## Abstract

We study a Markovian model for a perishable inventory system with random input and an external source of obsolescence: at Poisson random times the whole current content of the system is spoilt and must be scrapped. The system can be described by its virtual death time process. We derive its stationary distribution in closed form and find an explicit formula for the Laplace transform of the cycle length, defined as the time between two consecutive item arrivals in an empty system. The results are used to compute several cost functionals. We also derive these functionals under the corresponding heavy traffic approximation, which is modeled using a Brownian motion in [0, 1] reflected at 0 and 1 and restarted at 1 at the Poisson disaster times.

Original language | English |
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Pages (from-to) | 61-75 |

Number of pages | 15 |

Journal | Advances in Applied Probability |

Volume | 33 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2001 |

## Keywords

- Cost functionals
- Inventory system
- Perishable items
- Reflected Brownian motion
- Stationary distribution
- Virtual death process

## ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics