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Markovian Demands on Two Commodity Inventory System with Queue-Dependent Services and an Optional Retrial Facility

Author

Listed:
  • K. Jeganathan

    (Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chepauk, Chennai 600005, India)

  • M. Abdul Reiyas

    (Department of Food Business Management, College of Food and Dairy Technology, The Tamil Nadu Veterinary and Animal Sciences University (TANUVAS), Chennai 600051, India)

  • S. Selvakumar

    (Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chepauk, Chennai 600005, India)

  • N. Anbazhagan

    (Department of Mathematics, Alagappa University, Karaikudi 630003, India)

  • S. Amutha

    (Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630003, India)

  • Gyanendra Prasad Joshi

    (Department of Computer Science and Engineering, Sejong University, Seoul 05006, Korea)

  • Duckjoong Jeon

    (Department of Convergence Science, Kongju National University, Gongju 32588, Korea)

  • Changho Seo

    (Department of Convergence Science, Kongju National University, Gongju 32588, Korea)

Abstract

The use of a Markovian inventory system is a critical part of inventory management. The purpose of this study is to examine the demand for two commodities in a Markovian inventory system, one of which is designated as a major item (Commodity-I) and the other as a complimentary item (Commodity-II). Demand arrives according to a Poisson process, and service time is exponential at a queue-dependent rate. We investigate a strategy of ( s , Q ) type control for commodity-I with a random lead time but instantaneous replenishment for commodity-II. If the waiting hall reaches its maximum capacity of N , any arriving primary client may enter an infinite capacity orbit with a specified ratio. For orbiting consumers, the classical retrial policy is used. In a steady-state setting, the joint probability distributions for commodities and the number of demands in the queue and the orbit, are derived. From this, we derive a waiting time analysis and a variety of system performance metrics in the steady-state. Additionally, the physical properties of various performance measures are evaluated using various numerical assumptions associated with diverse stochastic behaviours.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2046-:d:837663
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    References listed on IDEAS

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    Cited by:

    1. Wen Zhang & Xiaofeng Xu & Jun Wu & Kaijian He, 2023. "Preface to the Special Issue on “Computational and Mathematical Methods in Information Science and Engineering”," Mathematics, MDPI, vol. 11(14), pages 1-4, July.
    2. 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.

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