A fluid EOQ model of perishable items with intermittent high and low demand rates

Onno Boxma, David Perry, Shelley Zacks

Research output: Contribution to journalArticlepeer-review


We consider a stochastic fluid EOQ-type model with demand rates operating in a two-state random environment. This environment alternates between exponentially distributed periods of high demand and generally distributed periods of low demand. The inventory level starts at some level q, and decreases linearly at rate βH during the periods of high demand, and at rate βL < βH at periods of low demand. Refilling of the inventory level to level q is required when the first of two events takes place: Either the buffer level reaches zero, or the buffer content becomes outdated. If such an event occurs during a high demand period, an order is instantaneously placed; otherwise, ordering is postponed until the beginning of the next high demand period. We determine the steady-state distribution of the inventory level, as well as other quantities of interest such as the distribution of the time until a refill is required. Finally, for a given cost/revenue structure, we determine the long-run average profit, and we consider the problem of choosing q such that the profit is optimized.

Original languageEnglish
Pages (from-to)390-402
Number of pages13
JournalMathematics of Operations Research
Issue number2
StatePublished - 1 May 2015

Bibliographical note

Publisher Copyright:
© 2015 INFORMS.


  • Compound Poisson process
  • EOQ model
  • Laplace transform
  • Outdatings
  • Perishable inventories
  • Regenerative process
  • Unsatisfied demands

ASJC Scopus subject areas

  • General Mathematics
  • Computer Science Applications
  • Management Science and Operations Research


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