Control policies for inventory systems with perishable items: Outsourcing and urgency classes

Shaul K. Bar-Lev, David Perry, Wolfgang Stadje

Research output: Contribution to journalArticlepeer-review


We consider control policies for perishable inventory systems with random input whose purpose is to mitigate the effects of unavailability. In the basic uncontrolled system, the arrival times of the items to be stored and the ones of the demands for those items form independent Poisson processes. The shelf lifetime of every item is finite and deterministic. Every demand is for a single item and is satisfied by the oldest item on the shelf, if available. The first controlled model excludes the possibility of unsatisfied demands by introducing a second source of fresh items that is completely reliable and delivers without delay whenever the system becomes empty. In the second model, there is no additional ordering option by outsourcing. However, to avoid the most adverse effects of unavailability, the demands are classified into different categories of urgency. An incoming demand is satisfied or not according to its category and the current state of the system. For both models, we determine the steady-state distribution of the virtual outdating process, which is then used to derive the relevant cost functionals: the steady-state distribution and expected value of the number of items in the system, the rate of outdatings, as well as, for model 1, the rate of special orders from the external source and, for model 2, the rate of unsatisfied demands.

Original languageEnglish
Pages (from-to)309-326
Number of pages18
JournalProbability in the Engineering and Informational Sciences
Issue number3
StatePublished - 2005

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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