19. Gabor, A.F. & Guang, Y. & Axsäter, S., 2014. "Comparison of two methods for customer differentiation," ERIM Report Series Research in Management ERS-2014-003-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    20. van Jaarsveld, W.L. & Dekker, R., 2009. "Finding optimal policies in the (S - 1, S ) lost sales inventory model with multiple demand classes," Econometric Institute Research Papers EI 2009-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:330:y:2026:i:3:p:800-815. 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.