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Disasters in a Markovian inventory system for perishable items

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  01 July 2016

David Perry  and
Wolfgang Stadje
David Perry*
Affiliation:
University of Haifa
Wolfgang Stadje*
Affiliation:
Universität Osnabrück
*
∗ Postal address: Department of Statistics, University of Haifa, 31905 Haifa, Israel.
∗∗ Postal address: Universität Osnabrück, Fachbereich Mathematik/Informatik, 496069 Osnabrück, Germany. Email address: [email protected]
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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.

Keywords

inventory systemperishable itemsvirtual death processstationary distributioncost functionalsreflected Brownian motion

MSC classification

Primary: 90B05: Inventory, storage, reservoirs
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 1 , March 2001 , pp. 61 - 75
Copyright
Copyright © Applied Probability Trust 2001 

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