IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v214y2019icp151-162.html
   My bibliography  Save this article

Allocating spares to maximize the window fill rate in a periodic review inventory system

Author

Listed:
  • Dreyfuss, Michael
  • Giat, Yahel

Abstract

We study the spares allocation problem in a multiple-item, multiple-location inventory system with periodic review. The system allocates spares with the objective of maximizing the window fill rate, which is the probability that a random customer is served within a given time window. The advantage of the window fill rate as a service performance measure is that it takes into account that customers may tolerate a certain wait before they are served. We develop the window fill rate formula and show that, depending on the tolerable wait, it is either a constant, concave or convex-concave with the number of spares. We use this result to develop an efficient algorithm to find the optimal spares allocation for a given budget or for a given target window fill rate. We show that when the tolerable wait or the budget are small, spares will be clustered in a subgroup of the locations (or item-types), while the other locations (or item-types) do not receive any spares. In addition, we numerically illustrate the spares allocation problem using two different synthetic large-scale examples. In particular, we use these examples to demonstrate the cost (in terms of additional spares) of a periodic review compared to a continuous review. The numerical illustration also highlights the complexity of the window fill rate and the savings gained by using it as an optimality criterion.

Suggested Citation

  • Dreyfuss, Michael & Giat, Yahel, 2019. "Allocating spares to maximize the window fill rate in a periodic review inventory system," International Journal of Production Economics, Elsevier, vol. 214(C), pages 151-162.
    • Handle: RePEc:eee:proeco:v:214:y:2019:i:c:p:151-162
    DOI: 10.1016/j.ijpe.2019.04.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527319301409
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijpe.2019.04.017?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Cardós, Manuel & Babiloni, Eugenia, 2011. "Exact and approximate calculation of the cycle service level in periodic review inventory policies," International Journal of Production Economics, Elsevier, vol. 131(1), pages 63-68, May.
    2. Jiao, Hong-Wei & Liu, San-Yang, 2015. "A practicable branch and bound algorithm for sum of linear ratios problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 723-730.
    3. Cardós, Manuel & Babiloni, Eugenia, 2011. "Exact and approximated calculation of the cycle service level in a continuous review policy," International Journal of Production Economics, Elsevier, vol. 133(1), pages 251-255, September.
    4. Silver, Edward A. & Robb, David J., 2008. "Some insights regarding the optimal reorder period in periodic review inventory systems," International Journal of Production Economics, Elsevier, vol. 112(1), pages 354-366, March.
    5. Chiang, Chi, 2009. "A periodic review replenishment model with a refined delivery scenario," International Journal of Production Economics, Elsevier, vol. 118(1), pages 253-259, March.
    6. Johansen, Soren Glud & Hill, Roger M., 2000. "The (r,Q) control of a periodic-review inventory system with continuous demand and lost sales," International Journal of Production Economics, Elsevier, vol. 68(3), pages 279-286, December.
    7. Dreyfuss, Michael & Giat, Yahel, 2018. "Optimal allocation of spares to maximize the window fill rate in a two-echelon exchangeable-item repair system," European Journal of Operational Research, Elsevier, vol. 270(3), pages 1053-1062.
    8. Srivastava, Vaibhav & Bullo, Francesco, 2014. "Knapsack problems with sigmoid utilities: Approximation algorithms via hybrid optimization," European Journal of Operational Research, Elsevier, vol. 236(2), pages 488-498.
    9. Paul H. Zipkin, 1980. "Simple Ranking Methods for Allocation of One Resource," Management Science, INFORMS, vol. 26(1), pages 34-43, January.
    10. van Donselaar, Karel H. & Broekmeulen, Rob A.C.M., 2013. "Determination of safety stocks in a lost sales inventory system with periodic review, positive lead-time, lot-sizing and a target fill rate," International Journal of Production Economics, Elsevier, vol. 143(2), pages 440-448.
    11. Avinadav, Tal & Henig, Mordecai I., 2015. "Exact accounting of inventory costs in stochastic periodic-review models," International Journal of Production Economics, Elsevier, vol. 169(C), pages 89-98.
    12. Jing-Sheng Song & David D. Yao, 2002. "Performance Analysis and Optimization of Assemble-to-Order Systems with Random Lead Times," Operations Research, INFORMS, vol. 50(5), pages 889-903, October.
    13. Craig C. Sherbrooke, 1968. "Metric: A Multi-Echelon Technique for Recoverable Item Control," Operations Research, INFORMS, vol. 16(1), pages 122-141, February.
    14. Dreyfuss, Michael & Giat, Yahel, 2017. "Optimal spares allocation to an exchangeable-item repair system with tolerable wait," European Journal of Operational Research, Elsevier, vol. 261(2), pages 584-594.
    15. Disney, Stephen M. & Gaalman, Gerard J.C. & Hedenstierna, Carl Philip T. & Hosoda, Takamichi, 2015. "Fill rate in a periodic review order-up-to policy under auto-correlated normally distributed, possibly negative, demand," International Journal of Production Economics, Elsevier, vol. 170(PB), pages 501-512.
    16. Caggiano, Kathryn E. & Jackson, Peter L. & Muckstadt, John A. & Rappold, James A., 2009. "Efficient computation of time-based customer service levels in a multi-item, multi-echelon supply chain: A practical approach for inventory optimization," European Journal of Operational Research, Elsevier, vol. 199(3), pages 744-749, December.
    17. Steven T. Hackman & Loren K. Platzman, 1990. "Near-Optimal Solution of Generalized Resource Allocation Problems with Large Capacities," Operations Research, INFORMS, vol. 38(5), pages 902-910, October.
    18. Michael Dreyfuss & Yahel Giat, 2018. "Window Fill Rate in a Two-Echelon Exchangeable-Item Repair-System," Operations Research Proceedings, in: Andreas Fink & Armin Fügenschuh & Martin Josef Geiger (ed.), Operations Research Proceedings 2016, pages 293-299, Springer.
    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. Kouki, Chaaben & Arts, Joachim & Babai, M. Zied, 2024. "Performance evaluation of a two-echelon inventory system with network lost sales," European Journal of Operational Research, Elsevier, vol. 314(2), pages 647-664.
    2. Yang, Jie & Liu, Wei & Ma, Kai & Yue, Zhiyuan & Zhu, Anhu & Guo, Shiliang, 2023. "An optimal battery allocation model for battery swapping station of electric vehicles," Energy, Elsevier, vol. 272(C).
    3. Yahel Giat, 2024. "Stock Levels and Repair Sourcing in a Periodic Review Exchangeable Item Repair System," Logistics, MDPI, vol. 8(2), pages 1-19, March.
    4. Wang, Ziqi & Hou, Sizu, 2023. "A real-time strategy for vehicle-to-station recommendation in battery swapping mode," Energy, Elsevier, vol. 272(C).

    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. Dreyfuss, Michael & Giat, Yahel, 2017. "Optimal spares allocation to an exchangeable-item repair system with tolerable wait," European Journal of Operational Research, Elsevier, vol. 261(2), pages 584-594.
    2. Yahel Giat, 2024. "Stock Levels and Repair Sourcing in a Periodic Review Exchangeable Item Repair System," Logistics, MDPI, vol. 8(2), pages 1-19, March.
    3. García-Benito, Juan Carlos & Martín-Peña, María-Luz, 2021. "A redistribution model with minimum backorders of spare parts: A proposal for the defence sector," European Journal of Operational Research, Elsevier, vol. 291(1), pages 178-193.
    4. Kouki, Chaaben & Arts, Joachim & Babai, M. Zied, 2024. "Performance evaluation of a two-echelon inventory system with network lost sales," European Journal of Operational Research, Elsevier, vol. 314(2), pages 647-664.
    5. Basten, Rob J.I. & Ryan, Jennifer K., 2019. "The value of maintenance delay flexibility for improved spare parts inventory management," European Journal of Operational Research, Elsevier, vol. 278(2), pages 646-657.
    6. Hedenstierna, Carl Philip T. & Disney, Stephen M., 2016. "Inventory performance under staggered deliveries and autocorrelated demand," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1082-1091.
    7. Wang, Ziqi & Hou, Sizu, 2023. "A real-time strategy for vehicle-to-station recommendation in battery swapping mode," Energy, Elsevier, vol. 272(C).
    8. Chia-Nan Wang & Thanh-Tuan Dang & Ngoc-Ai-Thy Nguyen, 2020. "A Computational Model for Determining Levels of Factors in Inventory Management Using Response Surface Methodology," Mathematics, MDPI, vol. 8(8), pages 1-23, July.
    9. Lamghari-Idrissi, Douniel & Basten, Rob & van Houtum, Geert-Jan, 2020. "Spare parts inventory control under a fixed-term contract with a long-down constraint," International Journal of Production Economics, Elsevier, vol. 219(C), pages 123-137.
    10. Lee, Zu-Hsu & Deng, Shiming & Lin, Beixin & Yang, James G.S., 2010. "Decision model and analysis for investment interest expense deduction and allocation," European Journal of Operational Research, Elsevier, vol. 200(1), pages 268-280, January.
    11. Selçuk, B., 2013. "An adaptive base stock policy for repairable item inventory control," International Journal of Production Economics, Elsevier, vol. 143(2), pages 304-315.
    12. Westerink-Duijzer, L.E. & Schlicher, L.P.J. & Musegaas, M., 2019. "Fair allocations for cooperation problems in vaccination," Econometric Institute Research Papers EI2019-06, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Araceli Zavala & David Nowicki & Jose Emmanuel Ramirez-Marquez, 2019. "Quantitative metrics to analyze supply chain resilience and associated costs," Journal of Risk and Reliability, , vol. 233(2), pages 186-199, April.
    14. Patriarca, Riccardo & Costantino, Francesco & Di Gravio, Giulio & Tronci, Massimo, 2016. "Inventory optimization for a customer airline in a Performance Based Contract," Journal of Air Transport Management, Elsevier, vol. 57(C), pages 206-216.
    15. Yao Zhao, 2008. "Evaluation and Optimization of Installation Base-Stock Policies in Supply Chains with Compound Poisson Demand," Operations Research, INFORMS, vol. 56(2), pages 437-452, April.
    16. Lotty E. Westerink‐Duijzer & Loe P. J. Schlicher & Marieke Musegaas, 2020. "Core Allocations for Cooperation Problems in Vaccination," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1720-1737, July.
    17. Renato de Matta & Vernon Ning Hsu & Timothy J. Lowe, 1999. "The selection allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 707-725, September.
    18. Petropoulos, Fotios & Wang, Xun & Disney, Stephen M., 2019. "The inventory performance of forecasting methods: Evidence from the M3 competition data," International Journal of Forecasting, Elsevier, vol. 35(1), pages 251-265.
    19. Yang, Liu & Liu, Kanglin & Zhang, Juan & Zelbst, Pamela J., 2024. "Inventory management with actual palletized transportation costs and lost sales," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
    20. Tsai, Shing Chih & Zheng, Ya-Xin, 2013. "A simulation optimization approach for a two-echelon inventory system with service level constraints," European Journal of Operational Research, Elsevier, vol. 229(2), pages 364-374.

    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:proeco:v:214:y:2019:i:c:p:151-162. 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/ijpe .

    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.