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Queuing-Inventory Models with MAP Demands and Random Replenishment Opportunities

Author

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  • Srinivas R. Chakravarthy

    (Departments of Industrial and Manufacturing Engineering & Mathematics, Kettering University, Flint, MI 48504, USA)

  • B. Madhu Rao

    (Department of Business Systems and Analytics, School of Business Administration, Stetson University, Deland, FL 32723, USA)

Abstract

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.

Suggested Citation

  • Srinivas R. Chakravarthy & B. Madhu Rao, 2021. "Queuing-Inventory Models with MAP Demands and Random Replenishment Opportunities," Mathematics, MDPI, vol. 9(10), pages 1-26, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1092-:d:553248
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    References listed on IDEAS

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    1. Arnoud den Boer & Ohad Perry & Bert Zwart, 2018. "Dynamic pricing policies for an inventory model with random windows of opportunities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 660-675, December.
    2. Mahdi Tajbakhsh, M. & Lee, Chi-Guhn & Zolfaghari, Saeed, 2011. "An inventory model with random discount offerings," Omega, Elsevier, vol. 39(6), pages 710-718, December.
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    7. Kamran Moinzadeh, 1997. "Replenishment and Stocking Policies for Inventory Systems with Random Deal Offerings," Management Science, INFORMS, vol. 43(3), pages 334-342, March.
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    Cited by:

    1. Agassi Melikov & Ramil Mirzayev & Janos Sztrik, 2023. "Double-Sources Queuing-Inventory Systems with Finite Waiting Room and Destructible Stocks," Mathematics, MDPI, vol. 11(1), pages 1-16, January.

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