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A lost sales inventory model with a compound poisson demand pattern

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  • SPRINGAEL, Johan
  • VAN NIEUWENHUYSE, Inneke

Abstract

In this paper, we study the decision problem of a retailer, who wants to optimize the amount of shelf inventory of a particular product, given that the demand for the product is stochastic and replenishment lead times (from the store’s stockroom to the shelf) are negligible. The shelf inventory is managed according to a (0,B*)-inventory policy: when the shelf inventory is sold out, the retailer gets a fixed amount of B* units from the central stockroom to replenish the shelf inventory. To adequately reflect the shopping behavior of retail customers, the demand process is modeled as a compound Poisson process, with Poisson distributed purchase quantities. When the purchase quantity of a customer exceeds the amount of shelf inventory still available, the unsatisfied demand is considered to be lost sales. As the demand process is stochastic, the runout time of the shelf in-ventory will be stochastic too. The costs per cycle related to keeping inventory on the shelf can be split up into three components: average holding costs (which may be related to the scarcity of shelf space), a fixed handling cost (per replenishment trip), and an average lost sales cost. The purpose of the model is to determine the value of B* that minimizes the average total cost per time unit.

Suggested Citation

  • SPRINGAEL, Johan & VAN NIEUWENHUYSE, Inneke, 2005. "A lost sales inventory model with a compound poisson demand pattern," Working Papers 2005017, University of Antwerp, Faculty of Business and Economics.
    • Handle: RePEc:ant:wpaper:2005017
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    File URL: https://repository.uantwerpen.be/docman/irua/75927c/b27320dd.pdf
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    Citations

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    Cited by:

    1. Y. Barron, 2019. "A state-dependent perishability (s, S) inventory model with random batch demands," Annals of Operations Research, Springer, vol. 280(1), pages 65-98, September.
    2. Sachs, Anna-Lena & Minner, Stefan, 2014. "The data-driven newsvendor with censored demand observations," International Journal of Production Economics, Elsevier, vol. 149(C), pages 28-36.
    3. Michael N. Katehakis & Benjamin Melamed & Jim Junmin Shi, 2022. "Optimal replenishment rate for inventory systems with compound Poisson demands and lost sales: a direct treatment of time-average cost," Annals of Operations Research, Springer, vol. 317(2), pages 665-691, October.
    4. Kouki, Chaaben & Jouini, Oualid, 2015. "On the effect of lifetime variability on the performance of inventory systems," International Journal of Production Economics, Elsevier, vol. 167(C), pages 23-34.
    5. Jim Shi, 2022. "Optimal continuous production-inventory systems subject to stockout risk," Annals of Operations Research, Springer, vol. 317(2), pages 777-804, October.

    More about this item

    Keywords

    Discrete inventory models; Compound Poisson process; Lost sales; Jonquière’s function;
    All these keywords.

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