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

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  • 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.

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    5. Tamer Boyaci & Guillermo Gallego, 2001. "Serial Production/Distribution Systems Under Service Constraints," Manufacturing & Service Operations Management, INFORMS, vol. 3(1), pages 43-50, June.
    6. 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.
    7. 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.
    8. 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.
    9. de Kok, A. G., 1990. "Hierarchical production planning for consumer goods," European Journal of Operational Research, Elsevier, vol. 45(1), pages 55-69, March.
    10. 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.
    11. 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.
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    Cited by:

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    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

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