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Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Author

Listed:
  • Serife Ozkar

    (Department of International Trade and Logistics, Balikesir University, Balikesir 10145, Turkey)

  • Agassi Melikov

    (Department of Mathematics, Baku Engineering University, Baku 0101, Azerbaijan)

  • Janos Sztrik

    (Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary)

Abstract

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an infinite buffer. The service time of a consumer customer follows a phase-type distribution. The system receives negative customers which have Poisson flows and as soon as a negative customer comes into the system, he causes a consumer customer to leave the system, if any. One of two inventory policies is used in the systems: either ( s , S ) or ( s , Q ) . If the inventory level is zero when a consumer customer arrives, then this customer is either lost (lost sale) or joins the queue (backorder sale). The system is formulated by a four-dimensional continuous-time Markov chain. Ergodicity condition for both systems is established and steady-state distribution is obtained using the matrix-geometric method. By numerical studies, the influence of the distributions of the arrival process and the service time and the system parameters on performance measures are deeply analyzed. Finally, an optimization study is presented in which the criterion is the minimization of expected total costs and the controlled parameter is warehouse capacity.

Suggested Citation

  • Serife Ozkar & Agassi Melikov & Janos Sztrik, 2023. "Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies," Mathematics, MDPI, vol. 11(23), pages 1-24, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4854-:d:1292903
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    References listed on IDEAS

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    1. Agassi Melikov & Laman Poladova & Sandhya Edayapurath & Janos Sztrik, 2023. "Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    2. Vijay Rajan Lumb & Indra Rani, 2022. "Analytically simple solution to discrete-time queue with catastrophes, balking and state-dependent service," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 783-817, April.
    3. Nitin Kumar & U. C. Gupta, 2023. "Analysis of BMAP/MSP/1 queue with MAP generated negative customers and disasters," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(12), pages 4283-4309, June.
    4. Srinivas R. Chakravarthy & Alexander N. Dudin & Valentina I. Klimenok, 2010. "A Retrial Queueing Model With Map Arrivals, Catastrophic Failures With Repairs, And Customer Impatience," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(06), pages 727-752.
    5. Zhaotong Lian & Liming Liu & Marcel F. Neuts, 2005. "A Discrete-Time Model for Common Lifetime Inventory Systems," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 718-732, August.
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