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A state-dependent perishability (s, S) inventory model with random batch demands

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  • Y. Barron

    (Ariel University)

Abstract

We consider continuous-review perishable inventory models with random lead times and state-dependent Poisson demand. The paper revises an earlier work of Barron and Baron (IISE Trans 1–52, 2019). While the former studies unit Poisson demands, this paper deals with demand uncertainty and allows for random batch demands. We conduct a comprehensive analysis of two main models that have different lead times and perish times under backorders or lost sales. Thus, our models can be applied to many industries, in situations where the system is subject to random perishability, random lead time, and demand uncertainty. With a probabilistic approach, we derive a long-run average cost function under the (S, s) replenishment policy. Numerical examples are used to demonstrate the impact of changing batch size and other system parameters on the optimal policy. Our numerical study indicates that, although the Markovian policy can be used as a good approximation of the average total cost, it performs better for a general perish time. We further show that the optimal cost may differ for a different average batch size, while the batch variability seems to provide some robustness.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:280:y:2019:i:1:d:10.1007_s10479-019-03302-2
    DOI: 10.1007/s10479-019-03302-2
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    References listed on IDEAS

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    Cited by:

    1. Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.
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    3. Yonit Barron & Opher Baron, 2020. "The residual time approach for (Q, r) model under perishability, general lead times, and lost sales," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 601-648, December.
    4. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    5. Gong, Min & Lian, Zhaotong & Xiao, Hua, 2022. "Inventory control policy for perishable products under a buyback contract and Brownian demands," International Journal of Production Economics, Elsevier, vol. 251(C).
    6. Qingzhe Xu & Jianjun Li & Liwei Liu & Lixue Guo, 2024. "A Queueing-Inventory System with Modified Delayed Vacation under Bernoulli Schedule," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-22, December.
    7. Walid W. Nasr, 2022. "Inventory systems with stochastic and batch demand: computational approaches," Annals of Operations Research, Springer, vol. 309(1), pages 163-187, February.
    8. Gharbi, Ali & Kenné, Jean-Pierre & Kaddachi, Rawia, 2022. "Dynamic optimal control and simulation for unreliable manufacturing systems under perishable product and shelf life variability," International Journal of Production Economics, Elsevier, vol. 247(C).

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