Perishable inventories with random input: a unifying survey with extensions

Onno Boxma, David Perry, Wolfgang Stadje

Research output: Contribution to journalArticlepeer-review


This paper is devoted to the theory of perishable inventory systems. In such systems items arrive and stay ‘on the shelf’ until they are either taken by a demand or become outdated. Our aim is to survey, extend and enrich the probabilistic analysis of a large class of such systems. A unifying principle is to consider the so-called virtual outdating process V , where V(t) is the time that would pass from t until the next outdating if no new demands arrived after t. The steady-state density of V is determined for a wide range of perishable inventory systems. Key performance measures like the rate of outdatings, the rate of unsatisfied demands and the distribution of the number of items on the shelf are subsequently expressed in that density. Some of the main ingredients of our analysis are level crossing theory and the observation that the V process can be interpreted as the workload process of a specific single server queueing system.

Original languageEnglish
JournalAnnals of Operations Research
Issue number1
StateAccepted/In press - 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).


  • Busy period
  • Laplace Transform
  • Level crossings methodology
  • Perishable inventories
  • Satisfied demand conservation law
  • Steady state analysis

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research


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