Continuous review inventory models for perishable items ordered in batches

Opher Baron, Oded Berman, David Perry

Research output: Contribution to journalReview articlepeer-review


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.

Original languageEnglish
Pages (from-to)217-247
Number of pages31
JournalMathematical Methods of Operations Research
Issue number2
StatePublished - Oct 2010


  • Continuous review
  • Fluid approximation
  • Inventory system
  • Kella-Whitt martingale
  • Perishable items
  • Stochastic (s, S)

ASJC Scopus subject areas

  • Software
  • General Mathematics
  • Management Science and Operations Research


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