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Analysis of a Stochastic Inventory Model on Random Environment with Two Classes of Suppliers and Impulse Customers

Author

Listed:
  • V. Vinitha

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

  • N. Anbazhagan

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

  • S. Amutha

    (Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630004, India)

  • K. Jeganathan

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

  • Bhanu Shrestha

    (Department of Electronic Engineering, Kwangwoon University, Seoul 01897, Korea)

  • Hyoung-Kyu Song

    (Department of Information and Communication Engineering and Convergence Engineering for Intelligent Drone, Sejong University, Seoul 05006, Korea)

  • Gyanendra Prasad Joshi

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

  • Hyeonjoon Moon

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

Abstract

This paper explores the random environment with two classes of suppliers and impulse customers. The system’s greatest inventory size is S , and it has an infinitely large orbit. In this case, there are two categories of suppliers: temporary suppliers and regular suppliers. Whenever the inventory approaches r , we place on order Q 1 (= S − r ) unit items to a temporary supplier. Similarly, when the inventory level drops to s (< Q 1 < r ), we place an order for Q 2 (= S − s > s + 1 ) units of items to our regular supplier. Two types of suppliers’ lead times are considered to be exponentially distributed. Here, the customers who arrive from different states of the random environment (RE) are followed by the Markovian arrival process. If there is no inventory in the system when the customer arrives, they are automatically assigned to an orbit. The model was examined in steady state by using the matrix-analytic approach. Finally, the numerical examples for our structural model are discussed.

Suggested Citation

  • V. Vinitha & N. Anbazhagan & S. Amutha & K. Jeganathan & Bhanu Shrestha & Hyoung-Kyu Song & Gyanendra Prasad Joshi & Hyeonjoon Moon, 2022. "Analysis of a Stochastic Inventory Model on Random Environment with Two Classes of Suppliers and Impulse Customers," Mathematics, MDPI, vol. 10(13), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2235-:d:848135
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    References listed on IDEAS

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    1. Dudin, Alexander & Kim, Chesoong & Dudin, Sergey & Dudina, Olga, 2015. "Priority retrial queueing model operating in random environment with varying number and reservation of servers," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 674-690.
    2. M. F. Yang & Wei-Chung Tseng, 2014. "Three-Echelon Inventory Model with Permissible Delay in Payments under Controllable Lead Time and Backorder Consideration," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-16, April.
    3. Valentina Klimenok & Alexander Dudin & Olga Dudina & Irina Kochetkova, 2020. "Queuing System with Two Types of Customers and Dynamic Change of a Priority," Mathematics, MDPI, vol. 8(5), pages 1-25, May.
    4. Seokjun Lee & Sergei Dudin & Olga Dudina & Chesoong Kim & Valentina Klimenok, 2020. "A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities," Mathematics, MDPI, vol. 8(8), pages 1-20, August.
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    Cited by:

    1. Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.
    2. Agassi Melikov & Ramil Mirzayev & Janos Sztrik, 2023. "Double-Sources Queuing-Inventory Systems with Finite Waiting Room and Destructible Stocks," Mathematics, MDPI, vol. 11(1), pages 1-16, January.

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