September 2016 Ergodicity of age-dependent inventory control systems
Fredrik Olsson, Tatyana S. Turova
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J. Appl. Probab. 53(3): 688-699 (September 2016).

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.

Citation

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Fredrik Olsson. Tatyana S. Turova. "Ergodicity of age-dependent inventory control systems." J. Appl. Probab. 53 (3) 688 - 699, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.60115
MathSciNet: MR3570088

Subjects:
Primary: 60K10
Secondary: 60K25 , 90B05

Keywords: base-stock policy , doubly stochastic Poisson process , ergodicity , inventory

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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