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Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers

Author

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  • Jeganathan, K.
  • Abdul Reiyas, M.
  • Prasanna Lakshmi, K.
  • Saravanan, S.

Abstract

This paper discusses about Markovian (s,Q) inventory-queueing system with server interruptions of two heterogeneous servers. Matrix method is applied to obtain the steady state joint probability distribution of customers level in the queue, retrial group, status of the servers and stock level of heterogeneous system. This paper studies the significant effect of heterogeneous system (each server work with different service rate) as compared with homogeneous system (all servers work with same service rate). Performance measures are derived for heterogeneous system and homogeneous system. Appropriate cost functions for both models are defined. Numerical examples are used to compare the total expected cost rates of both systems. Heterogeneous system yields the minimum total expected cost value and therefore the heterogeneous system is effective.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:155:y:2019:i:c:p:177-200
    DOI: 10.1016/j.matcom.2018.03.001
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    1. Oded Berman & Eungab Kim, 2004. "Dynamic inventory strategies for profit maximization in a service facility with stochastic service, demand and lead time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 497-521, December.
    2. C. Suganya & B. Sivakumar & G. Arivarignan, 2017. "Numerical investigation on MAP/PH(1), PH(2)/2 inventory system with multiple server vacations," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 29(1), pages 1-33.
    3. Oded Berman & Eungab Kim, 2001. "Dynamic order replenishment policy in internet-based supply chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(3), pages 371-390, July.
    4. Jacob K. Daniel & R. Ramanarayanan, 1988. "An (s,S) inventory system with rest periods to the server," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 119-123, February.
    5. A. Krishnamoorthy & R. Manikandan & Dhanya Shajin, 2015. "Analysis of a Multiserver Queueing-Inventory System," Advances in Operations Research, Hindawi, vol. 2015, pages 1-16, January.
    6. K. Jeganathan & N. Anbazhagan & B. Vigneshwaran, 2015. "Perishable Inventory System with Server Interruptions, Multiple Server Vacations, and N Policy," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 6(2), pages 32-52, April.
    7. Vijendra P. Singh, 1970. "Two-Server Markovian Queues with Balking: Heterogeneous vs. Homogeneous Servers," Operations Research, INFORMS, vol. 18(1), pages 145-159, February.
    8. 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.
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    Cited by:

    1. K. Jeganathan & S. Selvakumar & S. Saravanan & N. Anbazhagan & S. Amutha & Woong Cho & Gyanendra Prasad Joshi & Joohan Ryoo, 2022. "Performance of Stochastic Inventory System with a Fresh Item, Returned Item, Refurbished Item, and Multi-Class Customers," Mathematics, MDPI, vol. 10(7), pages 1-37, April.
    2. 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.
    3. 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.
    4. 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.
    5. Jeganathan, K. & Abdul Reiyas, M., 2020. "Two parallel heterogeneous servers Markovian inventory system with modified and delayed working vacations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 273-304.
    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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