Disasters in a Markovian inventory system for perishable items

Autor(en): Perry, D
Stadje, W 
Stichwörter: cost functionals; DEMAND; inventory system; Mathematics; MODELS; perishable items; RANDOM LIFETIMES; reflected Brownian motion; stationary distribution; Statistics & Probability; STOCHASTIC CLEARING SYSTEMS; virtual death process
Erscheinungsdatum: 2001
Herausgeber: APPLIED PROBABILITY TRUST
Journal: ADVANCES IN APPLIED PROBABILITY
Volumen: 33
Ausgabe: 1
Startseite: 61
Seitenende: 75
Zusammenfassung: 
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.
ISSN: 00018678
DOI: 10.1017/S0001867800010636

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