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Queueing-Inventory System for Two Commodities with Optional Demands of Customers and MAP Arrivals

Author

Listed:
  • N. Anbazhagan

    (Department of Mathematics, Alagappa University, Karaikudi 630003, India
    These authors contributed equally to this work.)

  • Gyanendra Prasad Joshi

    (Department of Computer Science and Engineering, Sejong University, Seoul 05006, Korea
    These authors contributed equally to this work.)

  • R. Suganya

    (Department of Mathematics, Alagappa University, Karaikudi 630003, India)

  • S. Amutha

    (Ramanujan Center for Higher Mathematics, Alagappa University, Karaikudi 630003, India)

  • V. Vinitha

    (Department of Mathematics, Alagappa University, Karaikudi 630003, India)

  • Bhanu Shrestha

    (Department of Electronic Engineering, Kwangwoon University, Seoul 01897, Korea)

Abstract

This research analyses the performance of a perishable queueing-inventory system for two commodities with optional customers demands. We assume in the article that all customers who come to the system can only purchase the first item or the second item or service (they do not purchase both items). This is the original aspect of the paper. We show the significance of the impact of optional demands on the system’s performance, which is the purpose of the paper. In this system, customers arrive, using the Markovian arrival process (MAP), to a demand for a single unit. The system is composed of a waiting hall with a limited capacity of F . The arriving customer observes the waiting hall is filled to capacity or the stock stage is zero, and they decide to leave the system. In the steady-state case, the joint probability distribution for the first commodity, the second commodity, and the number of customers in the system are computed using matrix geometric methods. We evaluate diverse system performance measures. Finally, we provide a numerical illustration of the optimal value for diverse parameters of the system, which highlights the results and implications of the article.

Suggested Citation

  • N. Anbazhagan & Gyanendra Prasad Joshi & R. Suganya & S. Amutha & V. Vinitha & Bhanu Shrestha, 2022. "Queueing-Inventory System for Two Commodities with Optional Demands of Customers and MAP Arrivals," Mathematics, MDPI, vol. 10(11), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1801-:d:823433
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    References listed on IDEAS

    as
    1. Steven Nahmias, 2011. "Perishable Inventory Systems," International Series in Operations Research and Management Science, Springer, edition 1, number 978-1-4419-7999-5, April.
    2. 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.
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    Cited by:

    1. Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.
    2. WonIl Lee & JaeWook Shin & BumYong Park, 2024. "The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates," Mathematics, MDPI, vol. 12(5), pages 1-14, February.
    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.

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