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A queueing-inventory system with random order size policy and server vacations

Author

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  • Yuying Zhang

    (Yanshan University)

  • Dequan Yue

    (Yanshan University)

  • Wuyi Yue

    (Konan University)

Abstract

In this paper, we consider a queueing-inventory system under continuous review with a random order size policy and lost sales. If the inventory is depleted after the service of a customer, a replenishment order is instantaneously triggered. The replenishment order size may be randomized according to a discrete probability distribution. Customers arrive in the system according to a Poisson process and require service from a server. The server takes multiple vacations once the inventory is depleted. The service time, the lead time, and the vacation time are all assumed to be distributed exponentially. We derive the stationary joint distribution of the queue length, the on-hand inventory level, and the status of the server in explicit product form. Furthermore, the conditional distributions of the on-hand inventory level when the server is off due to a vacation or depleted inventory, and when the server is on and working, are derived. Then, we calculate some of the system performance measures. The effect of the server’s vacation on the performance measures is investigated analytically. Finally, some numerical results are presented. The simulation study of the model in the context of more general arrival processes and service time distributions is presented.

Suggested Citation

  • Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    • Handle: RePEc:spr:annopr:v:310:y:2022:i:2:d:10.1007_s10479-020-03859-3
    DOI: 10.1007/s10479-020-03859-3
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    References listed on IDEAS

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    1. Y. Barron, 2019. "A state-dependent perishability (s, S) inventory model with random batch demands," Annals of Operations Research, Springer, vol. 280(1), pages 65-98, September.
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    3. Krishnamoorthy, A. & Viswanath, Narayanan C., 2013. "Stochastic decomposition in production inventory with service time," European Journal of Operational Research, Elsevier, vol. 228(2), pages 358-366.
    4. I. Padmavathi & A. Shophia Lawrence & B. Sivakumar, 2016. "A finite-source inventory system with postponed demands and modified M vacation policy," OPSEARCH, Springer;Operational Research Society of India, vol. 53(1), pages 41-62, March.
    5. Jeganathan, K. & Abdul Reiyas, M., 2020. "Two parallel heterogeneous servers Markovian inventory system with modified and delayed working vacations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 273-304.
    6. A. Krishnamoorthy & R. Manikandan & B. Lakshmy, 2015. "A revisit to queueing-inventory system with positive service time," Annals of Operations Research, Springer, vol. 233(1), pages 221-236, October.
    7. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
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    Cited by:

    1. Agassi Melikov & Laman Poladova & Sandhya Edayapurath & Janos Sztrik, 2023. "Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
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    3. N. Nithya & N. Anbazhagan & S. Amutha & K. Jeganathan & Gi-Cheon Park & Gyanendra Prasad Joshi & Woong Cho, 2023. "Controlled Arrivals on the Retrial Queueing–Inventory System with an Essential Interruption and Emergency Vacationing Server," Mathematics, MDPI, vol. 11(16), pages 1-24, August.
    4. Subramanian Selvakumar & Kathirvel Jeganathan & Krishnasamy Srinivasan & Neelamegam Anbazhagan & Soojeong Lee & Gyanendra Prasad Joshi & Ill Chul Doo, 2023. "An Optimization of Home Delivery Services in a Stochastic Modeling with Self and Compulsory Vacation Interruption," Mathematics, MDPI, vol. 11(9), pages 1-34, April.

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