Markov Models of Inventory Management Systems with a Positive Service Time

Melikov, Agassi; Shahmaliyev, Mammad

doi:10.1134/s106423071805009x

Cited by 6 publications

(1 citation statement)

References 24 publications

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“…Research in queuing-inventory systems may be classified based on features such as the nature of customer arrival process, service time distribution, server vacation, service discipline, customer behavior, inventory review policy, replenishment policy, stock-out assumptions, perishability of units, lead time for replenishment, among others. We refer the readers to Krishnamurthy, Shajin, and Narayanan [12] for a general review of queuing-inventory models, to Choi et al [13] for a survey of QI models with phase-type service times, and to Melikova and Shahmaliyeva [14] for a discussion of QI models for perishable items. Recent generalizations of QI models are due to Chakravarthy, Maity and Gupta [15], who studied a QI model in which the service is carried out in batches, Chakravathy [16], who studied a QI model in which the demand occurs in batches, and Chakravarthy and Rumyantsev [17], who study a QI system with batch demand, Markovian Arrival Process (MAP), and phase-type service time and exponential replenishment lead times.…”

Section: Introductionmentioning

confidence: 99%

Queuing-Inventory Models with MAP Demands and Random Replenishment Opportunities

Chakravarthy

Rao

2021

Mathematics

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Combining the study of queuing with inventory is very common and such systems are referred to as queuing-inventory systems in the literature. These systems occur naturally in practice and have been studied extensively in the literature. The inventory systems considered in the literature generally include (s,S)-type. However, in this paper we look at opportunistic-type inventory replenishment in which there is an independent point process that is used to model events that are called opportunistic for replenishing inventory. When an opportunity (to replenish) occurs, a probabilistic rule that depends on the inventory level is used to determine whether to avail it or not. Assuming that the customers arrive according to a Markovian arrival process, the demands for inventory occur in batches of varying size, the demands require random service times that are modeled using a continuous-time phase-type distribution, and the point process for the opportunistic replenishment is a Poisson process, we apply matrix-analytic methods to study two of such models. In one of the models, the customers are lost when at arrivals there is no inventory and in the other model, the customers can enter into the system even if the inventory is zero but the server has to be busy at that moment. However, the customers are lost at arrivals when the server is idle with zero inventory or at service completion epochs that leave the inventory to be zero. Illustrative numerical examples are presented, and some possible future work is highlighted.

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