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Continuous review inventory models for perishable items ordered in batches

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  • Opher Baron
  • Oded Berman
  • David Perry

Abstract

This paper is an in-depth treatment of an inventory control problem with perishable items. We focus on two prototypes of perishability for items that have a common shelflife and that arrive in batches with zero lead time: (i) sudden deaths due to disasters (e.g., spoilage because of extreme weather conditions or a malfunction of the storage place) and (ii) outdating due to expirations (e.g., medicine or food items that have an expiry date). By using known mathematical tools we generalize the stochastic analysis of continuous review (s, S) policies to our problems. This is achieved by integrating with each inventory cycle stopping times that are independent of the inventory level. We introduce special cases of compound Poisson demand processes with negative jumps and consider demands (jumps) that are exponentially distributed or of a unit (i.e., Poisson) demand. For these special cases we derive a closed form expression of the total cost, including that of perishable items, given any order up to level. Since the stochastic analysis leads to tractable expressions only under specific assumptions, as an added benefit we use a fluid approximation of the inventory level to develop efficient heuristics that can be used in general settings. Numerical results comparing the solution of the heuristics with exact or simulated optimal solutions show that the approximation is accurate. Copyright Springer-Verlag 2010

Suggested Citation

  • Opher Baron & Oded Berman & David Perry, 2010. "Continuous review inventory models for perishable items ordered in batches," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 217-247, October.
    • Handle: RePEc:spr:mathme:v:72:y:2010:i:2:p:217-247
    DOI: 10.1007/s00186-010-0318-1
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    References listed on IDEAS

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    5. 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.
    6. Onno Boxma & David Perry & Wolfgang Stadje & Shelley Zacks, 2022. "A compound Poisson EOQ model for perishable items with intermittent high and low demand periods," Annals of Operations Research, Springer, vol. 317(2), pages 439-459, October.
    7. S. R. Chakravarthy & Arunava Maity & U. C. Gupta, 2017. "An ‘(s, S)’ inventory in a queueing system with batch service facility," Annals of Operations Research, Springer, vol. 258(2), pages 263-283, November.
    8. Onno Boxma & David Perry & Shelley Zacks, 2015. "A Fluid EOQ Model of Perishable Items with Intermittent High and Low Demand Rates," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 390-402, February.
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