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

Onno Boxma, David Perry, Wolfgang Stadje

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)106-126
Number of pages21
JournalJournal of Applied Probability
Issue number1
StatePublished - 4 Mar 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© The Author(s) 2022.


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

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Stationary analysis of an (R, Q) inventory model with normal and emergency orders'. Together they form a unique fingerprint.

Cite this