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QMCD approach for perishability models: The (S, s) control policy with lead time

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  • Yonit Barron
  • Opher Baron

Abstract

We consider cost minimization for an (S, s) continuous-review perishable inventory system with random lead times and times to perishability, and a state-dependent Poisson demand. We derive the stationary distributions for the inventory level using the Queueing and Markov Chain Decomposition (QMCD) methodology. Applying QMCD, we develop an intuitive approach to characterizing the distribution of the residual time for the next event in different states of the system. We provide comprehensive analysis of two main models. The first model assumes a general random lifetime and an exponential distributed lead time. The second model assumes an exponential distributed lifetime and a general lead time. Each model is analyzed under both backordering and lost sales assumptions. We consider a fixed cost for each order, a purchase cost, a holding cost, a cost for perished items, and a penalty cost in the case of shortage. Numerical examples are provided and show that variability of lead time is more costly than that of perishability time. Therefore, after reducing lead time and increasing perishability time, managers should focus on reducing variability of lead time.

Suggested Citation

  • Yonit Barron & Opher Baron, 2020. "QMCD approach for perishability models: The (S, s) control policy with lead time," IISE Transactions, Taylor & Francis Journals, vol. 52(2), pages 133-150, February.
    • Handle: RePEc:taf:uiiexx:v:52:y:2020:i:2:p:133-150
    DOI: 10.1080/24725854.2019.1614697
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    Cited by:

    1. 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).
    2. Angelos Kourepis & Alexandros Diamantidis & Stylianos Koukoumialos, 2022. "Exact analysis of a push–pull system with multiple non identical retailers, a distribution center and multiple non identical unreliable suppliers with supply disruptions," Operational Research, Springer, vol. 22(5), pages 4801-4827, November.
    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. M. A. Hoque, 2021. "An optimal solution policy to an integrated manufacturer-retailers problem with normal distribution of lead times of delivering equal and unequal-sized batches," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 483-512, June.

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