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Ergodicity of age-dependent inventory control systems

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  24 October 2016

Fredrik Olsson  and
Tatyana S. Turova
Fredrik Olsson*
Affiliation:
Lund University
Tatyana S. Turova*
Affiliation:
Lund University
*
*Postal address: Department of Industrial Management and Logistics,Lund University, Box 118, SE-221 00 Lund, Sweden. Email address: fredrik.olsson@iml.lth.se
**Postal address: Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden. Email address: tatyana@maths.lth.se
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Abstract

We consider continuous review inventory systems with general doubly stochastic Poisson demand. In this specific case the demand rate, experienced by the system, varies as a function of the age of the oldest unit in the system. It is known that the stationary distributions of the ages in such models often have a strikingly simple form. In particular, they exhibit a typical feature of a Poisson process: given the age of the oldest unit the remaining ages are uniform. The model we treat here generalizes some known inventory models dealing with partial backorders, perishable items, and emergency replenishment. We derive the limiting joint density of the ages of the units in the system by solving partial differential equations. We also answer the question of the uniqueness of the stationary distributions which was not addressed in the related literature.

Keywords

Inventorybase-stock policyergodicitydoubly stochastic Poisson process

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60K25: Queueing theory 90B05: Inventory, storage, reservoirs
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 688 - 699
Copyright
Copyright © Applied Probability Trust 2016 

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