IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v218y2012i2p442-447.html
   My bibliography  Save this article

On the exact calculation of the fill rate in a periodic review inventory policy under discrete demand patterns

Author

Listed:
  • Guijarro, Ester
  • Cardós, Manuel
  • Babiloni, Eugenia

Abstract

The primary goal of this paper is the development of a generalized method to compute the fill rate for any discrete demand distribution in a periodic review policy. The fill rate is defined as the fraction of demand that is satisfied directly from shelf. In the majority of related work, this service metric is computed by using what is known as the traditional approximation, which calculates the fill rate as the complement of the quotient between the expected unfulfilled demand and the expected demand per replenishment cycle, instead of focusing on the expected fraction of fulfilled demand. This paper shows the systematic underestimation of the fill rate when the traditional approximation is used, and revises both the foundations of the traditional approach and the definition of fill rate itself. As a result, this paper presents the following main contributions: (i) a new exact procedure to compute the traditional approximation for any discrete demand distribution; (ii) a more suitable definition of the fill rate in order to ignore those cycles without demand; and (iii) a new standard procedure to compute the fill rate that outperforms previous approaches, especially when the probability of zero demand is substantial. This paper focuses on the traditional periodic review, order up to level system under any uncorrelated, discrete and stationary demand pattern for the lost sales scenario.

Suggested Citation

  • Guijarro, Ester & Cardós, Manuel & Babiloni, Eugenia, 2012. "On the exact calculation of the fill rate in a periodic review inventory policy under discrete demand patterns," European Journal of Operational Research, Elsevier, vol. 218(2), pages 442-447.
    • Handle: RePEc:eee:ejores:v:218:y:2012:i:2:p:442-447
    DOI: 10.1016/j.ejor.2011.11.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711010344
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2011.11.025?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. George J. Feeney & Craig C. Sherbrooke, 1966. "Correction to "(s - 1, s) Inventory Policy Under Compound Poisson Demand"," Management Science, INFORMS, vol. 12(11), pages 908-908, July.
    3. Silver, Edward A. & Bischak, Diane P., 2011. "The exact fill rate in a periodic review base stock system under normally distributed demand," Omega, Elsevier, vol. 39(3), pages 346-349, June.
    4. Tamer Boyaci & Guillermo Gallego, 2001. "Serial Production/Distribution Systems Under Service Constraints," Manufacturing & Service Operations Management, INFORMS, vol. 3(1), pages 43-50, June.
    5. M Cardós & C Miralles & L Ros, 2006. "An exact calculation of the cycle service level in a generalized periodic review system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(10), pages 1252-1255, October.
    6. John A. Muckstadt & L. Joseph Thomas, 1980. "Are Multi-Echelon Inventory Methods Worth Implementing in Systems with Low-Demand-Rate Items?," Management Science, INFORMS, vol. 26(5), pages 483-494, May.
    7. G. J. Feeney & C. C. Sherbrooke, 1966. "The (S - 1, S) Inventory Policy Under Compound Poisson Demand," Management Science, INFORMS, vol. 12(5), pages 391-411, January.
    8. 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.
    9. Johansen, Soren Glud, 2005. "Base-stock policies for the lost sales inventory system with Poisson demand and Erlangian lead times," International Journal of Production Economics, Elsevier, vol. 93(1), pages 429-437, January.
    10. Matthew J. Sobel, 2004. "Fill Rates of Single-Stage and Multistage Supply Systems," Manufacturing & Service Operations Management, INFORMS, vol. 6(1), pages 41-52, June.
    11. de Kok, A. G., 1990. "Hierarchical production planning for consumer goods," European Journal of Operational Research, Elsevier, vol. 45(1), pages 55-69, March.
    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. Hongzhe Zhang & Xiaohang Zhao & Xiao Fang & Bintong Chen, 2024. "Proactive Resource Request for Disaster Response: A Deep Learning-Based Optimization Model," Information Systems Research, INFORMS, vol. 35(2), pages 528-550, June.
    2. 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.
    3. 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.
    4. Eugenia Babiloni & Ester Guijarro & Juan R. Trapero, 2023. "Stock control analytics: a data-driven approach to compute the fill rate considering undershoots," Operational Research, Springer, vol. 23(1), pages 1-25, March.
    5. Teunter, R.H. & Syntetos, A.A. & Babai, M.Z., 2017. "Stock keeping unit fill rate specification," European Journal of Operational Research, Elsevier, vol. 259(3), pages 917-925.
    6. Manuel Cardós & Ester Guijarro & Eugenia Babiloni, 2017. "On the estimation of on-hand stocks for base-stock policies and lost sales systems and its impact on service measures," International Journal of Production Research, Taylor & Francis Journals, vol. 55(16), pages 4680-4694, August.
    7. Ye, Yuan & Lu, Yonggang & Robinson, Powell & Narayanan, Arunachalam, 2022. "An empirical Bayes approach to incorporating demand intermittency and irregularity into inventory control," European Journal of Operational Research, Elsevier, vol. 303(1), pages 255-272.
    8. Bruzda, Joanna, 2020. "Demand forecasting under fill rate constraints—The case of re-order points," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1342-1361.
    9. Abbasi, B. & Hosseinifard, Z. & Alamri, O. & Thomas, D. & Minas, J.P., 2018. "Finite time horizon fill rate analysis for multiple customer cases," Omega, Elsevier, vol. 76(C), pages 1-17.
    10. Eugenia Babiloni & Ester Guijarro, 2020. "Fill rate: from its definition to its calculation for the continuous (s, Q) inventory system with discrete demands and lost sales," 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. 28(1), pages 35-43, March.

    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. 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.
    2. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    3. Jovan Grahovac & Amiya Chakravarty, 2001. "Sharing and Lateral Transshipment of Inventory in a Supply Chain with Expensive Low-Demand Items," Management Science, INFORMS, vol. 47(4), pages 579-594, April.
    4. Prak, Derk & Teunter, Rudolf & Babai, M. Z. & Syntetos, A. A. & Boylan, D, 2018. "Forecasting and Inventory Control with Compound Poisson Demand Using Periodic Demand Data," Research Report 2018010, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    5. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2019. "Solution procedures for lost sales base-stock inventory systems with compound Poisson demand," International Journal of Production Economics, Elsevier, vol. 209(C), pages 172-182.
    6. 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.
    7. Kathryn E. Caggiano & John A. Muckstadt & James A. Rappold, 2006. "Integrated Real-Time Capacity and Inventory Allocation for Reparable Service Parts in a Two-Echelon Supply System," Manufacturing & Service Operations Management, INFORMS, vol. 8(3), pages 292-319, August.
    8. Porras, Eric & Dekker, Rommert, 2008. "An inventory control system for spare parts at a refinery: An empirical comparison of different re-order point methods," European Journal of Operational Research, Elsevier, vol. 184(1), pages 101-132, January.
    9. Sang-Hyun Kim & Morris A. Cohen & Serguei Netessine, 2007. "Performance Contracting in After-Sales Service Supply Chains," Management Science, INFORMS, vol. 53(12), pages 1843-1858, December.
    10. Ulrich W. Thonemann & Alex O. Brown & Warren H. Hausman, 2002. "Easy Quantification of Improved Spare Parts Inventory Policies," Management Science, INFORMS, vol. 48(9), pages 1213-1225, September.
    11. Saldanha, John P., 2022. "Estimating the reorder point for a fill-rate target under a continuous review policy in the presence of non-standard lead-time demand distributions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    12. 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.
    13. Ki Ling Cheung, 1996. "On the (S‐1, S) inventory model under compound poisson demands and i.i.d. unit resupply times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(4), pages 563-572, June.
    14. Lengu, D. & Syntetos, A.A. & Babai, M.Z., 2014. "Spare parts management: Linking distributional assumptions to demand classification," European Journal of Operational Research, Elsevier, vol. 235(3), pages 624-635.
    15. Karsten, Frank & Basten, Rob J.I., 2014. "Pooling of spare parts between multiple users: How to share the benefits?," European Journal of Operational Research, Elsevier, vol. 233(1), pages 94-104.
    16. Diks, E. B. & de Kok, A. G. & Lagodimos, A. G., 1996. "Multi-echelon systems: A service measure perspective," European Journal of Operational Research, Elsevier, vol. 95(2), pages 241-263, December.
    17. Silver, Edward A. & Bischak, Diane P., 2011. "The exact fill rate in a periodic review base stock system under normally distributed demand," Omega, Elsevier, vol. 39(3), pages 346-349, June.
    18. 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.
    19. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    20. Lejeune, Miguel A., 2013. "Probabilistic modeling of multiperiod service levels," European Journal of Operational Research, Elsevier, vol. 230(2), pages 299-312.

    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:218:y:2012:i:2:p:442-447. 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.