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A queueing-inventory system with two classes of customers

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  • Zhao, Ning
  • Lian, Zhaotong

Abstract

We consider a queueing-inventory system with two classes of customers. Customers arrive at a service facility according to Poisson processes. Service times follow exponential distributions. Each service uses one item in the attached inventory supplied by an outside supplier with exponentially distributed lead time. We find a priority service rule to minimize the long-run expected waiting cost by dynamic programming method and obtain the necessary and sufficient condition for the priority queueing-inventory system being stable. Formulating the model as a level-dependent quasi-birth-and-death (QBD) process, we can compute the steady state probability distribution by Bright-Taylor algorithm. Useful analytical properties for the cost function are identified and extensive computations are conducted to examine the impact of different parameters to the system performance measures.

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  • 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.
    • Handle: RePEc:eee:proeco:v:129:y:2011:i:1:p:225-231
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    References listed on IDEAS

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    5. 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).
    6. Khamis A. K. ALMaqbali & Varghese C. Joshua & Achyutha Krishnamoorthy, 2023. "Multi-Class, Multi-Server Queueing Inventory System with Batch Service," Mathematics, MDPI, vol. 11(4), pages 1-29, February.
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    8. K. Jeganathan & J. Kathiresan & N. Anbazhagan, 2016. "A retrial inventory system with priority customers and second optional service," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 808-834, December.
    9. Sina Nayeri & Mahdieh Tavakoli & Mehrab Tanhaeean & Fariborz Jolai, 2022. "A robust fuzzy stochastic model for the responsive-resilient inventory-location problem: comparison of metaheuristic algorithms," Annals of Operations Research, Springer, vol. 315(2), pages 1895-1935, August.
    10. Kangzhou Wang & Shouchang Chen & Zhibin Jiang & Weihua Zhou & Na Geng, 2021. "Capacity Allocation of an Integrated Production and Service System," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2765-2781, August.
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    12. Xin Li & Guanlai Zhu, 2023. "Green Supply Chain Coordination Considering Carbon Emissions and Product Green Level Dependent Demand," Mathematics, MDPI, vol. 11(10), pages 1-23, May.
    13. 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.
    14. Sha, Yue & Zhang, Junlong & Cao, Hui, 2021. "Multistage stochastic programming approach for joint optimization of job scheduling and material ordering under endogenous uncertainties," European Journal of Operational Research, Elsevier, vol. 290(3), pages 886-900.
    15. 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.
    16. Thulaseedharan Salini Sinu Lal & Varghese Chaukayil Joshua & Vladimir Vishnevsky & Dmitry Kozyrev & Achyutha Krishnamoorthy, 2022. "A Multi-Type Queueing Inventory System—A Model for Selection and Allocation of Spectra," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
    17. Baek, Jung Woo & Bae, Yun Han, 2022. "A queuing-inventory model for manufacturing systems with fluid-type inventory," Omega, Elsevier, vol. 111(C).
    18. Güler, M. Güray & Bilgiç, Taner & Güllü, Refik, 2014. "Joint inventory and pricing decisions when customers are delay sensitive," International Journal of Production Economics, Elsevier, vol. 157(C), pages 302-312.
    19. Jalili Marand, Ata & Li, Hongyan & Thorstenson, Anders, 2019. "Joint inventory control and pricing in a service-inventory system," International Journal of Production Economics, Elsevier, vol. 209(C), pages 78-91.
    20. 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.
    21. Fong-Fan Wang & Amita Bhagat & Tsan-Ming Chang, 2017. "Analysis of priority multi-server retrial queueing inventory systems with MAP arrivals and exponential services," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 44-66, March.
    22. Hanukov, Gabi, 2022. "A service system where junior servers approach a senior server on behalf of customers," International Journal of Production Economics, Elsevier, vol. 244(C).
    23. Umay Uzunoglu Kocer & Bahar Yalcin, 2020. "Continuous review (s, Q) inventory system with random lifetime and two demand classes," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 104-118, March.
    24. Jung Woo Baek, 2024. "On the Control Policy of a Queuing–Inventory System with Variable Inventory Replenishment Speed," Mathematics, MDPI, vol. 12(2), pages 1-19, January.

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