IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v233y2015i1p321-33310.1007-s10479-013-1405-5.html
   My bibliography  Save this article

The multi server M/M/(s,S) queueing inventory system

Author

Listed:
  • Anoop Nair
  • M. Jacob
  • A. Krishnamoorthy

Abstract

We consider a multiserver Markovian queuing model where each server provides service only to one customer. Arrival of customers is according to a Poisson process and whenever a customer leaves the system after getting service, that server is also removed from the system. Here the servers are considered as an inventory that will be replenished according to the standard (s,S) policy. Behavior of this system is studied using a two dimensional QBD process. The condition for checking ergodicity, the steady state solutions and average inventory cycle time are obtained using matrix analytic methods. Also we have studied an optimization problem that minimizes the total cost induced by the waiting cost of arrivals, holding cost of the inventory of servers and ordering cost. Some numerical illustrations are provided. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Anoop Nair & M. Jacob & A. Krishnamoorthy, 2015. "The multi server M/M/(s,S) queueing inventory system," Annals of Operations Research, Springer, vol. 233(1), pages 321-333, October.
  • Handle: RePEc:spr:annopr:v:233:y:2015:i:1:p:321-333:10.1007/s10479-013-1405-5
    DOI: 10.1007/s10479-013-1405-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-013-1405-5
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10479-013-1405-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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. Kathirvel Jeganathan & Thanushkodi Harikrishnan & Kumarasankaralingam Lakshmanan & Agassi Melikov & Janos Sztrik, 2023. "Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System," Mathematics, MDPI, vol. 11(22), pages 1-31, November.

    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:spr:annopr:v:233:y:2015:i:1:p:321-333:10.1007/s10479-013-1405-5. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.