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arXiv · 2109.12463

A Markov-Modulated (s, S) Inventory System with Repeated Calls and Blocked Demands

James Cordeiro·Ying-Ju Chen·Andres Larrain-Hubach·Mark Abramson
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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.

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James Cordeiro, Ying-Ju Chen, Andres Larrain-Hubach, Mark Abramson. 2021-09-26. A Markov-Modulated (s, S) Inventory System with Repeated Calls and Blocked Demands. https://arxiv.org/abs/2109.12463

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