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A production queueing-inventory system with two-customer and a server subject to breakdown

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  • Umay Uzunoglu Kocer

    (Dokuz Eylul University)

  • Serife Ozkar

    (Balikesir University)

Abstract

A queueing-inventory system where the server is subject to breakdown is examined. The products in inventory are provided by production. Two different types of customers are considered. Each customer type arrives in the system according to a Poisson process with different parameters. There is only one server and the service time follows an exponential distribution. Service may be interrupted randomly due to breakdowns. There may be minor or major breakdowns and after the recovery process, the priority customer class gets service first. The described system is formulated as a level-dependent quasi-birth-death process (LDQBD). The stationarity condition is provided and the steady-state probabilities are calculated. A comprehensive numerical study is presented that examines the sensitivity of the performance measures to the change of system parameters and also investigates the optimal inventory policy according to the considered cost function.

Suggested Citation

  • Umay Uzunoglu Kocer & Serife Ozkar, 2023. "A production queueing-inventory system with two-customer and a server subject to breakdown," Annals of Operations Research, Springer, vol. 331(2), pages 1089-1117, December.
    • Handle: RePEc:spr:annopr:v:331:y:2023:i:2:d:10.1007_s10479-023-05275-9
    DOI: 10.1007/s10479-023-05275-9
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    References listed on IDEAS

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    1. Zhao, Ning & Lian, Zhaotong, 2011. "A queueing-inventory system with two classes of customers," International Journal of Production Economics, Elsevier, vol. 129(1), pages 225-231, January.
    2. Oded Berman & Eungab Kim, 2004. "Dynamic inventory strategies for profit maximization in a service facility with stochastic service, demand and lead time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 497-521, December.
    3. Jeganathan, K. & Abdul Reiyas, M. & Prasanna Lakshmi, K. & Saravanan, S., 2019. "Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 177-200.
    4. Maike Schwarz & Hans Daduna, 2006. "Queueing systems with inventory management with random lead times and with backordering," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 383-414, December.
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    6. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2020. "A service system with perishable products where customers are either fastidious or strategic," International Journal of Production Economics, Elsevier, vol. 228(C).
    7. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2019. "Performance improvement of a service system via stocking perishable preliminary services," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1000-1011.
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    9. A. Krishnamoorthy & Sajeev S. Nair & Viswanath C. Narayanan, 2015. "Production inventory with service time and interruptions," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(10), pages 1800-1816, July.
    10. Liu, Mingwu & Feng, Mengying & Wong, Chee Yew, 2014. "Flexible service policies for a Markov inventory system with two demand classes," International Journal of Production Economics, Elsevier, vol. 151(C), pages 180-185.
    11. Oded Berman & Eungab Kim, 2001. "Dynamic order replenishment policy in internet-based supply chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(3), pages 371-390, July.
    12. Serife Ozkar & Umay Uzunoglu Kocer, 2021. "Two-commodity queueing-inventory system with two classes of customers," OPSEARCH, Springer;Operational Research Society of India, vol. 58(1), pages 234-256, March.
    13. 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.
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    Cited by:

    1. Nisha Mathew & V. C. Joshua & A. Krishnamoorthy & A. Melikov & Ambily P. Mathew, 2023. "A production inventory model with server breakdown and customer impatience," Annals of Operations Research, Springer, vol. 331(2), pages 1269-1304, December.

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