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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
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. 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.
    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. 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.

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