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A revisit to queueing-inventory system with positive service time

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  • A. Krishnamoorthy
  • R. Manikandan
  • B. Lakshmy

Abstract

A queueing-inventory system, with the item given with probability γ to a customer at his service completion epoch, is considered in this paper. Two control policies, (s,Q) and (s,S) are discussed. In both cases we obtain the joint distribution of the number of customers and the number of items in the inventory as the product of their marginals under the assumption that customers do not join when inventory level is zero. Optimization problems associated with both models are investigated and the optimal pairs (s,S) and (s,Q) and the corresponding expected minimum costs are obtained. Further we investigate numerically an expression for per unit time cost as a function of γ. This function exhibit convexity property. A comparison with Schwarz et al. (Queueing Syst. 54:55–78, 2006 ) is provided. The case of arbitrarily distributed service time is briefly indicated. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:233:y:2015:i:1:p:221-236:10.1007/s10479-013-1437-x
    DOI: 10.1007/s10479-013-1437-x
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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. A. Krishnamoorthy & T. G. Deepak & Viswanath C. Narayanan & K. Vineetha, 2006. "Effective utilization of idle time in an ( s , S ) inventory with positive service tim," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-13, September.
    3. 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.
    4. Krishnamoorthy, A. & Viswanath, Narayanan C., 2013. "Stochastic decomposition in production inventory with service time," European Journal of Operational Research, Elsevier, vol. 228(2), pages 358-366.
    5. T. Deepak & A. Krishnamoorthy & Viswanath Narayanan & K. Vineetha, 2008. "Inventory with service time and transfer of customers and/inventory," Annals of Operations Research, Springer, vol. 160(1), pages 191-213, April.
    6. Zhao, Ning & Lian, Zhaotong, 2011. "A queueing-inventory system with two classes of customers," International Journal of Production Economics, Elsevier, vol. 129(1), pages 225-231, January.
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    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. 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.
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    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. 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.
    7. 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.
    8. 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.
    9. Thulaseedharan Salini Sinu Lal & Varghese Chaukayil Joshua & Vladimir Vishnevsky & Dmitry Kozyrev & Achyutha Krishnamoorthy, 2022. "A Multi-Type Queueing Inventory System—A Model for Selection and Allocation of Spectra," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
    10. 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.
    11. 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.

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