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Performance of Stochastic Inventory System with a Fresh Item, Returned Item, Refurbished Item, and Multi-Class Customers

Author

Listed:
  • K. Jeganathan

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

  • S. Selvakumar

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

  • S. Saravanan

    (Madras School of Economics, Chennai 600025, India)

  • N. Anbazhagan

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

  • S. Amutha

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

  • Woong Cho

    (Department of Software Convergence, Daegu Catholic University, Gyeongsan 38430, Korea)

  • Gyanendra Prasad Joshi

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

  • Joohan Ryoo

    (Division of International Studies, Hanyang University, Seoul 04763, Korea)

Abstract

This paper deals with an integrated and interconnected stochastic queuing-inventory system with a fresh item, a returned item, and a refurbished item. This system provides a multi-type service facility to an arriving multi-class customer through a dedicated channel. It sells fresh and refurbished items, buys used items from customers, refurbishes the used items for resale, and provides a repair service for defective items. The assumption of purchasing a used item from the customer and allowing them to buy a fresh item is a new idea in stochastic queuing-inventory modeling. To do so, this system has four parallel queues to receive four classes of customers and five dedicated servers to provide a multi-type service facility. Customers are classified according to the type of service they require. Each class of arrival follows an independent Poisson process. The service time of each dedicated server is assumed to be exponentially distributed and independent. This system assumes an instantaneous ordering policy for the replenishment of a fresh item. In the long run of this considered system, the joint probability distribution of the seven-dimensional stochastic process, significant system performance measures, and the optimum total cost are to be derived using the Neuts matrix geometric technique. The main objective of the system was to increase the occurrence of all kinds of customers by providing a multi-type service facility in one place. Buying a used item is unavoidable in an emerging society because it helps form a green society. Furthermore, the numerical result shows that the assumption of a system that allows a customer to sell their used item and purchase a new item will increase the number of customers approaching the system.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1137-:d:785291
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    References listed on IDEAS

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    Cited by:

    1. K. Jeganathan & S. Vidhya & R. Hemavathy & N. Anbazhagan & Gyanendra Prasad Joshi & Chanku Kang & Changho Seo, 2022. "Analysis of M / M /1/ N Stochastic Queueing—Inventory System with Discretionary Priority Service and Retrial Facility," Sustainability, MDPI, vol. 14(10), pages 1-29, May.
    2. 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.
    3. N. Nithya & N. Anbazhagan & S. Amutha & K. Jeganathan & Gi-Cheon Park & Gyanendra Prasad Joshi & Woong Cho, 2023. "Controlled Arrivals on the Retrial Queueing–Inventory System with an Essential Interruption and Emergency Vacationing Server," Mathematics, MDPI, vol. 11(16), pages 1-24, August.
    4. 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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