Ergodicity of age-dependent inventory control systems

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Ergodicity of age-dependent inventory control systems. / Olsson, Fredrik; Turova, Tatyana S.

In: Journal of Applied Probability, Vol. 53, No. 3, 01.09.2016, p. 688-699.

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TY - JOUR

T1 - Ergodicity of age-dependent inventory control systems

AU - Olsson, Fredrik

AU - Turova, Tatyana S.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.

AB - 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.

KW - Base-stock policy

KW - Doubly stochastic Poisson process

KW - Ergodicity

KW - Inventory

U2 - 10.1017/jpr.2016.34

DO - 10.1017/jpr.2016.34

M3 - Article

VL - 53

SP - 688

EP - 699

JO - Journal of Applied Probability

T2 - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 1475-6072

IS - 3

ER -