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Queuing-Inventory System with Catastrophes in the Warehouse: Case of Rare Catastrophes

Author

Listed:
  • Agassi Melikov

    (Department of Mathematics, Baku Engineering University, Hasan Aliyev Str. 120, Baku AZ 0101, Azerbaijan)

  • Laman Poladova

    (Institute of Control Systems, b. Vahabzadeh Str. 9, Baku AZ 1141, Azerbaijan)

  • Janos Sztrik

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

Abstract

A model of a single-server queuing-inventory system (QIS) with a limited waiting buffer for consumer customers ( c -customers) and catastrophes has been developed. When a catastrophe occurs, all items in the system’s warehouse are destroyed, but c -customers in the system are still waiting for replenishment. In addition to c -customers, negative customers ( n -customers) are also taken into account, each of which displaces one c -customer (if any). The policy ( s , S ) is used to replenish stocks. If, when a customer enters, the system warehouse is empty, then, according to Bernoulli’s trials, this customer either leaves the system without goods or joins the buffer. The mathematical model of the investigated QIS is constructed in the form of a continuous-time Markov chain (CTMC). Both exact and approximate methods for calculating the steady-state probabilities of constructed CTMCs are proposed and closed-form expressions are obtained for calculating the performance measures. Numerical evaluations are presented, demonstrating the high accuracy of the developed approximate formulas, as well as the behavior of performance measures depending on the input parameters. In addition, an optimization problem is solved to obtain the optimal value of the reorder point to minimize the expected total cost.

Suggested Citation

  • Agassi Melikov & Laman Poladova & Janos Sztrik, 2024. "Queuing-Inventory System with Catastrophes in the Warehouse: Case of Rare Catastrophes," Mathematics, MDPI, vol. 12(6), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:906-:d:1359953
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    References listed on IDEAS

    as
    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. M. Amirthakodi & V. Radhamani & B. Sivakumar, 2015. "A perishable inventory system with service facility and feedback customers," Annals of Operations Research, Springer, vol. 233(1), pages 25-55, October.
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