IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i11p1801-d823433.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/11/1801/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/11/1801/
    Download Restriction: no
    ---><---

    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, September.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. V. Radhamani & B. Sivakumar & G. Arivarignan, 2022. "A Comparative Study on Replenishment Policies for Perishable Inventory System with Service Facility and Multiple Server Vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 229-265, March.
    2. Rozhkov, Maxim & Ivanov, Dmitry & Blackhurst, Jennifer & Nair, Anand, 2022. "Adapting supply chain operations in anticipation of and during the COVID-19 pandemic," Omega, Elsevier, vol. 110(C).
    3. Civelek, Ismail & Karaesmen, Itir & Scheller-Wolf, Alan, 2015. "Blood platelet inventory management with protection levels," European Journal of Operational Research, Elsevier, vol. 243(3), pages 826-838.
    4. Peng Hu & Stephen Shum & Man Yu, 2016. "Joint Inventory and Markdown Management for Perishable Goods with Strategic Consumer Behavior," Operations Research, INFORMS, vol. 64(1), pages 118-134, February.
    5. Xiuli Chao & Xiting Gong & Cong Shi & Chaolin Yang & Huanan Zhang & Sean X. Zhou, 2018. "Approximation Algorithms for Capacitated Perishable Inventory Systems with Positive Lead Times," Management Science, INFORMS, vol. 64(11), pages 5038-5061, November.
    6. Elena Belavina & Karan Girotra & Ashish Kabra, 2017. "Online Grocery Retail: Revenue Models and Environmental Impact," Management Science, INFORMS, vol. 63(6), pages 1781-1799, June.
    7. Yves Crama & Mahmood Rezaei & Martin Savelsbergh & Tom Van Woensel, 2018. "Stochastic Inventory Routing for Perishable Products," Transportation Science, INFORMS, vol. 52(3), pages 526-546, June.
    8. Besik, Deniz & Nagurney, Anna, 2017. "Quality in competitive fresh produce supply chains with application to farmers' markets," Socio-Economic Planning Sciences, Elsevier, vol. 60(C), pages 62-76.
    9. Zhou, Quan Spring & Olsen, Tava Lennon, 2018. "Rotating the medical supplies for emergency response: A simulation based approach," International Journal of Production Economics, Elsevier, vol. 196(C), pages 1-11.
    10. N. Saranya & A. Shophia Lawrence, 2019. "A stochastic inventory system with replacement of perishable items," OPSEARCH, Springer;Operational Research Society of India, vol. 56(2), pages 563-582, June.
    11. Yonit Barron & Opher Baron, 2020. "The residual time approach for (Q, r) model under perishability, general lead times, and lost sales," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 601-648, December.
    12. V. Yadavalli & Diatha Sundar & Swaminathan Udayabaskaran, 2015. "Two substitutable perishable product disaster inventory systems," Annals of Operations Research, Springer, vol. 233(1), pages 517-534, October.
    13. Larissa Janssen & Jürgen Sauer & Thorsten Claus & Alfred Wulff, 2017. "Abfallreduktion im Lebensmitteleinzelhandel mittels einer internen Warenumverteilung [Waste reduction in a retail food chain via a internal transfer of goods]," NachhaltigkeitsManagementForum | Sustainability Management Forum, Springer, vol. 25(1), pages 109-116, June.
    14. Onno Boxma & David Perry & Wolfgang Stadje & Shelley Zacks, 2022. "A compound Poisson EOQ model for perishable items with intermittent high and low demand periods," Annals of Operations Research, Springer, vol. 317(2), pages 439-459, October.
    15. Kouki, Chaaben & Babai, M. Zied & Minner, Stefan, 2018. "On the benefit of dual-sourcing in managing perishable inventory," International Journal of Production Economics, Elsevier, vol. 204(C), pages 1-17.
    16. Dillon, Mary & Vauhkonen, Ilmari & Arvas, Mikko & Ihalainen, Jarkko & Vilkkumaa, Eeva & Oliveira, Fabricio, 2023. "Supporting platelet inventory management decisions: What is the effect of extending platelets’ shelf life?," European Journal of Operational Research, Elsevier, vol. 310(2), pages 640-654.
    17. Madhukar Nagare & Pankaj Dutta & Pravin Suryawanshi, 2020. "Optimal procurement and discount pricing for single-period non-instantaneous deteriorating products with promotional efforts," Operational Research, Springer, vol. 20(1), pages 89-117, March.
    18. Hailun Zhang & Jiheng Zhang & Rachel Q. Zhang, 2020. "Simple Policies with Provable Bounds for Managing Perishable Inventory," Production and Operations Management, Production and Operations Management Society, vol. 29(11), pages 2637-2650, November.
    19. Lopez Alvarez, Jose A. & Buijs, Paul & Kilic, Onur A. & Vis, Iris F.A., 2020. "An inventory control policy for liquefied natural gas as a transportation fuel," Omega, Elsevier, vol. 90(C).
    20. Ehsan Ahmadi & Dale T. Masel & Seth Hostetler & Reza Maihami & Iman Ghalehkhondabi, 2020. "A centralized stochastic inventory control model for perishable products considering age-dependent purchase price and lead time," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 231-269, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1801-:d:823433. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.