A Markov-Modulated (s, S) Inventory System with Repeated Calls and Blocked Demands
Probability
2023-07-18 v2
Abstract
In this article, we consider a continuous review (s, S) inventory system with failures of demand fulfillment (service) modeled as a Markov-modulated retrial queueing system. The inventory system features a single product that experiences Markovian inter-demand and service intervals with random service interruptions and instantaneous replenishments. A recently developed criterion for the ergodicity of a class of discrete-time level-dependent-quasi-birth-and-death (LDQBD) processes with convergent transition matrix rows is applied to the jump chain of the process in order to elicit a closed-form traffic-intensity formula. An analytic solution for the steady-state average minimum cost is provided.
Keywords
Cite
@article{arxiv.2109.12463,
title = {A Markov-Modulated (s, S) Inventory System with Repeated Calls and Blocked Demands},
author = {James Cordeiro and Ying-Ju Chen and Andres Larrain-Hubach and Mark Abramson},
journal= {arXiv preprint arXiv:2109.12463},
year = {2023}
}
Comments
33 pages, 1 figure