IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i14p2423-d860499.html
   My bibliography  Save this article

Double Sources Queuing-Inventory System with Hybrid Replenishment Policy

Author

Listed:
  • Agassi Melikov

    (Institute of Control Systems, National Academy of Science, AZ 1141 Baku, Azerbaijan)

  • Ramil Mirzayev

    (Faculty of Engineering, National Aviation Academy, AZ 1045 Baku, Azerbaijan)

  • Sajeev S. Nair

    (Department of Mathematics, Government Engineering College, Thrissur 680009, India)

Abstract

A hybrid replenishment policy in double sources queuing-inventory system is proposed. If the inventory level drops to the reorder point s, then a regular order of the fixed volume Q = S − s is generated to a slow and cheap source, where S denotes the maximum size of the system’s warehouse. If the inventory level falls below a certain threshold value r , where r < s , then the system instantly cancels the regular order and generates an emergency order to a fast and expensive source where the replenishment quantity should be able to bring the inventory level back to S at the replenishment epoch. In addition to consuming customers, the system also receives destructive customers that do not require inventory but destroy them. The stability condition for the system under study is found, steady-state probabilities are calculated, and formulas for finding performance measures are proposed. The problem of minimizing the total cost of the system under the proposed hybrid replenishment policy is solved by choosing the appropriate values of the order point and the threshold value.

Suggested Citation

  • Agassi Melikov & Ramil Mirzayev & Sajeev S. Nair, 2022. "Double Sources Queuing-Inventory System with Hybrid Replenishment Policy," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2423-:d:860499
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/14/2423/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/14/2423/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. S. Otten & R. Krenzler & H. Daduna, 2016. "Models for integrated production-inventory systems: steady state and cost analysis," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6174-6191, October.
    2. O. Berman & K.P. Sapna, 2002. "Optimal service rates of a service facility with perishable inventory items," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(5), pages 464-482, August.
    3. K. Sapna Isotupa, 2015. "Cost analysis of an (S−1,S) inventory system with two demand classes and rationing," Annals of Operations Research, Springer, vol. 233(1), pages 411-421, October.
    4. P. V. Ushakumari, 2006. "On ( s , S ) inventory system with random lead time and repeated demands," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-22, January.
    5. Yuying Zhang & Dequan Yue & Li Sun & Jinpan Zuo & Bo Yang, 2022. "Analysis of the Queueing-Inventory System with Impatient Customers and Mixed Sales," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-12, May.
    6. 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.
    7. A. Krishnamoorthy & Dhanya Shajin & B. Lakshmy, 2016. "GI/M/1 type queueing-inventory systems with postponed work, reservation, cancellation and common life time," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(2), pages 357-388, June.
    8. S. R. Chakravarthy & Arunava Maity & U. C. Gupta, 2017. "An ‘(s, S)’ inventory in a queueing system with batch service facility," Annals of Operations Research, Springer, vol. 258(2), pages 263-283, November.
    9. M. Amirthakodi & V. Radhamani & B. Sivakumar, 2015. "A perishable inventory system with service facility and feedback customers," Annals of Operations Research, Springer, vol. 233(1), pages 25-55, October.
    10. Jinting Wang & Xuelu Zhang, 2017. "Optimal pricing in a service-inventory system with delay-sensitive customers and lost sales," International Journal of Production Research, Taylor & Francis Journals, vol. 55(22), pages 6883-6902, November.
    11. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    12. J. Artalejo & A. Krishnamoorthy & M. Lopez-Herrero, 2006. "Numerical analysis of(s, S) inventory systems with repeated attempts," Annals of Operations Research, Springer, vol. 141(1), pages 67-83, January.
    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.
    14. I. Padmavathi & B. Sivakumar & G. Arivarignan, 2015. "A retrial inventory system with single and modified multiple vacation for server," Annals of Operations Research, Springer, vol. 233(1), pages 335-364, October.
    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. Agassi Melikov & Laman Poladova & Sandhya Edayapurath & Janos Sztrik, 2023. "Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    2. Agassi Melikov & Ramil Mirzayev & Janos Sztrik, 2023. "Double-Sources Queuing-Inventory Systems with Finite Waiting Room and Destructible Stocks," Mathematics, MDPI, vol. 11(1), pages 1-16, January.

    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. M. Nithya & Gyanendra Prasad Joshi & C. Sugapriya & S. Selvakumar & N. Anbazhagan & Eunmok Yang & Ill Chul Doo, 2022. "Analysis of Stochastic State-Dependent Arrivals in a Queueing-Inventory System with Multiple Server Vacation and Retrial Facility," Mathematics, MDPI, vol. 10(17), pages 1-29, August.
    2. Agassi Melikov & Laman Poladova & Sandhya Edayapurath & Janos Sztrik, 2023. "Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    3. Dhanya Shajin & Jaison Jacob & A. Krishnamoorthy, 2022. "On a queueing inventory problem with necessary and optional inventories," Annals of Operations Research, Springer, vol. 315(2), pages 2089-2114, August.
    4. 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).
    5. 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.
    6. Baek, Jung Woo & Bae, Yun Han, 2022. "A queuing-inventory model for manufacturing systems with fluid-type inventory," Omega, Elsevier, vol. 111(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.
    8. Dhanya Shajin & A. Krishnamoorthy & A. N. Dudin & Varghese C. Joshua & Varghese Jacob, 2020. "On a queueing-inventory system with advanced reservation and cancellation for the next K time frames ahead: the case of overbooking," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 3-37, February.
    9. A. Krishnamoorthy & Dhanya Shajin & B. Lakshmy, 2016. "GI/M/1 type queueing-inventory systems with postponed work, reservation, cancellation and common life time," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(2), pages 357-388, June.
    10. Subramanian Selvakumar & Kathirvel Jeganathan & Krishnasamy Srinivasan & Neelamegam Anbazhagan & Soojeong Lee & Gyanendra Prasad Joshi & Ill Chul Doo, 2023. "An Optimization of Home Delivery Services in a Stochastic Modeling with Self and Compulsory Vacation Interruption," Mathematics, MDPI, vol. 11(9), pages 1-34, April.
    11. K. Jeganathan & M. Abdul Reiyas & S. Selvakumar & N. Anbazhagan & S. Amutha & Gyanendra Prasad Joshi & Duckjoong Jeon & Changho Seo, 2022. "Markovian Demands on Two Commodity Inventory System with Queue-Dependent Services and an Optional Retrial Facility," Mathematics, MDPI, vol. 10(12), pages 1-22, June.
    12. T. Harikrishnan & K. Jeganathan & S. Selvakumar & N. Anbazhagan & Woong Cho & Gyanendra Prasad Joshi & Kwang Chul Son, 2022. "Analysis of Stochastic M / M / c / N Inventory System with Queue-Dependent Server Activation, Multi-Threshold Stages and Optional Retrial Facility," Mathematics, MDPI, vol. 10(15), pages 1-37, July.
    13. Dhanya Shajin & Achyutha Krishnamoorthy & Agassi Z. Melikov & Janos Sztrik, 2022. "Multi-Server Queuing Production Inventory System with Emergency Replenishment," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    14. 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.
    15. Emre Berk & Ülkü Gürler & Saeed Poormoaied, 2020. "On the $$\varvec{(Q,r)}$$(Q,r) policy for perishables with positive lead times and multiple outstanding orders," Annals of Operations Research, Springer, vol. 284(1), pages 81-98, January.
    16. Dhanya Shajin & A. Krishnamoorthy & R. Manikandan, 2022. "On a queueing-inventory system with common life time and Markovian lead time process," Operational Research, Springer, vol. 22(1), pages 651-684, March.
    17. Agassi Melikov & Laman Poladova & Janos Sztrik, 2024. "Queuing-Inventory System with Catastrophes in the Warehouse: Case of Rare Catastrophes," Mathematics, MDPI, vol. 12(6), pages 1-19, March.
    18. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    19. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    20. Agassi Melikov & Ramil Mirzayev & Janos Sztrik, 2023. "Double-Sources Queuing-Inventory Systems with Finite Waiting Room and Destructible Stocks," Mathematics, MDPI, vol. 11(1), pages 1-16, January.

    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:14:p:2423-:d:860499. 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.