Queuing-Inventory Models with MAP Demands and Random Replenishment Opportunities

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 in...

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Bibliographic Details
Published in:Mathematics (Basel) 2021-05, Vol.9 (10), p.1092
Main Authors: Chakravarthy, Srinivas R., Rao, B. Madhu
Format: Article
Language:English
Subjects:
algorithmic probability
Arrivals
batch demands
Customer services
Customers
Inventory
Inventory management
lead times
Mathematical models
Mathematics
matrix-analytic methods
Order quantity
Probability
Queuing
queuing-inventory systems
random opportunities
Random variables
Replenishment
Statistical analysis
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9101092