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Queueing-Inventory with One Essential and m Optional Items with Environment Change Process Forming Correlated Renewal Process (MEP)

Author

Listed:
  • Jaison Jacob

    (Department of Mathematics, St. Aloysius College, Elthuruth, Thrissur 680611, India)

  • Dhanya Shajin

    (Department of Mathematics, Sree Narayana College, Chempazhanthy, Thiruvanathapuram 695587, India)

  • Achyutha Krishnamoorthy

    (Centre for Research in Mathematics, CMS College, Kottayam 686001, India)

  • Vladimir Vishnevsky

    (V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 65 Profsoyuznaya Street, 117997 Moscow, Russia)

  • Dmitry Kozyrev

    (V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 65 Profsoyuznaya Street, 117997 Moscow, Russia
    Applied Probability and Informatics Department, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia)

Abstract

We consider a queueing inventory with one essential and m optional items for sale. The system evolves in environments that change randomly. There are n environments that appear in a random fashion governed by a Marked Markovian Environment change process. Customers demand the main item plus none, one, or more of the optional items, but were restricted to at most one unit of each optional item. Service time of the main item is phase type distributed and that of optional items have exponential distributions with parameters that depend on the type of the item, as well as the environment under consideration. If the essential item is not available, service will not be provided. The lead times of optional and main items have exponential distributions having parameters that depend on the type of the item. The condition for stability of the system is analyzed by considering a multi-dimensional continuous time Markov chain that represent the evolution of the system. Under this condition, various performance characteristics of the system are derived. In terms of these, a cost function is constructed and optimal control policies of the different types of commodities are investigated. Numerical results are provided to give a glimpse of the system performance.

Suggested Citation

  • Jaison Jacob & Dhanya Shajin & Achyutha Krishnamoorthy & Vladimir Vishnevsky & Dmitry Kozyrev, 2021. "Queueing-Inventory with One Essential and m Optional Items with Environment Change Process Forming Correlated Renewal Process (MEP)," Mathematics, MDPI, vol. 10(1), pages 1-26, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:104-:d:713601
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    References listed on IDEAS

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    2. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
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