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An ‘(s, S)’ inventory in a queueing system with batch service facility

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  • S. R. Chakravarthy

    (Kettering University)

  • Arunava Maity

    (Indian Institute of Technology Kharagpur)

  • U. C. Gupta

    (Indian Institute of Technology Kharagpur)

Abstract

This paper considers a single-server queueing model in which the customers are served in batches of varying size depending on predetermined thresholds as well as available inventory. There is a finite buffer for the inventory and the service of every customer requires an inventory item. An (s, S) -type inventory system is used for the models considered in this paper. Initially, the model is studied in detail using the matrix-analytic method by assuming all the underlying random variables to be exponentially distributed. Thereafter, an outline of the model in a more general set up is also presented. Due to complexity of the model when more general assumptions are made on the underlying random variables, simulation is opted after a satisfactory validation with the analytic counterpart of the exponential model. Finally, some illustrative numerical examples are also presented to accomplish our analysis.

Suggested Citation

  • S. R. Chakravarthy & Arunava Maity & U. C. Gupta, 2017. "An ‘(s, S)’ inventory in a queueing system with batch service facility," Annals of Operations Research, Springer, vol. 258(2), pages 263-283, November.
    • Handle: RePEc:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-015-2041-z
    DOI: 10.1007/s10479-015-2041-z
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    Cited by:

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    2. Karumbathil Rasmi & Machuveettil Joseph Jacob & Alexander S. Rumyantsev & Achyutha Krishnamoorthy, 2021. "A Multi-Server Heterogeneous Queuing-Inventory System with Class-Dependent Inventory Access," Mathematics, MDPI, vol. 9(9), pages 1-23, May.
    3. Srinivas R. Chakravarthy, 2022. "Analysis of a Queueing Model with MAP Arrivals and Heterogeneous Phase-Type Group Services," Mathematics, MDPI, vol. 10(19), pages 1-30, September.
    4. 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.
    5. Achyutha Krishnamoorthy & Anu Nuthan Joshua & Dmitry Kozyrev, 2021. "Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation," Mathematics, MDPI, vol. 9(4), pages 1-29, February.

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