Stationary analysis of an (R, Q) inventory model with normal and emergency orders

Onno Boxma; David Perry; Wolfgang Stadje

doi:10.1017/jpr.2022.43

Stationary analysis of an (R, Q) inventory model with normal and emergency orders

Onno Boxma, David Perry, Wolfgang Stadje

Research output: Contribution to journal › Article › peer-review

Abstract

We consider an (R, Q) inventory model with two types of orders, normal orders and emergency orders, which are issued at different inventory levels. These orders are delivered after exponentially distributed lead times. In between deliveries, the inventory level decreases in a state-dependent way, according to a release rate function. This function represents the fluid demand rate; it could be controlled by a system manager via price adaptations. We determine the mean number of downcrossings of any level x in one regenerative cycle, and use it to obtain the steady-state density f (x) of the inventory level. We also derive the rates of occurrence of normal deliveries and of emergency deliveries, and the steady-state probability of having zero inventory.

Original language	English
Pages (from-to)	106-126
Number of pages	21
Journal	Journal of Applied Probability
Volume	60
Issue number	1
DOIs	https://doi.org/10.1017/jpr.2022.43
State	Published - 4 Mar 2023
Externally published	Yes

Bibliographical note

Funding Information:
The research of Onno Boxma is partly funded by the NWO Gravitation Programme NETWORKS (grant 024.002.003). The research of David Perry was partly funded by ISF (Israel Science Foundation), grant 3274/19.

Publisher Copyright:
© The Author(s) 2022.

Keywords

(R, Q) inventory
level crossings
steady-state analysis
stochastic lead time

ASJC Scopus subject areas

Statistics and Probability
Mathematics (all)
Statistics, Probability and Uncertainty

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10.1017/jpr.2022.43

Cite this

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Stationary analysis of an (R, Q) inventory model with normal and emergency orders

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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