Ergodicity of age-dependent inventory control systems. (September 2016)

• Record Type: Journal Article
• Authors: Olsson, Fredrik; Turova, Tatyana S.
• Is Part Of: Journal of applied probability. Volume 53:Number 3(2016)
• Page Start: 688
• Page End: 699
• Publication Date: 2016-09
• Subjects: Inventory, -- base-stock policy, -- ergodicity, -- doubly stochastic Poisson process; Primary 60K10, -- Secondary 60K25, -- 90B05; 519.2
• DOI: 10.1017/jpr.2016.34
• Languages: English
• ISSNs: 0021-9002

Abstract

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.