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

  • S.I. : QueueStochMod2019
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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.

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China (No. 71971189), and the Key Research Project of Science and Technology, University of Hebei Province, China (No. ZD2018042), and is supported in part by MEXT, Japan.

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Authors and Affiliations

  1. School of Economics and Management, Yanshan University, Qinhuangdao, 066004, China

    Yuying Zhang

  2. School of Science, Yanshan University, Qinhuangdao, 066004, China

    Dequan Yue

  3. Faculty of Intelligence and Informatics, Konan University, Kobe, 658-8501, Japan

    Wuyi Yue

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  1. Yuying Zhang
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  2. Dequan Yue
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Correspondence to Dequan Yue.

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Zhang, Y., Yue, D. & Yue, W. A queueing-inventory system with random order size policy and server vacations. Ann Oper Res 310, 595–620 (2022). https://doi.org/10.1007/s10479-020-03859-3

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