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A retrial inventory system with single and modified multiple vacation for server

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  • I. Padmavathi
  • B. Sivakumar
  • G. Arivarignan

Abstract

This paper considers a continuous review stochastic (s,S) inventory system with Poisson demand and exponentially distributed delivery time. The demands that occur during the stock out period or during the server vacation period enter into an orbit of infinite size. These orbiting demands retry to get satisfied by sending out signals so that the time durations are exponentially distributed. We consider two models which differ in the way that server go for vacation. The joint probability distribution of the inventory level, the number of demands in the orbit and the server status is obtained in the steady state case. Various system performance measures in the steady state is derived and the long-run total expected cost rate is calculated. Several numerical examples, which provide insight into the behaviour of the cost function, are presented. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:233:y:2015:i:1:p:335-364:10.1007/s10479-013-1417-1
    DOI: 10.1007/s10479-013-1417-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, December.
    4. Sivakumar, B., 2008. "Two-commodity inventory system with retrial demand," European Journal of Operational Research, Elsevier, vol. 187(1), pages 70-83, May.
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    Cited by:

    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. 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.
    3. 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.

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