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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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    1. C. Jeenanunta & V. Kongtarat & J. Buddhakulsomsiri, 2021. "A simulation-optimisation approach to determine optimal order-up-to level for inventory system with long lead time," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 38(2), pages 253-276.
    2. Pablo Becerra & Josefa Mula & Raquel Sanchis, 2022. "Sustainable Inventory Management in Supply Chains: Trends and Further Research," Sustainability, MDPI, vol. 14(5), pages 1-19, February.
    3. Leopoldo Eduardo Cárdenas-Barrón & María José Lea Plaza-Makowsky & María Alejandra Sevilla-Roca & José María Núñez-Baumert & Buddhadev Mandal, 2021. "An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    4. Yan Zhang & Yanyan He & Jinfeng Yue & Qinglong Gou, 2019. "Pricing decisions for a supply chain with refurbished products," International Journal of Production Research, Taylor & Francis Journals, vol. 57(9), pages 2867-2900, May.
    5. M. Amirthakodi & B. Sivakumar, 2019. "An inventory system with service facility and feedback customers," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 33(3), pages 374-411.
    6. Jeganathan, K. & Abdul Reiyas, M. & Prasanna Lakshmi, K. & Saravanan, S., 2019. "Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 177-200.
    7. Zelin Zhang & Jianghua Wu & Feiqiong Wei, 2019. "Refurbishment or quality recovery: joint quality and pricing decisions for new product development," International Journal of Production Research, Taylor & Francis Journals, vol. 57(8), pages 2327-2343, April.
    8. 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.
    9. Tseng-Fung Ho & Chi-Chung Lin & Chih-Ling Lin, 2020. "Determining the Optimal Inventory and Number of Shipments for a Two-Resource Supply Chain with Correlated Demands and Remanufacturing Products Allowing Backorder," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    10. Thulaseedharan Salini Sinu Lal & Varghese Chaukayil Joshua & Vladimir Vishnevsky & Dmitry Kozyrev & Achyutha Krishnamoorthy, 2022. "A Multi-Type Queueing Inventory System—A Model for Selection and Allocation of Spectra," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
    11. Yi He & Qingyun Xu & Pengkun Wu, 2020. "Omnichannel retail operations with refurbished consumer returns," International Journal of Production Research, Taylor & Francis Journals, vol. 58(1), pages 271-290, January.
    12. Jeganathan, K. & Abdul Reiyas, M., 2020. "Two parallel heterogeneous servers Markovian inventory system with modified and delayed working vacations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 273-304.
    13. A. Krishnamoorthy & R. Manikandan & Dhanya Shajin, 2015. "Analysis of a Multiserver Queueing-Inventory System," Advances in Operations Research, Hindawi, vol. 2015, pages 1-16, January.
    14. Serife Ozkar & Umay Uzunoglu Kocer, 2021. "Two-commodity queueing-inventory system with two classes of customers," OPSEARCH, Springer;Operational Research Society of India, vol. 58(1), pages 234-256, March.
    15. A. Krishnamoorthy & R. Manikandan & B. Lakshmy, 2015. "A revisit to queueing-inventory system with positive service time," Annals of Operations Research, Springer, vol. 233(1), pages 221-236, October.
    16. Sivakumar, B., 2008. "Two-commodity inventory system with retrial demand," European Journal of Operational Research, Elsevier, vol. 187(1), pages 70-83, May.
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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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