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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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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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    1. 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.
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    3. 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.
    4. 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.
    5. Olga Dudina & Alexander Dudin, 2019. "Optimization of Queueing Model with Server Heating and Cooling," Mathematics, MDPI, vol. 7(9), pages 1-14, August.
    6. 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).
    7. 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.
    8. Gabi Hanukov, 2023. "A queueing-inventory model with skeptical and trusting customers," Annals of Operations Research, Springer, vol. 331(2), pages 763-786, December.
    9. 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.
    10. Umay Uzunoglu Kocer & Serife Ozkar, 2023. "A production queueing-inventory system with two-customer and a server subject to breakdown," Annals of Operations Research, Springer, vol. 331(2), pages 1089-1117, December.
    11. 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.
    12. 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.
    13. 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.
    14. Serife Ozkar, 2023. "Two-commodity queueing-inventory system with phase-type distribution of service times," Annals of Operations Research, Springer, vol. 331(2), pages 711-737, December.
    15. Subrata Golui & Chandan Pal & R. Manikandan & Abhay Sobhanan, 2024. "Optimal control of a dynamic production-inventory system with various cost criteria," Annals of Operations Research, Springer, vol. 337(1), pages 75-103, June.
    16. 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.
    17. Bara Kim & Jeongsim Kim & Sungji Lee, 2023. "Joint pricing and inventory control for a production–inventory queueing system," Annals of Operations Research, Springer, vol. 331(2), pages 787-805, December.
    18. Arputham Shophia Lawrence & Agassi Melikov & Balasubramanian Sivakumar, 2023. "Analysis and optimization of hybrid replenishment policy in a double-sources queueing-inventory system with MAP arrivals," Annals of Operations Research, Springer, vol. 331(2), pages 1249-1267, December.

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