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On two-echelon inventory systems with Poisson demand and lost sales

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  • Alvarez, Elisa
  • van der Heijden, Matthieu

Abstract

We consider a two-echelon, continuous review inventory system under Poisson demand and a one-for-one replenishment policy. Demand is lost if no items are available at the local warehouse, the central depot, or in the pipeline in between. We give a simple, fast and accurate approach to approximate the service levels in this system. In contrast to other methods, we do not need an iterative analysis scheme. Our method works very well for a broad set of cases, with deviations to simulation below 0.1% on average and below 0.36% for 95% of all test instances.

Suggested Citation

  • Alvarez, Elisa & van der Heijden, Matthieu, 2014. "On two-echelon inventory systems with Poisson demand and lost sales," European Journal of Operational Research, Elsevier, vol. 235(1), pages 334-338.
    • Handle: RePEc:eee:ejores:v:235:y:2014:i:1:p:334-338
    DOI: 10.1016/j.ejor.2013.12.031
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    References listed on IDEAS

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    1. Stephen C. Graves, 1985. "A Multi-Echelon Inventory Model for a Repairable Item with One-for-One Replenishment," Management Science, INFORMS, vol. 31(10), pages 1247-1256, October.
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    5. 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.
    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. Andersson, Jonas & Melchiors, Philip, 2001. "A two-echelon inventory model with lost sales," International Journal of Production Economics, Elsevier, vol. 69(3), pages 307-315, February.
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    Cited by:

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    2. 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.
    3. Yongquan, Sun & Xi, Chen & He, Ren & Yingchao, Jin & Quanwu, Liu, 2016. "Ordering decision-making methods on spare parts for a new aircraft fleet based on a two-sample prediction," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 40-50.
    4. van den Berg, D. & van der Heijden, M.C. & Schuur, P.C., 2016. "Allocating service parts in two-echelon networks at a utility company," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 58-67.
    5. Johansson, Lina & Olsson, Fredrik, 2018. "Age-based inventory control in a multi-echelon system with emergency replenishments," European Journal of Operational Research, Elsevier, vol. 265(3), pages 951-961.

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